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Proceedings of the Seventh Joint Magnetism and Magnetic 
Materials-Intermag Conference 


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PROCEEDINGS OF THE SEVENTH JOINT 
MAGNETISM AND MAGNETIC 
MATERIALS-INTERMAG 
CONFERENCE 
6-9 JANUARY 1998 
San Francisco, California 


Sponsored by 

The American Institute of Physics 
The IEEE Magnetics Society 

In cooperation with 
TMS 

The Office of Naval Research 
The American Society for Testing and Materials 
The American Ceramic Society 


19980604 084 



AlP 


Journal of Applied Physics 
Volume 83, Number 11, Part 2, 1998 


International Standard Book Number: 1-56396-801-0 
CONF-980102 

Copyright © 1998 by the American Institute of Physics 
Published by the American Institute of Physics 
500 Sunnyside Blvd., Woodbury, New York 11797-2999 
Printed in the United States of America 





Conference Organization 

Management Committee of the 
Seventh Joint Magnetism and Magnetic 
Materiais-Intermag 
Conference 


Chairman 

W. D. Doyle 


Chairman Elect 

G. Prinz 


Past Chairman 

R. E, Fontana, Jr. 


Treasurer 

W. Yelon 


Program Co-Chairmen 

A. Chaiken and T. Jagielinski 

Members 


M. Alex 

B. Gallagher 

J. Borchers 

P. George 

F. Cadieu 

R. Gerber 

T. Carr 

H. How 

Z. Celinski 

Y. Idzerda 

R. Coehoom 

R. Indeck 

S. Dey 

R. R. Katti 

A. Edelstein 

A. Kim 

G. Fish 

Y. Kim 

H. Fujiwara 

K. Klaassen 


B. Lairson 

R. Ramesh 

M. Lederman 

D. Sellmyer 

J. MacLaren 

N. Smith 

M. Mallary 

J. Tang 

R. Maimhall 

S. Ueno 

1. Mayergoyz 

R. Walser 

M. McHenry 

S. Wang 

Y. Miura 

D. Weller 

B. Pratt 

W. Yelon 

A. Pohm 



Publications Committee 

R. R. Katti and J. M. MacLaren, Co-Chairmen 


M. Alex 

J. Fernandez de Castro 
P. George 
Y. K. Kim 


B. M. Lairson 
M. E. McHenry 
J. Tang 
S. Wang 


Editors 


Local Chairman 

H. Gill 


Publicity Chairman 

J. Nyenhuis 


Exhibits Coordinators 

J. Teter and R. Dopkin 


industrial Support 

M. Sharrock 


Student Travel Coordinator 

S. Gangopadhyay 


iEEE Representative 

E. Fontana, Jr. 


AlP Representative 

J. T. Scott 


Editor, J. Appl. Phys. 

S. Rothman 


Editor, IEEE Trans. Mag. 

R. Goldfarb 


Conference Management 

D. Suiters 
D. Arnold 
R. Dopkin 
Courtesy Associates 


AiP Coordinator 


J. Bennett 




MMM Advisory Committee 


R. E. Fontana, Jr., Chairman 
R. O’Handley, Secretary 


Term Expires January 1998 

E. Della Torre 
G. Felcher 
P. M. Levy 
J. E. Opfer 

C. M, Perlov 

D. Sellmyer 
D. D. Standi 
T. Suzuki 

S. von Molnar 
W. Yelon 


Term Expires November 1998 

D. E. Dahlberg 
W. D. Doyle 

J. Fidler 
G. E. Fish 

K. Hathaway 
R. R. Katti 

J. W. Lynn 
R. O’Handley 
M. Pardavi-Horvath 
G. A. Prinz 


Term Expires November 1999 

A. Chaiken 

S. H. Charap 
C. L. Chien 
Y. Idzerda 

T. M. Jagielinski 
M. H. Kryder 

J. M. MacLaren 

J. Nyenhuis 

K. O’Grady 
R. H. Victora 


IEEE Magnetics Society 1998 

Officers 


D. D. Stancil 
President 


E. Della Torre R. E. Fontana, Jr. J. E. Opfer 

Vice President Secretary-Treasurer Past President 


Administrative Committee 


Term Expires 12/31/98 


Term Expires 12/31/99 


A. Chaiken 
F. J. Friedlaender 
R. F. Hoyt 
D. C. Jiles 


J. H, Judy 
D. N. Lambeth 
M. Pardavi-Horvath 
P. E. Wigen 


G. E. Fish 
T. Jagielinski 
F. E. Luborsky 
I. Mayergoyz 


E. Murdock 

J. A. Nyenhuis 

K. O’Grady 
J. G. Zhu 


Term Expires 12/31/00 


G. Bertotti 
S. H. Charap 
E. D. Dahlberg 
R. Gerber 


R. S.Indeck 

R. R. Katti 
Y. Miura 

S. X. Wang 


Sponsoring Society Representatives 


American Institute of Physics 
J. T. Scott 

IEEE Magnetics Society 
R. E. Fontana, Jr. 

Cooperating Society Representatives 

TMS 

ASTM Comm. A-6 
C. D. Graham, Jr. 

Office of Naval Research 
K. B, Hathaway 

American Ceramic Society 


CONTRIBUTORS TO THE SEVENTH JOINT MAGNETISM 
AND MAGNETIC MATERIALS-INTERMAG CONFERENCE 


The Conference expresses its appreciation to the following organizations for their generous support. 


$2500 and above 
Motorola 

$2000 and above 

EMTEC Magnetics GmbH, formerly BASF Magnetics GmbH 
IBM 

TDK Corporation 

$1000 and above 
Fuji Photo Film Co., Ltd. 

Hewlett-Packard 

Hitachi, Ltd. Central Research Laboratory 
Imation 

Quantum Corporation 
Sony Corporation 
Toda Kogyo Corp. 


$500--$999 

3M 

Applied Magnetics Corporation 
Komag 

$250-$499 

Digital Measurement Systems Di¬ 
vision of ADE Technologies, Inc. 
Eastman Kodak Company 
Hyundai Electronics America, 
MaxMedia Division 

Other Contributions 

F. G. Jones Associates, Ltd. 

Innovative Instrumentation 



PREFACE 


The Seventh Joint MMM-Intermag Conference was held 6-9 January 1998, in San Francisco, 
California at the Hyatt Embarcadero Hotel The Conference was attended by more than 1,800 
registrants, and represents the largest conference on magnetic materials and devices held to date. 
The high attendance indicates the worldwide research in magnetism and expanding applications 
for new magnetic materials, particularly in the field of magnetic storage. 

An exciting program of 1,143 papers included six invited symposia on Present and Future 
Tape Systems, Layered Manganites, Electrodeposited Magnetic Nanostructures, Exchange Bias¬ 
ing, High Speed Magnetic Recording, and Advances in Magnetic Imaging. Additional highlights 
included a panel discussion on the history and future of magnetic storage data and a tutorial 
session on magnetic imaging sponsored by the IEEE Magnetics Society Education Committee. In 
the IEEE Awards Session, Dr. Jean-Pierre Lazzari was honored as the recipient of the Johnson 
Storage Medal, and Professor Stanley Charap was the recipient of the Magnetic Society Achieve¬ 
ment Award. 

The number of abstract submissions representing 45 countries was an astounding 1,940; 
which was 50% more than at any previous MMM, Intermag, or Joint MMM-Intermag Conference. 
The size of the program, however, was limited by hotel space and page allotments in the Journal 
of Applied Physics and the IEEE Transactions on Magnetics. By creatively using poster space, up 
to six parallel oral and six parallel poster sessions were accommodated, and, at times, the meeting 
rooms were crowded. Publication constraints helped limit the allowed number of accepted ab¬ 
stracts at 1,143, resulting in a rejection rate for contributed abstracts of 41% versus a historical 
figure of approximately 30-35%. This was a painful, but unavoidable process for everyone. It is 
difficult to make narrow distinctions between hundreds of diverse abstracts and it emphasizes the 
importance of carefully written submissions. 

The conferences historically have had difficulty with social events, largely as a result of the 
contrary demands within our community of high expectations and low cost. This year, after 
considerable soul searching, a nearby restaurant-brewery was selected which happily provided an 
enjoyable, sudsy evening. 

This year, as the Conference took shape, I was impressed with our community’s ever- 
increasing use of electronic document processing and handling. This contrasts with processes used 
in the “early” days. In 1963, for example, the MMM Program Committee met at IBM-Yorktown 
Heights, New York. After the Program Committee met, the Program Chairman took the accepted 
abstracts, drove to a rest stop halfway down the Garden State Parkway, and turned the accepted 
abstracts over to the Local Chairman who then raced back to Philadelphia to have all the abstracts 
re-typed manually in a common font. Each abstract was then cut-and-pasted one-by-one to fit into 
the Program Book before going to the printer! Although technology has changed significantly in 
35 years, both conferences were very successful. 

Questions have been raised about the usefulness of the Joint Conference. The first Joint 
MMM-Intermag Conference was held in 1976, and, Dr. Emerson Pugh, the General Chairman, 
summarized the results as follows: “The real success lies in the opportunity afforded scientists, 
technologists, and engineers from all over the world to discuss topics of mutual interest, to learn 
to understand each other better, and thus to return to their own laboratories invigorated and better 
prepared to contribute to this rapidly evolving field of modem technology.” I believe this is still 
a compelling reason to continue having the Joint Conference, which is supported by attendees 
surveyed at this Joint Conference by a margin of two to one. 

A unique feature of our field is the extent to which its history is documented in the familiar, 
annual printed issues of two journals. Economic realities combined with technological innovation 
may lead to changes in our traditions. Future Chairmen will be forced to confront these changes, 
hopefully with the same wisdom shown by the organizers of the first MMM (1955) and the first 
Intermag (1963) Conferences. Somehow, a conference held solely on the World Wide Web would 
seem to be a poor substitute for direct contact and interchange in a beautiful city. 

Finally, I extend my sincerest thanks to all the members of the organizing committees who 
worked continually and diligently for more than a year to make this Joint Conference a success. 


Bill Doyle 
General Chairman 

Seventh Joint MMM-Intemational Magnetics Conference 

University of Alabama 
Tuscaloosa, Alabama 



This issue of the Journal of Applied Physics contains 389 
papers presented at the Seventh Joint MMM-Intermag Confer¬ 
ence. This issue also contains the Table of Contents for the 
papers which are being published in the IEEE Transactions on 
Magnetics. 



Journal of APPLIED PHYSICS 


Vol. 83, No. 11, Part 2, 1 June 1998 


xxix Table of Contents for the Papers Appearing in the IEEE Transactions on 
Magnetics 

Magnetic Microscopy and Imaging I 

6217 Time-resolved scanning Kerr microscopy of ferromagnetic structures 
(invited) 

6223 Magnetic force microscopy image restoration technique for removing tip 
dependence 

6226 Quantification of magnetic force microscopy images using combined 
electrostatic and magnetostatic imaging 

6229 Magnetic force microscopy using nonoptical piezoelectric quartz tuning 
fork detection design with applications to magnetic recording studies 

6232 Kerr effect enhancement by photon tunneling and possible application to 
a new scanning probe magnetic microscope 

6235 Design and construction of a sensitive nuclear magnetic resonance force 
microscope 


Nanocomposite and Film Hard Magnets 

6238 Exchange-spring behavior in epitaxial hard/soft magnetic bilayer films 

6241 Magnetization reversal of Nd(Dy)-Fe-B thin films on Si(111) or Ta/ 
Si(111) 

6244 Phase formation and magnetic properties of Co-rare earth magnetic films 

6247 High coercivity SmCo based films made by pulsed laser deposition 

6250 Mechanism of composition change In sputter deposition of barium ferrite 
films with sputtering gas pressure 

6253 Magnetic and structural properties of high coercivity Sm(Co, Ni, Cu) 
sputtered thin films 

6256 Mechanically alloyed nanocomposite magnets (invited) 

6262 Micromagnetic simulation of magnetizabillty of nanocomposite Nd-Fe-B 
magnets 

6265 Thick Fe 3 B/Nd 2 Fei 4 B nanocomposite permanent magnet flakes prepared 
by slow quenching 

6268 Analysis of magnetic behavior of exchange-enhanced SmFeCo magnets 

• 6271 The effect of boron and rare earth contents on the magnetic properties of 
La and Cr substituted a-Fe/R 2 Fei 4 B-type nanocomposites 

6274 Anomalous high-temperature coercivities in hard nanocomposite alloys 

6277 Magnetic interactions in Fe-Ba hexaferrite nanocomposite materials 


Surface and Interface Effects 

6280 Infrared studies of magnetic surface modes on antiferromagnets (invited) 


(Continued) 

ix 


M. R. Freeman, W. K. Hiebert, A. 
Stanklewicz 

Jian-Gang Zhu, Xiangdong Lin, 
Rick C. Shi, Yansheng Luo 

R. D. Gomez, A. O. Pak, A. J. 
Anderson, E. R. Burke, A. J. 
Leyendecker, I. D. Mayergoyz 

M. Todorovic, S. Schultz 

A. Kikitsu, C. M. Falco, M. 
Mansuripur 

T. A. Barrett, C. R. MIers, H. A. 
Sommer, K. Mochizuki, J. T. 
Marked 


J. S. Jiang, Eric E. Fullerton, M. 
Grimsditch, C. H. Sowers, S. D. 
Bader 

J. L. Tsai, T. S. Chin, E. Y. Huang, 
S. K. Chen 

Y. Liu, Richard A. Thomas, S. S. 
Malhotra, Z. S. Shan, S. H. Liou, 

D. J. Sellmyer 

F. J. Cadieu, R. Rani, X. R. Qian, 
Li Chen 

E. Suzuki, Y. Hoshi, M. Naoe 

C. Prados, G. C. Hadjipanayis 

P. G. McCormick, W. F. Miao, 

P. A. L Smith, J. Ding, R. Street 

Thomas SchrefI, Josef Fidler 

H. Kanekiyo, S. Hirosawa 

M. Dahlgren, R. Grossinger, D. R. 
Cornejo, F. P. Missell 

W. C. Chang, D. Y. Chiou, S. H. 
Wu, B. M. Ma, Q. Chen, C. O. 
Bounds 

L. H. Lewis, J.-Y. Wang, D. O. 
Welch, V. Panchanathan 

M. I. Montero, F. Cebollada, M. P. 
Morales, J. M. Gonzalez, A. 
Hernando 


R. E. Camley, M. R. F. Jensen, 

S. A. Feiven, T. J. Parker 


© 1998 American Institute of Physics 


X 


J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


6284 Strain induced alteration of the gadolinium surface state 


6287 Effect of surface roughness on magnetization reversal of Co films on 
plasma-etched Si(IOO) substrates 

6290 Exploring magnetic roughness in CoFe thin films 

6293 Soft x-ray resonant magnetic reflectivity study of thin films and multilayers 


6296 Dependence of anti-Stokes/Stokes intensity ratios on substrate optical 
properties for Brillouin light scattering from ultrathin iron films 

Critical Phenomena, Spin Glasses, and Frustration 

6299 Magnetic phase diagrams of holmium determined from magnetoresistance 
measurements 

6302 Magnetostatic critical point phenomena of ErIGa garnet 

6305 Monte Carlo investigation of the eight-state Potts model on quasiperiodic 
tilings 

6308 Exact renormalization group equation for systems of arbitrary symmetry 
free of redundant operators 

6311 Random-exchange and random-field Ising model-like behaviors in 

Feo.482*^0.52F 2 

6314 Magnetic structures of the triangular lattice magnets AFe(S 04)2 (A^K, 

Rb, Cs) 


6317 Phase transition and phase diagram of the J^-J 2 Heisenberg model on a 
simple cubic lattice 

6320 Spin fluctuations and thermal expansion of La(NlxAli_;f)i 3 amorphous 
alloys 

6323 Magnetic relaxation in Gao. 6 Mo 2 S 4 spinel 

Nanocrystalline and Amorphous Soft Materials 

6326 New bulk amorphous Fe-(Co,Ni)-M-B (M=Zr,Hf,Nb,Ta,Mo,W) alloys with 
good soft magnetic properties 

6329 Influence of Si addition on thermal stability and soft magnetic properties 
for Fe-Al-Ga-P-C-B glassy alloys 

6332 Application of nanocrystalline soft magnetic Fe-M-B (M=Zr, Nb) alloys to 
choke coils 

6335 Soft magnetic properties and structures of nanocrystalline Fe-AI-Si-B- 
Cu-Nb alloy ribbons 

6338 Compositional dependence of the effective magnetic anisotropy in 
nanocrystalline Fe-Zr-B-(Cu) alloys 


6341 Approach to the magnetic saturation in nanocrystalline ferromagnets in 
the random anisotropy model 

Numerical Methods 

6344 Multigrid methods for computation of magnetostatic fields in magnetic 
recording problems 


C, Waldfried, D. N. Mcliroy, T. 
McAvoy, D. Welipitlya, P. A. 
Dowben, E. Vescovo 

M. Li, Y.-P. Zhao, G.-C. Wang, 
H.-G, Min 

J. W. Freeland, V. Chakarian, K. 
Bussmann, Y. U. Idzerda, H. 
Wende, C.-C. Kao 

J. M. Tonnerre, L Seve, A. 
Barbara-Dechelette, F. Bartolome, 

D. Raoux, V. Chakarian, C. C. Kao, 
H. Fischer, S. Andrieu, O. Fruchart 

J. F. Cochran, M. From, B. 

Heinrich 


Jeffrey R. Gebhardt, Naushad All 

Toshiro Tanaka, Kazuo Miyatani 

D. Ledue, D. P. Landau, J. Teillet 

A. A. LIsyansky, D. Nicolaldes 

E. P. Raposo, M. D. Coutinho-Filho 

H. Serrano-Gonzalez, S. T. 
Bramwell, K. D. M. Harris, B. M. 
Kariuki, L Nixon, I. P. Parkin, C. 
Ritter 

C. PInettes, H. T. Diep 
A. Fujita, K. Fukamichi 


T. Taniyama, I. Nakatani 


Akihisa Inoue, Tao Zhang, Hisato 
Koshiba, Akihiro Makino 

T. Mizushima, A. Makino, A. Inoue 

Y. Naitoh, T. Bitoh, T. Hatanai, A. 
Makino, A. Inoue 

B. J. Tate, B, S. Parmar, I. Todd, 
H. A. Davies, M. R. J. Gibbs, R. V. 
Major 

P. Garcia Tello, J. M. Blanco, N. 
Murillo, J. Gonzalez, R. Zuberek, 

A. Slawska-Waniewska, J. M. 
Gonzalez 

G. R. Aranda, J. Gonzalez, K. 
Kulakowski 


Igor Tsukerman, Alexander Plaks, 
H. Neal Bertram 


(Continued) 




J. Appl. Phys., Vol. 83. No. 11, 1 June 1998 


xl 


6347 Modified scalar potential solution for three-dimensional magnetostatic 
problems 

6350 Numerical simulation of the magnetization structures in thin polycrystalline 
films with the random anisotropy and intergrain exchange 

6353 Finite element analysis of the influence of a fatigue crack on magnetic 
properties of steel 

6356 Magnetohydrodynamic calculation for free surfaces 

6359 Differential Preisach model for the description of dynamic magnetization 
processes 

6362 Influence of the permanent magnet overhang on the performance of the 
brushless dc motor 

6365 Optimization of coils for detecting initial rotor position in permanent 
magnet synchronous motor 

6368 Temperature analysis of induction motors using a hybrid thermal model 
with distributed heat sources 

6371 Bifurcation phenomena and chaotic attractors in a six-dimensional 
nonlinear system 

Symposium on Layered Manganites 

6374 Two-dimensional ferromagnetic correlations above Tq in the naturally 
layered CMR manganite La 2 - 2 xSri+ 2 xMn 207 (x=0.3~0.4) (invited) 


6379 Chemistry of naturally layered manganites (invited) 


6385 Role of intergrowths in the properties of naturally layered manganite 
single crystals (invited) 


Rare Earth and Boride Hard Magnets 

6390 The development of high performance Nd-Fe-Co-Ga-B die upset 
magnets 

6393 Plastic deformation modeling of die-upset process for magnequench 
NdFeB magnets 

6396 Microstructural analysis of strip cast Nd-Fe-B alloys for high (BH)max 
magnets 

6399 Extension of the primary solidification region of Nd 2 Fei 4 B by levitation of 
undercooled melts 

6402 High performance Nd-Fe-B sintered magnets made by the wet process 

6405 Hydrogen absorption and desorption behavior in Pr-Fe-B type alloys 

6408 Coercivity of sintered Nd(Feo. 92 -xGaxBo.o 8 ) 5.5 permanent magnets 

6411 The origin and interpretation of fine scale magnetic contrast in magnetic 
force microscopy: A study using single-crystal NdFeB and a range of 
magnetic force microscopy tips 

6414 Off-axis electron holographic mapping of magnetic domains In Nd 2 Fei 4 B 

6417 Improvement of protective coating on Nd-Fe-B magnet by pulse nickel 
plating 

6420 A pump with flat-ring-shaped magnets 


K. Sivasubramaniam, S. Salon, 

M. V. K. Chari, I. D. Mayergoyz 

D. V. Berkov, N. L. Gorn 

Y. Shi, D. C. Jiles 

Keisuke Fujisaki, Takatsugu 
Ueyama 

P. Andrei, Al. Stancu, O. Caltun 

J. P. Wang, D. K. Lieu, W. L 
Lorimer, A. Hartman 

S. Wakao, T. Onuki, K. Tatematsu, 

T. Iraha 

S. C. Mukhopadhyay, S. K. Pal 

T. Sutani, T. Czaszejko, A. Nafalski 


D. N. Argyriou, T. M. Kelley, J. F. 
Mitchell, R. A. Robinson, R. 
Osborn, S. Rosenkranz, R. I. 
Sheldon, J. D. Jorgensen 

P. D. Battle, N. Kasmir, J. E. 
Millburn, M. J. Rosseinsky, R. T. 
Patel, L E. Spring, J. F. Vente, 

S. J. Blundell, W. Hayes, A. K. 
Klehe, A. Mihut, J. Singleton 

S. D. Bader, R. M. Osgood III, 

D. J. Miller, J. F. Mitchell, J. S. 
Jiang 


T. Saito, M. Fujita, T. Kuji, K. 
Fukuoka, Y. Syono 

S. Guruswamy, Y. R. Wang, V. 
Panchanathan 

J. Bernardi, J. Fidler, M. Sagawa, 
Y. Hirose 

R. Hermann, W. Loser 

M. Takahashi, K. Uchida, F. 
Taniguchi, T. Mikamoto 

Yoon B. Kim, W. Y. Jeung 

X. C. Kou, F. R. de Boer, H. 
Kronmiiller 

M. Al-Khafaji, W. M. Rainforth, 

M. R. J. Gibbs, J. E. L. Bishop, 

H. A. Davies 

M. R. McCartney, YImei Zhu 

C. W. Cheng, F. T. Cheng, H. C. 
Man 

H. Saotome, T. Hagiwara, Y. Sato 


(Continued) 


xii 


J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Heavy Fermions 

6423 New phase boundary between magnetic and non-Fermi-liquid in 
Ce(Rhi_;fRU;^)3B2, forO^x^O.4 

6426 Magnetic ordering of Ce in the heavy-fermion compound CesAI 

6429 Size and dimensionality effect in single-impurity Anderson model 

6432 f-Electron delocalization/localization and the abrupt disappearance of 
uranium magnetic ordering with dilution alloying 

6435 Evidence for an extended critical region near the metamagnetic transition 
of UCoAl 

6438 Electronic structure and magnetic properties of URhSi 


Biomagnetism and Magnetochemistry 

6441 Weighted minimum-norm source estimation of magnetoencephalography 
utilizing the temporal information of the measured data 

6444 A comparative study of the magnetic separation characteristics of 
magnetotactic and sulphate reducing bacteria 

6447 Magnetoelectrolysis of copper 

6450 Impedance magnetic resonance imaging: A method for imaging of 
impedance distributions based on magnetic resonance imaging 

6453 Polymerization and dissolution of fibrin under homogeneous magnetic 
fields 

6456 Bioluminescence under static magnetic fields 

6459 Structure of water molecules under 14 T magnetic field 

6462 Estimation of multiple sources using a three-dimensional vector 
measurement of a magnetoencephalogram 

6465 Measurements of biomagnetic fields using a high-resolution dc 
superconducting quantum interference device magnetometer 

Crystalline Soft Magnetic Materials 

6468 Magnetic properties and ordering in C-coated Fe^Co-i-x nanocrystals 

6471 Soft magnetic properties of LaCoia and La(Co, Fe)i 3 alloys 

6474 Effects of heat treatment on the magnetic properties of polymer-bound 
Iron particle cores 

6477 Alternating current magnetic properties of cores made from pressed 
acicular steel particles 

6480 Magnetic induction and surface segregation in thin-gauged 3% Si steel 

6483 New method to predict the magnetic properties of thin gauged Sl-Fe 
sheets 

6486 Local distribution on magnetic properties in grain-oriented silicon steel 
sheet 

Computational Micromagnetics 

6489 Anisotropy design in magnetic media: A micromagnetics study 

6491 A variational approach to exchange energy calculations in micromagnetics 


E. Bauer, R. Hauser, A. Galatanu, 

A. Lindbaum, G. Hilscher, H. 
Sassik, H. Kirchmayr, J. G. Sereni, 
P. RogI 

W.-H. Li, J. C. Peng, Y.-C. Lin, 

K. C. Lee, J. W. Lynn, Y. Y. Chen 

Feng Chen, Nicholas Kioussis 

B. R. Cooper, Y.-L Lin 

A. V. Kolomiets, L. Havela, V. 
Sechovsky, L. E. DeLong, D. B. 
Watkins, A. V. Andreev 

M. Gain, F. Marabelli, A. 
Continenza, P. Monachesi, F. 
Canepa, M. L. Fornasini 


Sunao Iwaki, Shoogo Ueno 

A. S, Bahaj, P. A. B. James, F. D. 
Moeschler 

G. Hinds, J. M. D. Coey, M. E. G. 
Lyons 

S. Ueno, N. Iriguchi 

M. Iwasaka, M. Takeuchi, S. Ueno, 

H. Tsuda 

M. Iwasaka, S. Ueno 
M. Iwasaka, S. Ueno 

Koichiro Kobayashi, Yoshinori 
Uchikawa 

K. Iramina, B. Hong, S. Uchida, K. 
Goto, S. Ueno, S. Nakayama 


Z. Turgut, J. H. Scott, M. Q. 

Huang, S. A. Majetich, M. E. 
McHenry 

M. Q. Huang, W. E. Wallace, M. E. 
McHenry, Q. Chen, B. M. Ma 

M. Namkung, B. Wincheski, R. G. 
Bryant, A. Buchman 

R. F. Krause, J. H. Bularzik, H. R. 
Kokal 

N. H. Heo, K. H. Chai, J. G. Na, 

J. S. Woo 

J. G. Na, C. H. Park, J, Kim, N. H. 
Heo, S. R. Lee, C. S. Lee, J. S. 
Woo 

Masato Enokizono, Ikuo Tanabe, 
Takeshi Kubota 


J. H. Kaufman, T. Koehler, A. 
Moser, D. Weller, B. Jones 

M. J. Donahue 


(Continued) 



J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


6494 Hysteresis loop areas in kinetic Ising models: Effects of the switching 
mechanism 

6497 Domain-wall motion in random potential and hysteresis modeling 
6500 The field-space perspective on hysteresis in uniaxial ferromagnets 
6503 MIcromagnetic localization 

6506 Computational micromagnetic investigation of magnetization reversal in 
Nd-Fe-B nanocomposite magnets 

6509 Influence of the system parameters on the non-Arrhenius magnetic 
relaxation of systems having distributed properties 


Spin-Dependent Tunneling I 

6512 Voltage dependence of magnetoresistance in spin dependent tunneling 
junctions 

6515 Bias voltage and temperature dependence of magnetotunneling effect 


6518 Finite bias spin dependent tunneling: A nonequilibrium Green’s function 
approach 

6521 Spin-dependent tunneling in epitaxial systems: Band dependence of 
conductance 

6524 Anomalous behavior of temperature and bias-voltage dependence of 
tunnel-type giant magnetoresistance in insulating granular systems 

New Materials and Magnetic Semiconductors 

6527 High perpendicular anisotropy and magneto-optical activities in ordered 
CoaPt alloy films 

6530 Thermopower studies of percolating magnetic metallic nanostructures 

6533 Structural and magnetic properties of Fe^Sey thin films during their 
selenization process 

6536 Magnetic behavior of the new low-T^ phase of SrRuOa 

6539 Growth and characterization of epitaxial thin films of conductive 
ferromagnetic oxide SrRuOa 

6542 A field induced ferromagnetic-like transition below 2.8 K in LigCuOa: An 
experimental and theoretical study 

6545 Magneto-optic study of Ni-based diluted magnetic semiconductors 
6548 Magneto-optic effect of the ferromagnetic diluted magnetic semiconductor 

Gai_;fMn;fAs 

6551 Hall effect and magnetic properties of Ml-V based (Gai_;fMn;^)As/AlAs 
magnetic semiconductor superlattices 

6554 Long-range antiferromagnetic couplings in [ZnTe|MnTe] superlattices 
6557 Magnetic measurements on the lll-VI diluted magnetic semiconductor 

Gai_;fMn;fSe 

6560 Second harmonic spectroscopy and control of domain size in 
antiferromagnetic YMnOa 


xiii 


S. W. Sides, P. A. Rikvold, M. A. 
Novotny 

M. Pasquale, V. Basso, G. Bertotti, 
D. C. Jiles, Y. Bi 

Y. T. Millev, J. R. Cullen, H. P. 
Oepen 

Ralph Skomski 

S. David, B. Kevorkian, J. C. 
Toussaint, D. Givord 

R. Smirnov-Rueda, O. A. 
Chubykalo, J. M. Gonzalez, J. 
Gonzalez 


J. Zhang, R. M. White 

Yu Lu, X. W. Li, Gang Xiao, R. A. 
Altman, W. J. Gallagher, A. Marley, 

K. Roche, S. Parkin 

Xindong Wang 

J. M. MacLaren, W. H. Butler, 

X.-G. Zhang 

S. Mitani, K. Takanashi, K. 
Yakushiji, H. Fujimori 


Y. Yamada, W. P. Van Drent, E. N. 
Abarra, T. Suzuki 

X. N. Jing, X. Yan 

T. Takahashi, S. Kuno, N. Honda, 

Y. Takemura, K. Kakuno, K. Saito 

P. A. Joy, S. K. Date, P. S. Anil 
Kumar 

C. B. Eom, R. A. Rao, Q. Gan, 

D. B. Kacedon 

R. J. Ortega, P. J. Jensen, K. V. 
Rao, F. Sapiha, D. Beltran, Z. 

Iqbal, J. C. Cooley, J. L. Smith 

K. Ando, A. Chiba, H. Tanoue 

K. Ando, T. Hayashi, M. Tanaka, A. 
Twardowski 

T. Hayashi, M. Tanaka, K. Seto, T. 
NIshinaga, H. Shimada, K. Ando 

J. Lin, J. J. Rhyne, J. K. Furdyna, 

T. M. Giebutowicz 

T. M. Pekarek, B. C. Crooker, I. 
Miotkowski, A. K. Ramdas 

M. Fiebig, D. Frohlich, S. Leute, 

R. V. Pisarev 


(Continued) 



xlv 


J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Giant Magnetoimpedance 

6563 High frequency behavior of soft magnetic wires using the giant 
magnetoimpedance effect 


6566 Modeling of domain structure and anisotropy in glass-covered amorphous 
wires 


6569 Phenonemological model for magnetoimpedance in soft ferromagnets 

6572 Field and stress dependence of the irreversible magnetization changes in 
pure iron 

6575 Temperature dependence of magnetoimpedance effect in amorphous 
C 066 Fe 4 NiBi 4 Sii 5 ribbon 

6578 Magneto-impedance effect in high permeability NiFeMo permalloy wires 

6581 The influence of field- and stress-induced magnetic anisotropy on the 
magnetoimpedance in nanocrystalline FeCuNbSiB alloys 


6584 Giant magneto-impedance effect In nanocrystalline glass-covered wires 
6587 High frequency properties of glass-coated microwire 


P. Ciureanu, M. Britel, D. Menard, 
A. Yelon, C. Akyel, M. Rouabhi, 

R. W. Cochrane, P. Rudkowski, 

J. O. Strom-Olsen 

D. Menard, D. Frankland, P. 
Ciureanu, A. Yelon, M. Rouabhi, 
F?. W. Cochrane, H. Chiriac, T. A. 
Ovari 

D. Atkinson, P. T. Squire 
J. Pearson, P. T. Squire 

Y. K. Kim, W. S. Cho, T. K. Kim, 
C. O. Kim, Heebok Lee 

M. Vazquez, J. M. 
Garcia-Beneytez, J. P. SInnecker, 
Lin Li 

G. V. Kurlyandskaya, J. M. 
Garcia-Beneytez, M. Vazquez, 

J. P. Sinnecker, V. A. Lukshina, 

A. P. Potapov 

H. Chiriac, T. A. Ovari, C. S. 
Marinescu 

A. N. Antonenko, E. Sorkine, A. 
Rubshtein, V. S. Larin, V. Manov 


Spin Dynamics 

6590 Frequency versus Lyapunov exponent map: A new approach to 
investigate dynamics of nonlinear magnetic systems 

6593 Coupling of reversal modes for an infinite ferromagnetic cylinder 

6596 Magnetism and Jahn-Teller effect in LaMnOa 

6599 Application of spin-dynamics methods to a study of magnetization 
tunneling in many-spin systems 

6602 Spin dynamics in S=1/2 chains and ladders from NMR and susceptibility 
measurements in Sr^ 4 _xNaxCu 2404 i 

6605 Magnetic properties and spin dynamics in hole-doped S= 1 AF chain: ®®Y 
NMR and susceptibility in Y 2 _xCaxBaNi 05 


N. Y. Piskun, P. E. Wigen 

Ching-Ray Chang, Ching-MIng Lee 

M. Z. Li, Liang-Jian Zou, Q. Q. 
Zheng 

V. V. DobrovitskI, B. N. Harmon 

P. Carretta, M. Corti, P. Ghigna, A. 
Lascialfari 

F. Tedoldi, A. Rigamonti, C. 
Brugna, M. Corti, A. Lascialfari, D. 
Capsoni, V. Massarotti 


Exchange and Film Hard Magnets 

6608 Coercivity and exchange coupling in PrCo:Co nanocomposite films 
6611 Nanostructured NdFeB films processed by rapid thermal annealing 

6614 Magnetic and structural properties of (Coi_xFex)Pt thin films 

6617 Magnetocrystalline anisotropy in (111) CoPtg thin film with growth-induced 
chemical anisotropy investigated by x-ray magnetic circular dichroism 


6620 Magnetic properties of NdFeB thin films synthesized via laser ablation 
processing 

6623 Maximum energy product of isotropic Nd-Fe-B-based nanocomposite 
magnets 

6626 Remanence enhancement in mechanically alloyed isotropic 
Nd(Fe, Mo)i 2 Nx compounds 


J. P. Liu, Y. Liu, D. J. Sellmyer 

M. Yu, Y. Liu, S. H. Liou, D. J. 
Sellmyer 

P. W. Jang, D. W. Kim, C. H. Park, 
J. G. Na, S. R. Lee 

W. Grange, J.-P. Kappler, M. 

Maret, J. Vogel, A. Fontaine, F. 
Petroff, G. Krill, A. Rogalev, J. 
Goulon, M. Finazzi, N. B. Brookes 

ChoongJin Yang, SangWon Kim, 
Jong Seog Kang 

J. Kuma, N. Kitajima, Y. Kanai, H. 
Fukunaga 

Yiaofu Xiao, Qi Zeng, Shengzhi 
Dong, Run Wang 


(Continued) 



J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


XV 


6628 Magnetic properties of Nd 8 Fe 77 Co 5 BeCuNb 3 melt-spun ribbons 

6631 Effect of TiC additions to the microstructure and magnetic properties of 
Nd 9 . 5 Fe 84 . 5 B 6 melt-spun ribbons 


6634 Application of the shock compaction technique for consolidation of hard 
magnetic powders 

6637 Reversible processes and magnetic viscosity of nanocrystalline 
permanent magnets 

6640 Magnetic properties of RFe^o.sMoi.sCx and their nitrides 


Soft Thin Films 

6643 Microstructure and magnetic properties of FeCoN thin films 
6646 Structure and magnetic properties of a Fe-Zr-N thin film 


6649 An effect of nitrogen on magnetic properties and microstructure of 
Fe-Nb-B-N nanocrystalline thin films 

6652 Soft magnetic properties of as-deposited Fe-Hf-C-N and Fe-Hf-N 
nanocrystalline thin films 

6655 Microstructure and soft magnetic properties of FeSIAI(Ti/Ta)(0)N 

6658 New applications of nanocrystalline Fe(Co-Fe)-Hf-0 magnetic films to 
micromagnetic devices 

6661 Study on the in-plane uniaxial anisotropy of high permeability granular 
films 

6664 Soft magnetic properties of Co-Cr-0 granular films 

6667 Magnetic properties of Fe films deposited by Ar, Kr, and Xe ion beam 
sputtering 

6670 Effects of plasma and bias power on magnetic properties of sendust films 

6673 Preparation of soft magnetic films of nanocrystalline Fe-Cu-Nb-Si-B 
alloy by facing targets sputtering 

6676 Measurement of the magnetostriction constants of amorphous thin films 
on kapton substrates 

6679 Longitudinal-transverse resonance and localization related to the random 
anisotropy In a-CoTbZr films 

Spin-Dependent Tunneling il 

6682 Influence of barrier impurities on the magnetoresistance in ferromagnetic 
tunnel junctions 

6685 Spin-dependent tunneling junctions with hard magnetic layer pinning 


6688 Picotesla field sensor design using spin-dependent tunneling devices 


6691 Ferromagnetic tunnel junctions with plasma-oxidized Al barriers and their 
annealing effects 


H. Chiriac, M. Marinescu 

M. J. Kramer, C. P. LI, K. W. 
Dennis, R. W. McCallum, C. H. 
Sellers, D. J. Branagan, L. H. 
Lewis, J. Y. Wang 

M. Leonowicz, W. Kaszuwara, E. 
Jezierska, D. Januszewski, G. 
Mendoza, H. A. Davies, J. Paszula 

D. R. Cornejo, V. Villas-Boas, F. P. 
Missell 

Weihua Mao, Jinbo Yang, Benpel 
Cheng, Yingchang Yang 


P, C. Kuo, S. S. Chang, C. M. Kuo, 
Y. D. Yao, H. L. Huang 

Jong-Sung Baek, Seong-Cho Yu, 
Woo-Young Urn, Chul-Sung Kim, 
Taek-Soo Kim, Chong-Oh Kim 

J. Y. Park, S. J. Suh, T. H. Noh, 

K. Y. Kim, H. J. Kim 

J. Y. Song, J. J. Lee, S. H. Han, 

H. J. Kim, J. Kim 

M. Hiramoto, N. Matsukawa, H. 
Sakakima, Y. Ichikawa, K. Ijima 

T. Sato, Y. Miura, S. Matsumura, 

K. Yamasawa, S. Morita, Y. 

Sasaki, T. Hatanai, A. Makino 

W. D. Li, O. Kitakami, Y. Shimada 

Takeshi Morikawa, Motofumi 
Suzuki, Yasunori Taga 

S. Iwatsubo, T. Takahashi, M. 

Naoe 

M. S. Araghi, R. E. Hurley, H. S. 
Gamble, P. M. Dodd, R. Atkinson 

Masahiko Naoe, Hiroaki 
Matsumiya, Takayuki Ichihara, 
Shigeki Nakagawa 

C. Ouyang, T. W. Kim, R. J. 
Gambino, C. Jahnes 

G. Suran, E. Boumaiz 


R. Jansen, J. S. Moodera 

J. F. Bobo, F. B. Mancoff, K. 
Bessho, M. Sharma, K. Sin, D. 
Guarisco, S. X. Wang, B. M. 
Clemens 

Mark Tondra, James M. Daughton, 
Dexin Wang, Russell S. Beech, 
Anita Fink, John A. Taylor 

M. Sato, H. Kikuchi, K. Kobayashi 


(Continued) 


xvi 


J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


6694 Tunneling magnetoresistance and current distribution effect in 
spin-dependent tunnel junctions 

6697 High conductance magnetoresistive tunnel junctions with multiply oxidized 
barrier 

6700 Area scaling of planar ferromagnetic tunnel junctions: From shadow 
evaporation to lithographic microfabrication 

6703 Nanometric cartography of tunnel current in metal-oxide junctions 


J. J. Sun, R. C. Sousa, T. T. P. 
Galvao, V. Soares, T. S. Plaskett, 
P. P. Freitas 

P. K. Wong, J. E. Evetts, M. G. 
Blamire 

H. Boeve, R. J. M. van de 
Veerdonk, B. Dutta, J. De Boeck, 
J. S. Moodera, G. Borghs 

V. Da Costa, F. Bardou, C. Beal, 
Y. Henry, J. P. Bucher, K. 
Ounadjela 


Hard Magnets I 

6706 Sm 2 (Co,Fe,Cu,Zr)i 7 magnets for use at temperature ^400 °C 

6709 Phase transformation and magnetic properties of 

Sm(Coo. 9 i-xFexCuo.o 7 Zro.o 2 )z powders for bonded magnet applications 

6712 The effect of particle size and consolidating pressure on the magnetic 
properties of Sm(Co, Fe, Cu, Zr)^ bonded magnets 

6715 High temperature stability of SmTM magnets 

6718 Structure and magnetic properties of SmC 07 _;^Zrx alloys (x=0-0.8) 

6721 Coercivity calculation of Sm 2 (Co,Fe,Cu,Zr)i 7 magnets 

6724 Finite-temperature behavior of anisotropic two-sublattice magnets 

6727 Magnetic properties of DyCoioV 2 

6730 Investigation of the magnetic properties of ErFe^Ti and ErFenTiH in high 
magnetic field 

6733 Magnetic properties of TbCo 3 B 2 studied by neutron diffraction, 
magnetization, and ac-susceptibility measurements 

6736 A Mossbauer spectral study of Tb 2 Fei 7 and the Tb 2 Fei 7 „xSix solid 
solutions 


C. H. Chen, M. S. Walmer, M. H. 
Walmer, S. Liu, E. Kuhl, G. Simon 

W. Gong, B. M. Ma, C. O. Bounds 


B. M. Ma, W. Gong, C. 0. Bounds, 

C. H. Chen, M. S. Walmer 

A. S. Kim 

M. Q. Huang, W. E. Wallace, M. 
McHenry, Q. Chen, B. M. Ma 

M. Katter 

Ralph Skomski 

C. Zhang, X. C. Kou, Z. G. Zhao, 
E. Briick, K. H. J. Buschow, F. R. 
de Boer 

O. Isnard, M. Guillot 

El’ad N. Caspi, Haim Pinto, Moshe 
Kuznietz, Hanania Ettedgui, 
Mordechai Melamud, Israel Felner, 
Hagai Shaked 

Dimitri Hautot, Gary J. Long, P. C. 
Ezekwenna, F. Grandjean, D. P. 
Middleton, K. H. J. Buschow 


Magneto-Optic Materials 

6739 Asymmetric nonlinear magneto-optic effects in PtMnSb thin films 

6742 Anisotropic third-order magneto-optical Kerr effect 

6745 Magneto-optical properties of MnPta: LDA+ U calculations 

6747 Thickness dependence of interfacial magneto-optic effects in Pt/Co 
multilayers 

6750 Optical and magneto-optical properties of Co/Pt/AIN multilayers 

6753 Effect of Pt in TbFeCo on magnetic and magneto-optical properties 

6756 Magnetooptical properties of Sc-substituted erbium-iron-garnet single 
crystals 

6759 Crystal ion slicing of single-crystal magnetic garnet films 

6762 Faraday rotation and magnetic properties of erbium gallium gallate under 
high magnetic field 

6765 On the origin of the magneto-optical effects in Li, Mg, Ni, and Co ferrite 


R. Carey, D. M. Newman, M. L. 
Wears 

A. V. Petukhov, Th. Rasing, T. 
Katayama, N. Nakajima, Y. Suzuki 

R. F. Sabiryanov, S. S. Jaswal 

Xiang Gao, Michael J. DeVries, 
Daniel W. Thompson, John A. 
Woollam 

R. Atkinson, P. M. Dodd, I. W. 
Salter, P. J. Grundy, C. J. Tatnall 

Y. Itoh, W. P. Van Drent, T. Suzuki 
J. Ostorero, M. Guillot 

M. Levy, R. M. Osgood, Jr., A. 
Kumar, H. Bakhru 

M. Guillot, T. Schmiedel, You Xu 

W. F. J. Fontijn, P. J. van der 
Zaag, R. Metselaar 


(Continued) 



J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


XVII 


6768 Magneto-optical properties of one-dimensional photonic crystals 
composed of magnetic and dielectric layers 

6771 Magneto-chromatic effects of tunable magnetic fluid grating 

Superconductivity I 

6774 Suppression of superconductivity by injection of spin-polarized current 


6777 Magnetoquenched superconducting valve 
6780 Novel high-Tc transistors with manganite oxides 


6783 Extended x-ray absorption fine structure measurements of 

nonsuperconducting PrBa 2 Cu 306 . 9 : Evidence against Ba site Pr 
substitution 

6786 Anisotropic thermal conductivity of c-axis aligned Bi 2 Sr 2 CaCu 20 ;f 
superconductor in high magnetic fields 

6789 Superconductivity in the new quaternary ruthenium borocarbide Y-Ru-B- 
C system 

6792 Electron correlation In antiferromagnet and superconductor thiospinel 
CU-C 0 -S 4 

6795 Plausible d-wave cuprate superconductivity: Muon-spin-relaxation studies 
of RBa 2 Cu 307 _^ vortex states 

6798 Flux patterns of multifilamentary Ag-sheathed (Pb,Bi) 2 Sr 2 Ca 2 Cu 30 -io +5 
tapes 


6801 Depth-dependent magnetism of layered superconductors: Nb/Si 

6804 Computation of the nonlinear magnetic response of a three dimensional 
anisotropic superconductor 

Exchange Biasing f 

6807 Temperature dependence of giant magnetoresistance properties of NiMn 
pinned spin valves 

6810 Exchange biasing of permalloy films by Mn;^Pti_;^: Role of composition 
and microstructure 

6813 Exchange coupling of NIFe/FeRh-lr thin films 

6816 Exchange anisotropy in Ni 82 Fei 80 { 100 }/Ni 8 oFe 2 o bilayers 


6819 Temperature dependence of ferromagnetic resonance as induced by NIO 
pinning layers 

6822 Dependence of exchange coupling on antiferromagnetic layer thickness in 
NiFe/CoO bilayers 

6825 Magnetic behavior of NiFe/NiO bilayers 


Mitsuteru Inoue, Ken’ichi Aral, 
Toshitaka Fuji!, Masanori Abe 

Chin-Yih Hong, H. E. Horng, I. J. 
Jang, J. M. Wu, S. L Lee, 

Wai Bong Yeung, H. C. Yang 


Daniel Koller, M. S. Osofsky, D. B. 
Chrisey, J. S. Horwitz, R. J. 

Soulen, Jr., R. M. Stroud, C. R. 
Eddy, J. Kim, R. C. Y. Auyeung, 

J. M. Byers, B. F. Woodfield, G. M. 
Daly, T. W. Clinton, Mark Johnson 

T. W. Clinton, Mark Johnson 

Z. W. Dong, S. P. Pal, R. Ramesh, 
T. Venkatesan, Mark Johnson, 

Z. Y. Chen, A. Cavanaugh, Y. G. 
Zhao, X. L. Jiang, R. P. Sharma, S. 
Ogale, R. L. Greene 

V. G. Harris, D. J. Fatemi, V. M. 
Browning, M. S. Osofsky, T. A. 
Vanderah 

S. C. Nakamae, J. Crow, J. Sarrao, 
J. Schwartz 

Y. Y. Hsu, H. C. Chiang, H. C. Ku 

Kazuo Miyatani, Toshiro Tanaka, 
Masayasu Ishikawa 

C. Boekema, E. J. Ruiz, Z. C. 
Pobre, S. R. Punjabi, F. Kong, O. 
Vera, D. W. Cooke 

M. R. Koblischka, T. H. Johansen, 
H. Bratsberg, L. Pust, A. Galkin, P. 
Nalevka, M. Marysko, M. JIrsa, M. 
Bentzon, P. Bodin, P. Vase, T. 
Freltoft 

S. M. Yusuf, E. E. Fullerton, R. M. 
Osgood II, G. P. Felcher 

Igor Zutic, Oriol T. Vails 


Sining Mao, Nurul Amin, Ed 
Murdock 

Kannan M. Krishnan, C. Nelson, 

C. J. Echer, R. F. C. Farrow, R, F. 
Marks, A. J. Kellock 

S. Yuasa, M. Nyvit, T. Katayama, 
Y. Suzuki 

Chih-Huang Lai, Robert L. White, 
Connie P. Wang, Thomas C. 
Anthony 

P. Lubitz, J. J. Krebs, M. M. Miller, 
Shufan Cheng 

T. Ambrose, C. L. Chien 

Zhenghong Qian, John M. 
Sivertsen, Jack H. Judy 


(Continued) 



xviii 


J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


6828 Direct experimental study of the magnetization reversal process In 
epitaxial and polycrystalline films with unidirectional anisotropy 


Magnetic Microscopy and Imaging II 

6831 Spin-polarized tunneling by spin-polarized scanning tunneling microscopy 

6834 Imaging of magnetic domains with scanning tunneling optical microscopy 

6837 Induction mapping of magnetostrictive materials 

6840 Influence of current density on the magnetization process in active 
spin-valve elements 

6843 Magnetic domains of single-crystal Nd 2 Fei 4 B imaged by unmodified 
scanning electron microscopy 

6846 A flexible two-dimensional phase correction for interleaved echo-planar 
imaging reconstruction 

6849 Metallic needle artifacts in magnetic resonance imaging 

Magnetic Ferrites 

6852 Magnetic properties of MnZnTi and NiZn ferrite films deposited by laser 
ablation 

6855 Structure and soft magnetic properties of sputter deposited MnZn-ferrite 
films 

6858 Emission studies of Ba-hexaferrite plume produced by a KrF excimer 
laser 

6861 Fine grained Mn-Zn ferrite for high frequency driving 

6864 Particle size dependence of rotational responses in Ni-Zn ferrite 

6867 Processing and cation redistribution of MnZn ferrites via high-energy ball 
milling 

6870 The effect of Intragranular domain walls in MgMnZn-ferrite 

6873 Line width of manganese-zinc ferrite polycrystals with oxygen partial 
pressure 

6876 The diffusion of tracer oxygen atoms in Ni ferrites 

6879 Conversion electron Mossbauer studies on strontium ferrite films with 
in-plane and perpendicular anisotropies 


V. 1. Nikitenko, V. S. Gornakov, 

L. M. Dedukh, Yu. P. Kabanov, 

A. F. Khapikov, A. J. Shapiro, R. D. 
Shull, A. Chaiken, R. P. Michel 


Hiroyoshi Kodama, Takuya 
UzumakI, Mitsumasa OshikI, 
Kazuhisa Sueoka, Kdichi Mukasa 

P. Bertrand, L. Conin, C. Hermann, 
G. Lampel, J. Peretti, V. I. Safarov 

Jennifer Dooley, Marc De Graef, 
Michael E. McHenry 

X. Portier, A. K. Petford-Long, T. C. 
Anthony, J. A. Brug 

L. H. Lewis, J.-Y. Wang, P. 

Canfield 

Haiying Liu 
Haiying Liu 


M. M. Amado, M. S. Rogalski, L 
Guimaraes, J. B. Sousa, 1. Bibicu, 
R. G. Welch, S. B. Palmer 

M. F. Gillies, R. Coehoorn, J. B. A. 
van Zon, D. Alders 

P. Papakonstantinou, M. C. O’Neill, 
R. Atkinson, R. Al-Wazzan, T. 
Morrow, I. W. Salter 

K. Takadate, Y. Yamamoto, A. 
Makino, T. Yamaguchi, I. Sasada 

P. S. Anil Kumar, S. R. Sainkar, 

J. J. Shrotri, S. D. Kulkarni, C. E. 
Deshpande, S. K. Date 

D, J. Fatemi, V. G. Harris, V. M. 
Browning, J. P. Kirkland 

P. J. van der Zaag, M. 
Kolenbrander, M. Th. Rekveldt 

Soon Cheon Byeon, Kug Sun 
Hong, In-Tae Kim 

V. B. Fetisov, G. A. Kozhina, 

A. Ya. Fishman, T. E. Kurennykh, 
V. B. Vykhodets 

Antony Ajan, B. Ramamurthy 
Acharya, Shiva Prasad, S. N. 
Shringi, N. Venkataramani 


Symposium on Exchange Biasing 

6882 Role of the antiferromagnet in exchange-biased FegO^CoO superlattices 
(invited) 

6888 Role of interfacial uncompensated antiferromagnetic spins in unidirectional 
anisotropy in NisiFeig/CoO bilayers (invited) 


Y. Ijiri, J. A. Borchers, R. W. Erwin, 
S.-H. Lee, P. J. van der Zaag, 

R. M. Wolf 

Kentaro Takano, R. H. Kodama, 

A. E. Berkowitz, W. Cao, G. 
Thomas 


6893 Measurements of the ferromagnetic/antiferromagnetic interfacial exchange 
energy in CO/CoO and Fe/FeFg layers (invited) 


E. Dan Dahiberg, Brad Miller, 
Bradford Hill, B. J. Jonsson, Valter 
Strom, K. V. Rao, Josep Nogues, 
Ivan K. Schuller 


(Continued) 



J. Appl. Phys., Vol. 83, No. 11. 1 June 1998 


XIX 


Rare Earth Nitride and Carbide Hard Magnets 

6896 Immobilization diffusion in R 2 Fei 7 nitrides 

6899 Magnetic anisotropy of R 2 Fei 7 N;f compounds 

6902 Coercive Sm 2 Fei 7 N 3 : A model pinning system created by heavy ion 
irradiation 

6905 Hydrogenation and disproportionation of Sm 2 Fei 7 _;fGa;f at high hydrogen 
pressures 

6908 Electron microscopy studies of high coercive melt-spun Sm 2 +^Fei 5 Ga 2 C 2 
permanent magnets 

6911 Pressure induced reversal of the volume expansion caused by interstitial 
nitrogen in Nd 2 Fei 7 N 3 


6914 A neutron diffraction structural study of R 2 Fei 7 _;^AI;^(C) (R=Tb, Ho) alloys 

6917 High remanence (Sm, Zr)Fe 7 Nx+a-Fe nanocomposite magnets through 
exchange coupling 

6920 Effect of Al substitution on the local environments and magnetic 

properties of partially nitrogenated (Ero. 5 Pro. 5 ) 2 Fe-i 7 permanent magnets 

6923 ^^Fe Mossbauer study of the interstitial nitrogen atom effects of 
NdFe10.5V1.5N, 

6926 A study of nitrogenation of a NdFei 2 -xMo, compound by in situ neutron 
powder diffraction 

6929 Crystallization and Mossbauer studies of melt-spun NdFeio^TiBo.sN^ 
alloys 

6932 A Mossbauer study of plasma nitrided iron 

Macroscopic Quantum Tunneling and Spin Dynamics 

6934 Experimental evidence of macroscopic resonant tunneling of 
magnetization in antiferromagnetic ferritin 

6937 Field-tuned quantum tunneling of the magnetization 

6940 Resonant magnetic quantum tunneling through thermally activated states 

6943 Unusual properties of the molecular nanomagnet Mni 2 ac 

6946 Comparison of the spin dynamics in different types of molecular magnetic 
rings from'’H NMR 

6949 Analysis of electron paramagnetic resonance experiments In colossal 
magnetoresistance materials 

6952 A novel method for quantitative study of domain reversal behavior 

6955 Surface spin waves in metamagnets with nonuniaxial single-ion anisotropy 

Itinerant Magnetism 

6958 Exchange narrowing effects in the EPR linewidth of Gd diluted In Ce 
compounds 


R. SkomskI, S. Wirth 

X. C. Kou, F. R. de Boer, G. 
Chouteau 

N. M. Dempsey, X. L. Rao, 

J. M. D. Coey, J. P. Nozieres, M. 
Ghidini, B. Gervais 

M. Kubis, K.-H. Muller L, Schutz 

O. Gutfleisch, I. R. Harris 

J. van Lier, A. Zern, H. Labitzke, J. 
Thomas, M. Seeger, H. Kronmuller 

G. K. Marasinghe, W. J. James, 

P. C. Ezekwenna, H. Luo, W. B. 
Yelon, Y. Zhao, R. B. Von Dreele, 
M. Ellouze, Ph. I’Heritier 

W. B. Yelon, H. Luo, M. Chen, 

W. C. Chang, S. H. Tsai 

T. Hidaka, T. Yamamoto, H. 
Nakamura, A, Fukuno 

V. G. Harris, D. J. Fatemi, K. G. 
Suresh, K. V. S. Rama Rao 

Jinbo Yang, Weihua Mao, 
Yingchang Yang, Zhenjie Zhao, 
Fashen Li 

C.-K. Loong, S. M. Short, J. Lin, Y. 
Ding 

Chul Sung Kim, Sung Yong An, 
Young Rang Uhm, Seung Wha 
Lee, Y. B. Kim, C. S. Kim 

F. A. O. Cabral, J. H. de Araujo, 

R. C. Araujo, S. Gama 


E. del Barco, F. Luis, J. Tejada, 

X. X. Zhang, J. Bartolome, J. M. 
Hernandez, E. M. Chudnovsky 

D. Garcia-Pablos, N. Garcia, H. De 
Raedt 

J. F. Fernandez, J. Bartolome, F. 
Luis 

M. A. Novak, A. M. Gomes, R. E. 
Rapp 

A. Lascialfari, Z. H. Jang, F. Borsa, 
D. Gatteschl, A. Cornia 

D. L Huber 


Sug-Bong Choe, Sung-Chul Shin 

D. H. A. L. Anselmo, E. L. 
Albuquerque, M. G. Cottam 


Pablo A. Venegas, Paulo R. S. 
Netto 


(Continued) 



XX 


J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


6961 High field magnetic properties in single crystal N6^Co 

6964 Evolution of magnetism in Nd(Coi„;fSy 2 and Ho(Coi_xSy 2 

6967 On the nature of the magnetic phase transition of the H 0 C 02 intermetallic 
6969 Recovery of ErCo 2 Fermi level by substitution of Co by Ni and Fe 

6971 Theoretical study of hyperfine fields at impurity nuclei in GdX (X=Zn,Cd) 
compounds: A two-center model 

6974 Magnetic transitions in Tbo. 7 Ndo. 3 Mn 2 Ge 2 compound 

6977 Magnetic moment, thermal and electrical transport in the inverse Mott 
systems BaCoo. 9 Nlo.iS 2 _y and 00^284 

6980 Magnetocrystaliine anisotropy of (Fei_;fCO;f) 3 P 

6983 Magnetic moment and hyperfine field on Fe sites in RFeeSng compounds 
6986 Hydrogen-induced changes in TbNiAl 

6989 Thermal transport in Sri_;fCaxRu 03 

6992 Magnetic transitions and oxygen content of Ca 3 Ru 207 


Izuru Umehara, Ying Lu, 

Qing Feng Lu, Yoshiya Adachi, 
Masato Endo, Kiyoo Sato, Michael 
Bartashevich, Tsuneaki Goto 

T. D. Cuong, L Havela, V. 
Sechovsky, Z. Arnold, J. Kamarad 

P. J. von Ranke, N. A. de Oliveira 

F. Garcia, H. dos Santos, M. R. 
Soares, A. Y. Takeuchl, S. F. da 
Cunha 

A. L. de Oliveira, V. P. Ramunni, 
M. V. Tovar Costa, N. A. de 
Oliveira, A. Troper 

Shibaji Saha, Naushad All, Sunil 
Labroo, Dale Zych 

H. Kang, P. Mandal, I. V. 
Medvedeva, J. Liebe, G. H. Rao, 

K. Barner, A. Poddar, E. Gmelin 

A. Broddefalk, P, Granberg, P. 
Nordblad, Hui-ping Liu, Y. 
Andersson 

Xiao-lei Rao, J. Cullen, V. 
Skumryev, J. M. D. Coey 

H. N. Bordallo, H. Nakotte, J. 
Eckert, A. V. Kolomiets, L. Havela, 
A. V. Andreev, H. Drulis, W. 
Iwasieczko 

M. Shepard, P. F. Henning, G. 
Cao, J. E. Crow 

S. McCall, G. Cao, J. E. Crow, 

R. P. Guertin 


Anisotropic Magnetoresistance and Granuiar GMR 

6995 Anisotropic magnetotransport properties of epitaxial thin films of 
conductive ferromagnetic oxide SrRu 03 

6998 Giant spontaneous Hall effect and magnetoresistance in Lai_xCa;fCo 03 
(0.1=^x^0.5) 

7001 Giant magnetoresistance in granular CuFeNi alloys 

7004 Microstructure and giant magnetoresistance of Co-Cu granular films 
fabricated under the extremely clean sputtering process 

7007 Giant magnetoresistance and remanence in granular CoCu codeposited 
films 

Thin Films: Structure and Magnetism 

7010 Structural and magnetic properties of “expanded” Mn 

7013 Growth and magnetism of one Mn monolayer on Ag(IOO) 


7016 Structural stability, magnetism, and surface magneto-optic Kerr effect 
spectra of MnAg(001) surface alloys 

7019 Artificial FeCu(IOO) epitaxial ordered alloy films: Element-selective 
magnetic properties 


R. A. Rao, D. B. Kacedon, C. B. 
Eom 

A. V. Samoilov, G. Beach, C. C. 
Fu, N.-C. Yeh, R. P. Vasquez 

C. S. Martins, H. R. Rechenberg, 
F. P. Missell 

Masakiyo Tsunoda, Kentaro 
Okuyama, Makoto Ooba, Migaku 
Takahashi 

A. D. C. Viegas, J. Geshev, J. E. 
Schmidt, E. F. Ferrari 


Ilya L. Grigorov, J. C. Walker, 

M. E. Hawley, G. W. Brown, M. 

Lutt, M. R. Fitzsimmons 

O. Elmouhssine, G. Moraitis, J. C. 
Parlebas, C. Demangeat, P. 
Schieffer, M. C. Hanf, C. Krembel, 
G. Gewinner 

Soon C. Hong, MIyoung Kim, A. J. 
Freeman 

W. Kuch, M. Salvietti, Xingyu Gao, 
M. Klaua, J. Barthel, Ch. V. Mohan, 
J. Kirschner 


(Continued) 



J, Appl. Phys., Vol. 83, No. 11, 1 June 1998 


xxi 


7022 Orbital magnetic moment enhancement at surfaces and interfaces within 
the framework of the local density approximation + U method 

7025 Magnetic extended x-ray absorption fine structure at the /_3 g edges of Fe 
and Co on Cu(001) 


7028 Probing local magnetic disorder by Investigating spin dependent 
photoelectron scattering 

7031 Magnetoresistance in single Fe(001) ultrathin films 

7034 Magnetic properties of very thin single and multilayer NiFeCo and CoFe 
films deposited by sputtering 

7037 Ferromagnetic resonance llnewldth in thin films coupled to NiO 

7040 Magnetic ordering in Co films on stepped Cu(IOO) surfaces 

7043 Overpotential driven perpendicular magnetization of electrodeposited 
ultrathin cobalt films 

7046 Magnetic and structural characterizations of HCP permalloy films grown 
by molecular beam epitaxy 

CMR Materials and Their Properties 

7049 Transport and magnetic properties of epitaxial and polycrystalline 
magnetite thin films 

7052 Observation of spin-dependent transport and large magnetoresistance in 
Lao.ySro.sMnOs/SrTiOs/Lao.ySro.aMnOa ramp-edge junctions 

7055 Grain boundary effects on transport in metalorganic chemical vapor 
deposition-grown, Ca-doped lanthanum manganites 

7058 Magnetic anisotropy and spin diffusion through spin disordered interfaces 
In magnetoresistive manganites 

7061 Scanning magnetoresistance microscopy of Lao.eTSro.asMnOa films 

7064 Magnetic anisotropy of doped manganite thin films and crystals 


7067 Investigation of granular films composed of interdispersed LavsCag/aMnOs 
particles and metallic Au particles 

7070 Magnetic and transport properties of radiation damaged Lao.yCao.aMnOs o 
thin films 


7073 Evolution of strain-dependent transport properties in ultrathin 
Lao.eySro.aaMnOg films 

7076 Contrasting magnetic and structural properties of two La manganites with 
the same doping levels 

7079 Magnetoresistance effects of Lao.yMo.sMnOa-^ far below the Curie 
temperature (M=Ca, Pb) 


A, B. Shick, A. J. Freeman, A. I. 
Liechtenstein 

P. Srivastava, L. Lemke, H. 

Wende, R. Chauvistre, N. Haack, 

K. Baberschke, J. Hunter-Dunn, D. 
Arvanitis, N. Martensson, A. 
Ankudinov, J. J. Rehr 

H. Wende, J. W. Freeland, V. 
Chakarian, Y. U. Idzerda, L. 

Lemke, K. Baberschke 

S. Yuasa, T. Katayama, M. NyvIt, 

Y. Suzuki, T. Yori 

D. Wang, J. M. Daughton, K. 
Bussmann, G. A. Prinz 

R. D. McMichael, M. D. Stiles, P. J. 
Chen, W. F. Egelhoff, Jr. 

S. T. Coyle, M. R. Scheinfein 

J. L. Bubendorff, E. Beaurepaire, 

C. Meny, J. P. Bucher 

J. C. A. Huang, Y. M. Hu, C. C. Yu 


X. W. Li, A. Gupta, Gang Xiao, 

G. Q. Gong 

C. Kwon, Q. X. Jia, Y. Fan, M. F. 
Hundley, D. W. Reagor 

J. J. Heremans, S. Watts, S. Wirth, 

X. Yu, E. S. Gillman, K. H. 
Dahmen, S. von Molnar 

B. Martinez, LI. Baicells, J. 
Fontcuberta, X. Obradors, C. H. 
Cohenca, R. F. Jardim 

D. K. Petrov, A. Gupta, J. R. 
Kirtley, L Krusin-Elbaum, H. S. Gill 

Y. Suzuki, H. Y. Hwang, S-W. 
Cheong, T. Siegrist, R. B. van 
Dover, A. Asamitsu, Y. Tokura 

Mark Rubinstein, P. R. Broussard, 

L. H. Allen, Kristi B. Hathaway, 
Michael M. Miller, Jonathan Z. Sun 

V. M. Browning, R. M. Stroud, 

W. W. Fuller-Mora, J. M. Byers, 

M. S. Osofsky, D. L. Knies, K. S. 
Grabowski, D. Koller, J. Kim, D. B. 
Chrisey, J. S. Horwitz 

H. L. Ju, Kannan M. Krishnan, D. 
Lederman 

T. R. McGuire, P. R. Duncombe, 

G. Q. Gong, A. Gupta, X. W. Li, 

S. J. Pickart, M. L. Crow 

K. Dorr, K.-H. Muller, E. S. 

Vlakhov, R. A. Chakalov, R. I. 
Chakalova, K. A. Nenkov, A. 
Handstein, B. Holzapfel, L. Schultz 


(Continued) 


xxii 


J. AppL Phys., Vol. 83, No. 11. 1 June 1998 


Electronic Structure 

7082 Fully relativistic theory for the magnetic extended x-ray absorption fine 
structure 

7085 Spin-dependent extended x-ray absorption fine structure in magnetic 
oxides 

7088 Probing the magnetic microstructure of an amorphous GdFe system with 
magnetic anomalous small angle x-ray scattering 

7091 Magnetic x-ray investigation at the /. 2,3 edges of Nd in Nd 2 Fei 4 B 


7094 Epitaxial Feioo-xCO;f/Ag(001) alloy films: Structure and element-specific 
magnetic moments from magnetic linear dichroism 

7097 Magnetic anisotropies of Ni-Pt and Co-Pt alloys 

7100 Ground state properties of a high-spin Mni 20 i 2 molecule in an organic 
compound 

Hard Magnets II 

7103 A comparison between a two-material and three-material magnetic current 
limiter 

7106 Reversible and irreversible components of tensor magnetization and 
magnetostriction 

7109 Fundamental study for rosary-shaped magnetic actuators 

7112 The design and analysis of axial field multipole impulse magnetizing 
fixtures 

7115 Fabrication of a micromotor driven by electromagnetic vibration 

7118 New permanent magnet couplings for screwing devices 

7121 A comparative analysis of permanent magnet-type bearingless 
synchronous motors for fully magnetically levitated rotors 

7124 Spin reorientation in (Pr,RE)-(Co,TM)-B magnets (RE=Tb, 
TM=Fe,Cr,Mn) 

7127 Magnetization processes in hybrid magnets 

7130 Mechanical strength of the solid-HDDR treated Nd-Fe-B-type materials 

7133 Thermal expansion of compounds Rn+iCo 3 n+ 5 B 2 n (R=Y and Gd; n= 1 , 2 , 
3, and 

7136 Specific-heat studies of RCU 4 AI 8 compounds (R=Er,Y) 

7139 Magnetic and structural properties of commercial 
Sm 2 (Co,Fe,Cu,Zr)i 7 -based magnets 

7142 The magnetization study of melt-spun ribbons of B containing TbFe 2 
alloys 

7145 Alternating current susceptibility study of Dy 2 Fe^ 7 _xGax compounds 


D. Ahlers, G. Schiitz, V. Popescu, 
H. Ebert 

D. Ahlers, K. Attenkofer, G. Schiitz 

P. Fischer, R. Zeller, G. Schiitz, G. 
Goerigk, H.-G. Haubold, K. Pruegl, 
G. Bayreuther 

F. Bartolome, J. M. Tonnerre, L 
Seve, D. Raoux, J. E. Lorenzo, J. 
Chaboy, L. M. Garcia, J. 
Bartolome, M. Krisch, A. Rogalev, 

R. Serimaa, C-C. Kao, G. Cibln, A. 
Marcelli 

E. Kisker, A. Faust, R. 
Schellenberg, A. Fanelsa, F. U. 
Hillebrecht 

S. S. A. Razee, J. B. Staunton, 

F. J. Pinski, B. Ginatempo, E. 
Bruno 

S. Y. Wang, Liang-Jian Zou, X, G. 
Gong, Q. Q. Zheng, H. Q. Lin 


S. Young, F. P. Dawson, M. 
Iwahara, S. Yamada 

F. Liorzou, Y. Yu, D. L, Atherton 

H. Saotome, K. Sakaguchi 

C. D. Riley, G. W. Jewell, D. Howe 

T. Honda, J. Yamasaki 

L Quellec, V. Lemarquand, G. 
Lemarquand 

J. F. Charpentier, G. Lemarquand 

D. H. Kim, G. Hadjipanayis 


M. Emura, A. C. Neiva, F. P. 
Missell, K. L. Babcock, J. Ormerod, 
S. Constantinides 

H. W. Kwon, S. J. Kang 

H. Ido, Y. Suzuki, T. Suzuki 

I. H. Hagmusa, F. E. Kayzel, E. 
Briick, K. H. J. Buschow 

X. Chen, J. F. Liu, C. Ni, G. 
Hadjipanayis, A. Kim 

K. S. Kim, S. C. Yu, S. R. Kim, 

S. H. Urn 

V. Skumryev, Xiao-lei Rao, J. M. D. 
Coey, N. Sheludko 


(Continued) 



J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


xxiii 


Colossal Magnetoresistance 

7148 Heat diffuslvity of Ndi _;,Sr;,Mn 03 _^ and Laicompounds 


7151 Magnetic properties of (Pr(Ca, Sr))Mn 03 studied by nuclear magnetic 
resonance 


7154 Anomalous low-field magnetization in La 2 / 3 Cai/ 3 Mn 03 near the critical 
point: Stable clusters? 


7157 Low field magnetotransport in Lao. 7 Sro. 3 Mn 03 films 

7160 Magnetostriction and field induced transitions in Lai_;^Sr;fMn 03 in pulsed 
magnetic fields 


7163 Magnetic properties, resistivity, and heat capacity of EuMn 03 and 
Euo. 7 Ao. 3 Mn 03 (A=Ca, Sr) compounds 

7166 Evidence for a gap in the excitation spectrum of Cr02 
7169 Effect of low Fe doping in Lao. 8 Sro. 2 Mn 03 


7171 Magnetic and transport properties of Pb perovskites and Fe containing 
giant magnetoresistance perovskites 

7174 90 MeV ion irradiation effects on transport and magnetization in 
epitaxial thin films of Lao. 75 Cao. 25 Mn 03 


7177 Colossal magnetoresistance in Lai.^fLi^^MnOs 

7180 Magnetic, dielectric, and transport properties of Lai_;^Sr;^Mn 03 at 
submillimeter wavelengths 


7183 Unusual substitutional properties of Ru in the Lao. 7 Sro. 3 Mni_;fRU ;^03 
system 

7186 Angle-resolved magnetic and transport properties of Pro. 7 Sro. 3 Mn 03 thin 
films 

7189 Fabrication of YBa 2 Cu 307 _^/SrTi 03 /Lao 7 Sro. 3 Mn 03 _^ junctions for the 
control of supercurrent by spin-polarized quasiparticle current injection 


7192 Magnetism and colossal magnetoresistance in the compound Sri 4 MnSbii 

7195 Polycrystalline and laminated Lao. 7 Sro. 3 Mn 03 films made by pulsed laser 
deposition 

7198 Colossal magnetoresistance and Mossbauer studies of the manganites 

Lai -00.985^00.015O3 + 


J. Llebe, H. Kang, L. Haupt, P. 
Mandal, I. V. Medvedeva, G. H. 
Rao, K. Barner, A. Poddar, P. 
Muruguraj, R. Fischer, E. Gmelin, 

E. Gommert, R. v. Helmolt, J. 
Wecker 

G. J. Tomka, P. C. Riedi, Cz. 
Kapusta, G. Balakrishnan, D. McK. 
Paul, M. R. Lees, J. Barratt 

V. S. Amaral, J. P. Araujo, Yu. G. 
Pogorelov, J. B. Sousa, P. B. 
Tavares, J. M. Vieira, J. M. B. 
Lopes dos Santos, A. A. C. S. 
Louren 9 o, P. A. Algarabel 

B. S. Teo, N. D. Mathur, S. P. 
Isaac, J. E. Evetts, M. G. Blamire 

Yu. F. Popov, A. M. Kadomtseva, 
G. P. Vorob’ev, V. Yu. Ivanov, 

A. A. Mukhin, A. K. Zvezdin, A. M. 
Balbashov 

Y. M. Mukovskli, G. Hilscher, H. 
Michor, A. M. Ionov 

A. Barry, J. M. D. Coey, L. Ranno, 

K. Ounadjela 

Antony Ajan, N. Venkataramani, 
Shiva Prasad, S. N. Shringi, A. K. 
Nigam, R. Pinto 

J. Gutierrez, J. M. Barandiaran, M. 
Insausti, L. Lezama, A. Pena, J. J. 
Blanco, T. Rojo 

Ravi Bathe, S. K. Date, S. R. 
Shinde, L. V. Saraf, S. B. Ogale, 

S. I. Patil, Ravi Kumar, S. K. Arora, 
G. K. Mehta 

X. L Wang, S. J. Kennedy, Peter 
Gehringer, Wolfgang Lang, H. K. 
Liu, S. X. Dou 

V. Yu. Ivanov, V. D. Travkin, A. A. 
Mukhin, S. P. Lebedev, A. A. 
Volkov, A. Pimenov, A. LoidI, A. M. 
Balbashov, A. V. Mozhaev 

S. Sundar Manoharan, H. L. Ju, 
Kannan M. Krishnan 

J. Wolfman, W. Prellier, Ch. Simon, 

B. Mercey 

R. M. Stroud, J. Kim, C. R. Eddy, 

D. B. Chrisey, J. S. Horwitz, D. 
Koller, M. S. Osofsky, R. J. Soulen, 
Jr., R. C. Y. Auyeung 

D. J. Webb, R. Cohen, P. Klavins, 

R. N. Shelton, J. Y. Chan, S. M. 
Kauziarich 

F. J. Cadieu, R. Rani, X. R. Qian, 

C. F. Cadieu, Li Chen, W. 
Mendoza, S. A. Shaheeen 

Z. W. LI, A. H. Morrish, X. Z. Zhou, 

S. Dai 


(Continued) 


xxlv J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


7201 Electron spin resonance and magnetization in perovskite and pyrochlore 
manganites 


7204 Thermal conductivity and magnetic transitions in Mn^'^/Mn'^'^ manganites 


Exchange Biasing fl 

7207 Influences on relaxation of exchange biasing in NiO/NigeCoisFe-ie bilayers 


7210 Thermal fluctuation aftereffect of exchange coupled films for spin valve 
devices 

7213 Effect of buffer layer on antiferromagnetic grain size and 
exchange-coupling field of CryoAlao/FeigNisi bilayers 

7216 Magnetic, temperature, and corrosion properties of the NiFe/IrMn 
exchange couple 

7219 Spin-flop tendencies in exchange-biased Co/CoO thin films 


7222 Dependence of exchange field and coercivity on cooling field in NiFe/CoO 
bi layers 

7225 First-principles exchange interactions between ferromagnetic and 
antiferromagnetic films: Co on NIMn, a case study 

Critical Phenomena and Phase Transitions 

7228 Local and global demagnetization process: Is there any self-organized 
critical behavior? 

7231 Non-Heisenberg couplings and ferromagnetic instability in a random 
antiferromagnetic spin-1 chain 

7234 Universal magnetic fluctuations in the two-dimensional XY model 

7237 Semiquantitative analysis of magnetic phase transitions in the 
MnFePi -xAs^ series of compounds 

7240 Magnetic behavior of the low-dimensional compounds Ba 2 Cu 304 Cl 2 and 
Ba3Cu204Cl2 

7243 Magnetic, electrical, and structural studies on the metal-insulator transition 
in Culr 2 S 4 _xSex (0=^x=^4) 

7246 Finite size scaling in the thin film limit 


7249 Phase diagram of a highly diluted, disordered Ising system: The Al-rich, 
Al-Fe system 

Magnetoelastic Materials 

7252 Processing effects on the magnetostrictive and physical properties of 
SmFe 2 /metal composites 

7255 Magnetomechanical coupling and elastic moduli of polymer-bonded 
Terfenol composites 


M. Tovar, M. T. Causa, G. Ibanez, 
C. A. Ramos, A. Butera, F. 
Rivadulla, B. Alascio, S. B. Oseroff, 
S-W. Cheong, X. Obradors, S. 

Pihol 

J. Hejtmanek, Z. Jirak, Z. Arnold, 

M. Marysko, S. Krupicka, C. Martin, 
F. Damay 


P. A. A. van der Heijden, 

T. F. M. M. Maas, J. C. S. Kools, 

F. Roozeboom, P. J. van der Zaag, 
W. J. M. de Jonge 

Junichi Fujikata, Kazuhiko Hayashi, 
Hidefumi Yamamoto, Masafumi 
Nakada 

K. Ikarashi, Y. Otani, K. Fukamichi, 
0. Kitakami, Y. Shimada, J. 
Echigoya, H. Uyama, A. Makino 

A. J. Devasahayam, P. J. Sides, 

M. H. Kryder 

J. A. Borchers, Y. Ijiri, S.-H. Lee, 

C. F. Majkrzak, G. P. Felcher, K. 
Takano, R. H. Kodama, A. E. 
Berkowitz 

T. Ambrose, C. L. Chien 
T. C. Schulthess, W. H. Butler 


O. A. Chubykalo, J. M. Gonzalez 

R. N. Bhatt, Kun Yang 

P. Archambault, S. T. Bramwell, 
J.-Y. Fortin, P. C. W. Holdsworth, 

S. Peysson, J.-F. Pinton 

R. Zach, M. Guillot, J. Tobota 

D. Eckert, K. Ruck, M. Wolf, G. 
Krabbes, K.-H. Muller 

P. Somasundaram, D. Kim, J. M. 
Honig, T. M. Pekarek, T. Gu, A. I. 
Goldman 

C. Waldfried, D. Welipitiya, T. 
McAvoy, P. A. Dowben, E. 
Vescovo 

J. Restrepo, G. A. Perez Alcazar, 
J. M. Gonzalez 


F. E. Pinkerton, T. W. Capehart, 
J. F. Herbst, E. G. Brewer, C. B. 
Murphy 

J. Hudson, S. C. Busbridge, A. R, 
Piercy 


(Continued) 



J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


XXV 


7258 First-principles theory of magnetoelastic coupling and magnetic anisotropy 
strain dependence in ultrathin Co films on Cu(OOI) 

7261 Effects of heteroepitaxial strain on Laves phases TbFe 2 and DyFe 2 
7264 Magnetomechanical instability In FeTb/Fe multilayers 


7267 Magnetic properties and microstructure of giant magnetostrictive TbFe/ 
FeCo multilayers 

7270 Magnetic properties of amorphous Sm-Fe and Sm-Fe-B thin films 
fabricated by radio-frequency magnetron sputtering 

7273 Application of the ratio AX/AA/f to giant magnetostrictive materials in the 
( 110 ) easy regime 

7276 Magnetostriction and susceptibilities of twinned single crystals of 
Terfenol-D 

7279 Magnetization and magnetostriction of dendritic [ 112 ] Tb;^Dy 3 ,Ho 2 Fei .95 (x 
+ y-i-z= 1 ) rods under compressive stress 

7282 Development of Terfenol-D transducer material 


7285 Magnetostrictive properties of polymer-bonded amorphous Tb-Fe-B 
composites 

7288 Piezomagnetic properties, saturation magnetostriction, and AE effect in 
DyZn at 77 K 

7291 Experimental evidence of pressure-induced magnetic phase transition in 
^© 72^^28 Invar alloy 

7294 Electrochemical deposition of amorphous FeB films with soft magnetic 
properties 

7297 Field-induced strain under load in Ni-Mn-Ga magnetic shape memory 
materials 


7300 Magnetoelastic behavior of the Heusler Ni 2 MnGa alloy 


7303 Trial on-sllicon micromagnetoelastic devices 

7306 Nonlinear self-localized magnetoelastic surface waves in 
antiferromagnetic media 

Superconductivity II 

7309 The Re-doped high superconductor HgBa 2 Ca 2 Cu 30 ;f: Magnetic 
irreversibility versus anisotropy 

7312 Structural and magnetic properties of RSr 2 Fe 309 (R=La, Y, Pr, and Gd) 


7315 Magnetic and superconducting properties of Pr in Lai_;fPr;fBaCaCu 307 
system with 0 . 0 =^x^ 1,0 

7318 Magnetic properties of Pb 2 Sr 2 PrCu 308 studied by ac susceptibility 

7321 Specific heat, magnetization and C-isotope effect of Y 2 C 2 (Br,l )2 
superconductors 


A. B. Shick, D. L. Novikov, A. J. 
Freeman 

M. Huth, C. P. Flynn 

Manfred Wuttig, Quanmin Su, 
Fabrice Masson, Eckhard Quandt, 
Alfred Ludwig 

E. Quandt, A. Ludwig, D. G. Lord, 
C. A. Faunce 

Y. S. Choi, S. R. Lee, S. H. Han, 

H. J. Kim, S. H. Urn 

S. C. Busbridge, A. R. Piercy 

X. G. Zhao, D. G. Lord 

M. Wun-Fogle, J, B. Restorff, A. E. 
Clark, J. F. LIndberg 

E. A. Lindgren, S. Haroush, J. C. 
Poret, A. D. Mazzatesta, M. Rosen, 
M. Wun-Fogle, J. B. Restorff, A. E. 
Clark, J. F. Lindberg 

S. R. Kim, S. Y. Kang, J. K. Park, 

J. T. Nam, Derac Son, S. H. LIm 

J. B. Restorff, M. Wun-Fogle, A. E. 
Clark 

S. Odin, F. Baudelet, J. P. Itie, A. 
Polian, S. Pizzini, A. Fontaine, Ch. 
Glorgetti, E. Dartyge, J. P. Kappler 

Naoyuki Fujita, Mitsuteru Inoue, 
Ken’Ichi Arai, Pang Boey Lim, 
Toshitaka Fujii 

S. J. Murray, M. Farinelli, C. 
Kantner, J. K. Huang, S. M. Allen, 
R. C. O’Handley 

Eduard Obrado, Alfons 
Gonzalez-Comas, Liu is Manosa, 
Antoni Planes 

M. Takezawa, M. Yamaguchl, K. 
Ishlyama, K. I. Arai 

Igor E. Dikshtein, Sung-Ho Suck 
Salk 


L. Fabrega, B. Martinez, J. 
Fontcuberta, A. Sin, S. Pihol, X. 
Obradors 

V. P. S. Awana, S. X. Dou, I. 
Felner, I. Nowik, S. K. Malik, 
Apurva Mehta, Rajvir Singh, A. V. 
Narlikar, W. B. Yelon 

V. P. S. Awana, S. X. Dou, Rajvir 
Singh, A. V. Narlikar, S. K. Malik, 

W. B. Yelon 

S. Y. Wu, Y. C. Chang, K. C. Lee, 
W.-H. LI 

W. Schnelle, R. W. Henn, Th. 
Gulden, R. K. Kremer, A. Simon 


(Continued) 



XXVI 


J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


7324 phase diagram for the giant magnetic flux jumps in low temperature 
superconductors and high temperature superconductors 


7327 Magnetic memory effect in YBa 2 Cu 307 _x/(BiDy) 3 (FeGa) 50 i 2 
heterostructures 

7330 Spin wave scattering and intermode transitions induced by the magnetic 
vortex lattice in the ferrite-high-temperature superconductor film structure 

Advances in Magnetic Force Microscopy 

7333 Magnetic dissipation force microscopy studies of magnetic materials 
(invited) 

Fundamental Aspects of CMR Materials 

7339 Long wavelength spin dynamics in Lao. 53 Cao. 47 Mn 03 

7342 Spin dynamics of strongly doped Lai^xSrxMn 03 

7345 Tilted antiferromagnetic ordering of Mn in Ndo.62Cao.38Mn03 

7348 Magnetic correlations in the bilayer manganite Lai. 2 Sri 8 Mn 207 

7351 The complex magnetic behavior and the role of dynamic structural 
fluctuations In Lai. 2 Sri. 8 Mn 207 crystals 

7354 Lattice effects in ferromagnetic manganite perovskites 

7357 Isotope effect and 7^ in manganites and high 7^ oxides 

7360 A mean field theory of magnets with competing double exchange and 
superexchange interactions 

7363 Composite polaron mechanism for colossal magnetoresistance in 
perovskite manganites 

7366 Tunneling evidence of half-metalllcity in epitaxial films of ferromagnetic 
perovskite manganites and ferrimagnetic magnetite 

7369 Metal-insulator transition induced by oxygen isotope exchange 

in colossal negative magnetoresistance manganites 


V. V. Chabanenko, A, L 
D’yachenko, A. V. Chabanenko, H. 
Szymczak, S. Piechota, A. 
Nabialek, N. D. Dung 

D. Mou, A. M. Grishin, K. V. Rao 


L. V. Lutsev, S. V. Yakovlev 


Y. Liu, P. Grutter 


J. J. Rhyne, H. Kaiser, H. Luo, 
Gang Xiao, M. L Gardel 

L Vasiliu-Doloc, J. W. Lynn, Y. M. 
Mukovskii, A. A. Arsenov, D. A. 
Shulyatev 

S. Y. Wu, W.-H. Li, K. C. Lee, 

J. W. Lynn, R. S. Liu, J. B. Wu, 

C. Y. Huang 

S. Rosenkranz, R. Osborn, J. F. 
Mitchell, L. Vasiliu-Doloc, J. W. 
Lynn, S. K. Sinha, D. N. Argyriou 

R. P. Sharma, P. Fournier, R. L 
Greene, T. Venkatesan, J. F. 
Mitchell, D. Miller 

D. J. Singh, W. E. Pickett 
Vladimir Z. Kresin, Stuart A. Wolf 

D. I. Golosov, M. R. Norman, K. 
Levin 

Liang-Jian Zou, H. Q. Lin, Q.-Q. 
Zheng 

J. Y. T. Wei, N.-C. Yeh, R. P. 
Vasquez, A. Gupta 

N. A. Babushkina, L. M. Belova, 

V. I. Ozhogin, O. Yu. Gorbenko, 

A. R. Kaul, A. A. Bosak, D. I. 
Khomskii, K. I. Kugel 


Spin Glasses and Fustrated Systems 

7372 Magnetic susceptibility of Fe/Cu multilayers: Ferromagnetic, 
antiferromagnetic, and spin-glass phases 

7375 Origin of magnetic anomalies in the spin glass system, Lao.85Sro.i5Co03 

7378 Canted antiferromagnetism and spin glasslike behavior in a family of 
two-dimensional organic/inorganic nanocomposites 

7381 Magnetic and structural properties of PrCo 3 _xSix compounds 

7384 Frustration in the paramagnetic phase of spin-density-wave CrFeV alloys 

7387 A new paradigm for two-dimensional spin liquids 


A. J. A. de Oliveira, W. A. Ortiz, 

D. H. Mosca, N. Mattoso, W. H. 
Schreiner, S. R. Teixeira 

P. S. Anil Kumar, P. A. Joy, S. K. 
Date 

M. A. Girju, C. M. Wynn, W. Fujita, 
K. Awaga, A. J. Epstein 

T. Matsui, R. D. Stevenson, R. D. 
Kirby, D. J. Sellmyer 

V. Yu. Galkin, W. A. Ortiz, E. 
Fawcett 

R. R. P. Singh, O. A. Starykh, P. J. 
Freitas 


7390 Calculation of the energy barriers in strongly interacting many-particle 
systems 


D. V. Berkov 


(Continued) 



J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 x> 

7393 Influence of the configurational degeneracy on the hysteretic behavior of J. M. Gonzalez, O. A. Chubykalo, 

a system of magnetostatically coupled magnetic moments A. Hernando, M. Vazquez 

7396 Domain models for aging in spin glasses Derek Walton 

7399 AUTHOR INDEX 


A publication of the American institute of Physics, 500 Sunnyside Bivd., Woodbury, NY 11797-2999 


A PUBLICATION OF THE IEEE MAGNETICS SOCIETY 


JULY 1998 VOLUME 34 NUMBER 4 lEMGAQ (ISSN 0018-9464) 


THE SEVENTH JOINT MAGNETISM AND MAGNETIC MATERIALS-INTERNATIONAL 
MAGNETICS CONFERENCE 

Hyatt Regency Embarcadero Hotel, San Francisco, California, January 6-9,1998 _ 

Cover Photograph Credit. 

Sponsoring Organizations .. 

Conference Organization. 

Preface . 

Contributors.. 

Exhibitors . 

Introduction . 

Editors . 

PARTI 

MAGNETIC MULTILAYERS 

Determination of the Copper Layer Thickness in Spin Valves by Grazing Incidence X-Ray Fluorescence — 

T. P. A. Hase, B. K. Tanner, P. Ryan, C. H. Marrows, and B. J. Hickey . 

Influence of the Top and Bottom Interface on Perpendicular Magnetic Anisotropy in Tb-Fe-Ag Multilayers — O. Marks, 

T. Ruckert, J. Tappert, W. Keune, W.-S. Kim, W. Kleemann, andJ. Voiron . 

Ni0/a-Fe203 Multilayers Prepared by PLD: A Model System for Magnetic Study of Interdiflusion — N. Keller, 

M. Guyot, A. Das, M. Porte, andR. Krishnan . 

Correlation Between Evolving Magnetic and Morphological Properties in Magnetic Multilayers — S. A. Doherty, 

J. -G. Zhu, M. Dugas, S. Anderson, and J. Tersteeg ... 

Spin Valve Structures on NiO Pinning Layers — C. Cowache, B. Dieny, S. Auffret, M. Cartier, R. H. Taylor, 

R. O 'Barr, and S. Y. Yamamoto . 

FMR and Magnetization Study of NiFe/Ag/CoNi Trilayer Film —A. R. Koymen, L R. Tagirov, R. T. Gilmutdinov, 

C. Topacli, C. Birlikseven, H. Z. Durusoy, and B. Aktas . 

Highly Localized Surface Modes in Epitaxial W/NiAV Films — G. Suran, J. Rothman, and C. Meyer . 

Iron and Nickel Surface and Interface Anisotropies — R. Skomski, D. Sander, C. Schmidthals, A. Enders, 
andJ. Kirschner . 

Second Harmonic Generation Study of Quantum Well States and Interdiflusion in a Co/Rh Multilayer — F. Manders, 

K. J. Veenstra, A. Kirilyuk, T. Rasing, H. A. M. van den Berg, and N. Persat .L, 

Role of Magnetoelastic Anisotropy in Ni/Pt Multilayer Films — Y.-S. Kim and S.-C. Shin . 





















Strong Anti-Ferromagnetic Coupling in xMnAl/Co Perpendicular Magnetic Superlattices on GaAs — C. Bruynseraede, 

G. Lauhoff, J. A. C. Bland, G. Strijkers, J. De Boeck, and G. Borghs . 

Competition Between Direct Exchange and Indirect RKKY Coupling in Fe/V(001) Superlattices — G. R. Harp, 

M. M. Schwicicert, M. A. Tomaz, T. Lin, D. Lederman, E. Mayo, and W. L. O'Brien . 

Growth of Giant Magnetoresistive Spin Valves with Strong Exchange Bias Field — G. Choe, A. Tsoukatos, 

and S. Gupta . 

Preferred Crystal Orientation of NiFe Underlayers and its Effect on Magnetostriction of Co/Cu/Co Thin Films — 

T. Yeh, J. M. Sivertsen, and C.-L. Lin . 

Magnetic Anisotropies of Fen Vm(OOl) Superlattices Determined by Ferromagnetic Resonance —A. N. Anisimov, 

W. Platow, P. Poulopoulos, M. Earle, K. Baberschke, P. Isberg, P. Granberg, and R. Wdppling . 

Magnetic Anisotropy and Reorientation in Co/Rh Superlattices — X. Ying, K. V. Rao, P. J. Jensen, andJ. J. Xu . 

Magnetic and Transport Properties of Sputter Deposited Ni/Co Multilayers — R. J. Pollard, S. E. McCartney, 

and R. Atkinson . 

Thin Soft Sendust Film Laminated CoPt Hard Films — S. S. Xue, J. E. Dolejsi, and P. J. Ryan . 

Spin Waves and Interlayer Coupling in CoFe/Mn/CoFe Structures — M. Chirita, G. Robins, R. L. Stamps, 

R. Sooryakumar, M. E. Eilipkowski, C. J. Gutierrez, and G. A. Prinz . 

First Principles Calculations of the Energetics of Co/Cu(l 11) Multilayers —X. Wang and C.LFu . 

Superlattices of III-V Semiconductor and Heterogeneous Magnetic Layers for CPP Magnetoransport — J. De Boeck, 

H. Akinaga, C. Bruynseraede, H. Bender, and G. Borghs . 

GIANT MAGNETORESISTANCE AND TRANSPORT 

Stress Effects on the Magnetic Properties of FeMn and NiMn Spin Valves — E. Linville, D. Han, J. Judy, J. Sivertson, 

and S. Mao . 

Time and Temperature Dependence of High Thermal Stability in NiO/Co/Cu/Co/M Spin Valves — R. D. McMichael, 

P. J. Chen, and W. F. Egelhoff, Jr. . 

Magnetoresistance Due to Domain Walls in Micron Scale Fe Wires with Stripe Domains — A. D. Kent, U. Ruediger, 

J. Yu, S. Zhang, P. M. Levy, Y. Zhong, and S. S. P. Parkin . 

Anisotropic Magnetoresistance as a Probe of Magnetization Reversal in Individual Nano-sized Nickel Wires — 

J.-E. Wegrowe, S. E. Gilbert, D. Kelly, B. Doudin, andJ.-P. Ansermet . 

Temperature Dependence of Interlayer Coupling in Fe/Si Superlattices — Y. Endo, O. Kitakami, and Y. Shimada . 

Mossbauer Studies of Fe-Pb-0 Granular Films with Enhanced Tunneling Magnetoresistance Effect - J.-//. Hsu, 

Y.H. Huang, P. K. Tseng, and D. E. Chen . 

Magnetic Microstructures from Magnetic Force Microscopy and Monte Carlo Simulation in CoFe-Ag-Cu Granular 

Films — V. Franco, X. Batlle, A. Valencia, A. Labarta, K. O'Grady, andM.L. Watson . 

GMR in DC Magnetron Sputtered NigiFcig/Cu Multilayers — M. Mao, C. Cerjan, M. Gibbons, B. Law, F. Grabner, 

S. P. Vernon, andM. Wall . 

Highly Field Sensitive and Thermally Stable DC Magnetron Sputtered Soft NigiFeig/Cu Multilayers — Y. Huai, M. Tan, 

and R. Rottmayer . 

Improvement of GMR Characteristics in [Nig,Fe,g/Cu] Multilayers by Interfacial Modulation Technique using Kr Ions 

— Y. Miyamoto, K Watanabe, K. Nishimura, S. Nakagawa, andM. Naoe . 

CPP Giant Magnetoresistance of NiFeCo/Cu/CoFe/Cu Multilayers — K. Bussmann, S. F. Cheng, G. A. Prinz, Y. Hu, 

R. Gutmann, D. Wang, R. Beech, and J. Zhu . 

First-Principles Based Semi-Classical Model for Transport in Magnetic Layered Structures — W. H. Butler, 

X. -G. Zhang, andJ. M. MacLaren . 

GMR in Magnetic Multilayers from a First Principles Band Structure Kubo-Greenwood Approach — F. Rao 

and A. J. Freeman . 

A Superlattice Effect in the Resistivity of Multilayers — T.-S. Choy, J. Chen, and S. Hershfield . 

Influence of Impurity Gas in the Sputtering Atmosphere on the Microstructure and the GMR in Co/Cu Multilayers — 

S. Miura, D. Takahashi, M. Tsunoda, and M. Takahashi . 

Giant Magnetoresistance of Current-Perpendicular Exchange-Biased Spin Valves of Co/Cu— A. C. Reilly, 

W.-C. Chiang, W. Park, S. Y. Hsu, R. Loloee, S. Steenwyk, W. P. Pratt, Jr., andJ. Bass . 

Comparison of Computed Amplitudes of Magnetoresistance in Spin-Valve Structures with Wafer Probe 

Measurements — B. Dieny, L. G. Peireira, R. H. Taylor, and S. Y. Yamamoto . 

Process Monitoring of Spin-Valve GMR Deposition — J. C. S. Kools, A. P. Paranjpe, P. V. Schwartz, R. Rubber, 

B. Bergner, W. Kula, and T. G. S. M. Rijks . 

Specular Reflection in Spin Valves Bounded by NiO Layers — H. J. M. Swagten, G. J. Strijkers, R. H. J. N. Bitter, 

W. J. M. de Jonge, and J. C. S. Kools . 

Thermal Stability of Spin Valve with NiO/a-FeiOs Bilayer Antiferromagnets — J. Fujikata, K. Hayashi, M. Saito, 

and M. Nakada . 


































Effect of Microstructure on Resistivity and GMR Ratio in Ion Beam Deposited Spin Valves — fV. E. Bailey, 

D. Guarisco, andS.X. Wang ... 

CoFe/IrMn Spin-Valves Prepared on Cu Islands — T. Umemoto, A. Maeda, S. Oikawa, K. Yoshioka, S. Takahashi, 

T. Tanuma, M. Kume, and K. Shibata ... 

MAGNETIC NANOSTRUCTURES 

Reversible Electrodeposition of Ultrathin Magnetic Co and Films — W. Schindler, T. Koop, D. Hofmann, 

and J. Kirschner . 

Magnetic and Transport Properties of Electrodeposited Nanostructured Nanowires — B. Doudin, J. E. Wegrowe, 

S. E. Gilbert, V. Scarani, D. Kelly, J. P. Meier, andJ.-P. Ansermet . 

Magnetization Reversal in Individual Nanoparticles Macroscopic Quantum Tunneling of Magnetization — 

W. Wernsdorfer, E. B. Orozco, B. Barbara, A. Benoit, D. Mailly, N. Demoncy, H. Pascard, O. Kubo, and 

H. Nakano . 

Single Particle Measurement Showing Agreement with the Model of Uniform Rotation — E. B. Orozco, 

W. Wernsdorfer, B. Barbara, K. Hasselbach, A. Benoit, and D. Mailly . 

The Magnetic Properties of Annealed Graphite-Coated Ni and Co Nanocrystals —I A. Block, K. Parvin, J. L Alpers, 

T. Sezen, R. LaDuca, J. J. Host, and V. P. Dravid . 

Size and Interaction Effects in the Magnetization Reversal in SmCos Nanoparticles — S. A. Majetich, 

K. M. Chowdary, and E. M. Kirkpatrick . 

Organizing Nanometer-Scale Magnets with Bacterial Threads — C. J. Smith, M. Field, C. J. Coakley, 

D. D. Awschalom, N. H Mendelson, E. L. Mayes, S. A. Davis, and S. Mann . 

Magnetic Aftereffect in Quasi-ID Amorphous Ferromagnetic Nanocolumns— J.-P. Nozieres, D. Givord, 

J. C. Toussaint, B. Kevorkian, M. Ghidini, and B. Gervais . 

Magnetic Properties of Au,_j^Fej^ Nanowires — J. Jorritsma andJ. A. Mydosh . 

End Domain States and Magnetization Reversal in Submicron Magnetic Structures — J. Shi, T. Zhu, M. Durlam, 

E. Chen, S. Tehrani, 7. F. Zheng, andJ.-G. Zhu ... 

Shape Dependence of the Switching Field in Small Structures — S. T. Chui . 

Dynamics of Magnetization Reversal in a 20x4 mm Permalloy Microstructure — A. Stankiewicz, W. K. Hiebert, 

G. E. Ballentine, K. W. Marsh, and M. R. Freeman . 

Reversal Mechanism of Submicron Patterned CoNi/Pt Multilayers — M. A. M. Haast, J. R. Schuurhuis, L Abelmann, 

J. C. Ladder, and T. J. Popma . 

Magnetization Reversal in Nanostructured Co/Pt Multilayer Dots and Films — M. Thielen, S. Kirsch, H. Weinforth, 

A. Carl, and E. F. Wassermann . 

Domain Structures Supported by Micron-Sized Patterned Co/Cu Multilayers with AF and FM Coupling — 

P. R. Aitchison, J. N. Chapman, K. J. Kirk, D. B. Jardine, andJ. E. Evetts . 

The Relationship Between Structure and Magnetic Properties in Nanostructured FePd Ferromagnets — 

H. Okumura, W. A. Soffa, T. J. Klemmer, andJ. A. Barnard . 

Chemical Synthesis of Nanostructured Cobalt at Elevated Temperatures — D. L. Leslie-Pelecky, M. Bonder, T. Martin, 

E. M. Kirkpatrick, X. Q. Zhang, S.-H. Kim, andR. D. Rieke .. 

Magnetic and Magneto-transport Properties of Novel Nanostructured Networks — K. Liu and C. L. Chien . 

Temperature Dependence of the Coercivity of Fe Films Sputtered On Nanochannel Alumina — A. Butera, J. L. Weston, 

and J. A. Barnard . 

Magnetization Reversal in (CoNi/Pt)6 Dots Connected to a Large Area through Submieron Wide Channels — 

F. Fournel, Y. Chen, F. Carcenac, N. Essaidi, H. Launois, V. Kottler, and C. Chappert ... 

Paramagnetic-Superparamagnetic Transition in Molecular Sieve Supported Antiferromagnetic Particles — F. J. Lazaro, 

A. Lopez, A. Larrea, Q. A. Pankhurst, J. M. Lopez Nieto, and A. Corma . 

Modifications of the Effective Surface and Crystalline Anisotropies of Ag/Fe/Ag-(001)-Layers by Ion Implantation — 

D. Kurowski, J. Pflaum, K. Brand, J. Pelzl, and P. Griinberg . 

Temperature Dependence of the Interface Interactions on Fe/Cr Studied by Fenomagnetic Resonance and SQUID — 

J. Pflaum, J. Pelzl, P. Bodeker, H. Zabel, Z. Frait, and M. Marysko . 

Evidence for Domain-Condensation near the Ferromagnetic to Paramagnetic Transition in Perpendicularly Magnetized, 

Ultrathin Fe/2 ML NiAVfllO) Films — C. S. Arnold and D. Venus . 

Electric Field Effects on Magnetic and Optical Properties of MnAs/GaAs(001) Thin Films — T. Shin, M. C. Park, 

Y. Park, G. M. Rothberg, M. Tanaka, andJ. P. Harbison . 

NMR Studies of Sputtered CoFe Alloy Thin Films — T. Thomson, P. C. Riedi, C. L. Platt, and A. E. Berkowitz . 

Magnetic Dipolium Model of Magnetization-Induced Surface Seeond Harmonic Generation — V.L. Brudny, 

W. L. Mochdn, B. S. Mendoza, A. V. Petukhov, and T. Rasing . 

Effect of Dipolar Interactions in Magnetic Thin Films — C. Santamaria and H. T. Diep . 

Hybrid Ferromagnet-Semiconductor Nonvolatile Gate —M. Johnson, B. R. Bennet, M. J. Yang, M. M. Miller, 
and B. V. Shanabrook . 

































Pseudo Spin Valve MRAM Cells with Sub-Micrometer Critical Dimension — B. A. Evehtt, A. V. Rohm, R. S, Beech, 

A. Fink, andJ. M. Daughton ... 

Characteristics of AP Bias in Spin Valve Memory Elements — J.-G. Zhu and Y. Zheng . 

The Effect of End Edge Shape on the Performance of Pseudo-Spin Valve Memories — J. Gadbois, J.-G. Zhu, 

W. Vavra, and A. Hurst ... 

A New Multilayered Structure for Multilevel Magnetoresistive Random Access Memory (MRAM) Cell — W.-C. Jeong, 

B. -L Lee, and S.-K. Joo . 

Nucleation of Periodic Domain Structure in Micro-Fabricated Spin valve Strip Pattern — K. Matsuyama, H. Asada, 

Y. Hosokawa, and K. Taniguchi . 

Generation, Gyroscopic Dynamics and Collisions of the Vertical Bloch Lines in the Orthoferrites — M V. Chetkin 

and Yu. N. Kurbatova . 

Memory Element Based on a Layered Galvanomagnetic Structure — Y. V. Timoshkov, A. L. Danilyuk, 1. S. Molchan, 

T. I. Orechovskaya, and V. 1. Kurmashev . 

PATTERNED AND HYBRID MAGNETIC MATERIALS 

Magnetic Coupling in Self-Organized Narrow-Spaced Fe Nanowire Arrays —A. Sugawara, D. Streblechenko, 

M. McCartney, and M. R. Scheinfein . 

Magnetic Singularities in Self-Organized Epitaxial Cobalt Structures —M Demand, M. Hehn, S. Cherifi, K. Cherifi, 

K. Ounadjela, and R. L. Stamps . 

Fabrication of Large Area Nanostructured Magnets by Interferometric Lithography — M Farhoud, M. Hwang, 

H I. Smith, M. L Schattenburg, J. M. Bae, K. YoucefToumi, andC. A. Ross . 

Magnetization Reversal in Submicron Ferromagnetic Dots and Antidots Arrays — Y. Otani, S. G. Kim, T. Kohda, 

K. Fukamichi, O. Kitakami, and Y. Shimada . 

Giant Positive Magnetoresistance in Arrays of Semi-metallic Bismuth Nanowires — K Liu, C. L. Chien, P. C. Searson, 

K. Yu-Zhang . 

Magnetic and Transport Properties of Sub-Micron Ferromagnetic Wires — Y. Otani, S. G. Kim, K Fukamichi, 

O. Kitakami, and Y. Shimada . 

Size Dependence of the Magnetization Vector Reversal Processes in Epitaxial Fe(OOl) Microstripes — F. Ahmad, 

J. A. C. Bland, and F. Gu . 

Magnetization Switching Behavior in Nanostructured Nife/Co/Cu/Co Spin-Valve — H. Asada, K. Matsuyama, 

Y. Hosokawa, and K. Taniguchi . 

Magnetic Anisotropy in Arrays of Nanometer-Scale Iron Particles — S. Wirth, J. J. Heremans, S Von Molndr, 

M. Field, K. L. Chapman, A. C. Gossard, and D. D. Awschalom . 

Highly Homogeneous Nanoparticulate Fe Films Prepared by Laser Ablation — J. M. Gonzalez, M. 1. Montero, 

L. Vdsquez, J. A. Martin Gago, D. Givord, C. De Julidn, and K Grady . 

Magnetic Properties of a Series of Ferrite Nanoparticles Synthesized in Reverse Micelles — C T. Seip, F. F. Carpenter, 

C. J. O'Connor, V. T. John, and S. Li . 

High Coercivity in Heterogenerous Co-Rich Co-Ag Very Thin Films — A. Butera, T. J. Klemmer, K Minor, H S. Cho, 

and J. A. Barnard . 

Superparamagnetism of Granular Fe-MgF 2 Films — T. Furubayashi and 1. Nakatani . 

Magnetization and Coercivity of Antiferromagnetic Particles — K N. Trohidou, X. Zianni, and J. A. Blackman . 

Magnetotransport and Magnetism in Granular EuS-Co and EuS-Ag Nanocomposites Prepared by Mechanical 

Alloying — C. F. O'Connor, L. Feng, C. T. Seip, and J. Tang .. 

Magnetization Curve for Iron-Nitride Fine Particles System with Random Anisotropy — H. Mamiya and 1. Nakatani ... 
Magnetic Properties of Ball Milled Fe-40A1 at.% Alloys — X. Amils, J. Nogues, S. Surihach, M. D. Bard, 

and J. S. Munoz . 

Structural, Electrical, and Magnetic Properties of COxCi.x Granular Films — H. Weinforth, C. Somsen, B. Rellinghaus, 

A. Carl, F. F. Wassermann, and D. Weller . 

Magnetic and Magneto-Transport Properties of Metastable GdxNbi-x Alloys — R. L. Sommer, J. Q. Xiao, 

and C. L. Chien . 

Algorithm for the Computation of the FC and ZFC Magnetization Curves for Nanoparticle Systems — C Papusoi, Jr., 

A. Stancu, C. Papusoi, J.L. Dormann, M. Nogues, and F. Tronc .. 

Preparation of Iron Nanoparticles by Reduction of Acicular p-FeOOH Particles — M. Chen, B. Tang, and D. F. Nikles 
Fabrication and Properties of Microforged Ferromagnetic Nanoflakes — R.M Walser and W. Kang . 

SOFT MAGNETIC MATERIALS AND DOMAINS 

Domain Walls and Magnetic Properties of Very Thin Permalloy Films for Magnetoresistive Sensors — M A. Akhter, 

D. J. Mapps, Y. Q. Ma,A. K. Petford-Long, andR. Doole . 

Characteristics of Stripe Domains in FeTaN Films Observed by Magnetic Force Microscopy — H. S. Cho, V. R. Inturi, 

J. A. Barnard, and H Fujiwara . 
































Magnetic Domains and Transverse Induced Anisotropy in Magnetically Soft CoFeB Amorphous Thin Films — 

D. Garcia, J. L. Murioz, G. Kurlyandskaya, M. Vazquez, M. Ali, andM. R. J. Gibbs . 

Incoherent Magnetization Reversal Process in Discontinuous FesoCoso/Ag Multilayer Thin Films — P. C. Kuo, 

Y. D. Yao, J. W. Chen, and H. C. Chiu . 

Giant Magnetoimpedance in CoFeBSi Wires and Polycrystalline Ferrites — £ Carrasco, K. L Garcia, 
and R. Valenzuela . 

The Effects of Axial DC Field on Magnetoimpedance: Circumferential Domain Wall Damping — K. L Garcia 
andR. Valenzuela .. 

Surface Magnetic Domain Observation on Thin-Gauged 3% Si-Fe Sheets by using Scanning Electron Microscopy with 

Polarization Analysis (SEMPA) — Y. Lee, A. R. Koymen, N. H. Heo, J. G. Na, andJ. S. Woo . 

Dynamic Preisach Model and Energy Dissipation in Soft Magnetic Materials — L. R. Dupre, G. Bertotti, 

and J. A. A. Melkebeek . 

Determination of Barkhausen Signal Scaling from Higher Order Spectral Analysis — J. R. Petta, M. B. Weissman, 

and G. Durin ... 

Identification of Microstructure Effects in Magnetic Loss Behaviour of 3.2% SiFe N.O. Electrical Steels by Means of 

Statistical Power Loss Model — G. Ban, P. E. Di Nunzio, S. Cicale, and T. Belgrand . 

Dynamic Effects Driven by Thermal Activation in the Magnetization of Nanocrystalline Soft Magnetic Materials — 

V. Basso, M. LoBue, C. Beatrice, P. Tiberto, and G. Bertotti . 

Influence of Surface Roughness on Magnetic Properties of Fe-Si-B Amorphous Alloys — K. Matsuki, F. Kogiku, 

and N. Morito . 

Magnetic Properties of 6.5% Silicon Steel Sheets Under PWM Voltage Excitation — M Namikawa, H. Ninomiya, 

Y. Tanaka, and Y. Takada . 

Comparison of Transformer Loss Prediction from Computed and Measured Flux Density Distribution —A. J. Moses ... 
Apparent Core Losses and Core Losses in Five-Limb Amorphous Transformer of 160 kVA — S. Sieradzki, R. Rygal, 
andM. Soinski . 

Reduction of Inrush Current in Single-Phase Transformer using Virtual Air Gap Technique — V. Molcrette, 

J. -L. Kotny, J.-P. Swan, andJ.-F. Brudny . 

MAGNETIC EFFECTS AND MODELING 

Shifted Magnetization Curves in Ultrathin Co Films on Stepped Cu(lOO) —A. Rettori, L. Trallori, M. G. Pini, 

C. Stamm, C. Wursch, S. Egger, and D. Peseta . 

Effect of Au Underlayer on Perpendicular Magnetic Anisotropy in Au/Co/Au(l 11) Sandwiched Films Murayama, 

K. Hyomi, J. Eickmann, and C. M. Falco . 

Interface Orbital Moment Anisotropy in CoPd Multilayers — H. A. Dlirr, G. Van Der Laan, J. Vogel, M. Finazzi, 
and J. B. Goedkoop . 

Magnetic Anisotropy and its Microstructural Origin in Epitaxially Grown SmCo Thin Films —M. Benaissa, 

K. M. Krishnan, E. E. Fullerton, and J. S. Jiang . 

Magnetoelectric Neel Anisotropies — R. Skomski .;. 

Spin-Reorientation Transitions in Ultrathin Ferromagnetic Films Under Applied Field — Y. T. Millev, H. P. Oepen, 

and J. Kirschner . 

Symmetry-Induced Magnetic Anisotropy in Ultrathin Planar Striped Co Films with and without Cu Decoration — 

L Zhong, X. Wang, and A. J. Freeman . 

Changes of Morphology, Structure, and Magnetism of Fe on Stepped Cu(l 11) — M. Klaua, J. Shen, P. Ohresser, 

H. Jenniches, J. Barthel, C. V. Mohan, andJ. Kirschner . 

The Effect of Interfacial Steps on the Ferromagnetic/Antiferromagnetic Interface of Thin Fe Films on Cr(OOl)_ 

E. J. Escorcia-Aparicio, H. J. Choi, W. L. Ling, R. K. Kawakami ,, andZ. Q. Qiu . 

Magnetic Easy Axis Engineering in Ultrathin Cu/Co/Cu(l 10) Structures — B.-C. Choi, S. Hope, E. Gu, and 

J. A. C. Bland . 

First Principles Calculations of Interlayer Exchange Coupling in bcc Fe/Cu/Fe Structures — M. Kowalewski, 

B. Heinrich, T.C. Schulthess, and W. H. Butler . 

On Rotational Eddy Current Losses in Steel Laminations — /. D. Mayergoyz . 

Dynamic Preisach Modelling of Fenomagnetic Laminations Under Distorted Flux Excitations — L. R. Dupre, 

O. Bottauscio, M. Chiampi, F. Fiorillo, M. L Bue, J. Melkebeeko, M. Repetto, andM. Von Rauch . 

Eddy Current Analysis for the Pipe Welding — /f. Tsuboi, K. Ikeda, M. Kurata, K. Kainuma, andK. Nakamura .......... 

Analysis of Eddy-Current Brake for High-Speed Railway — P. J. Wang and S. J. Chiueh . 

Loss Separation Analysis in Ferromagnetic Sheets Under PWM Inverter Supply —A. Boglietti, M. Chiampi, 

Mi Repetto, O. Bottauscio, and D. Chiarabaglio . 

Current Flow in Long Conductors with a Step Conductivity Change — K.V. Namjoshi, J. D. Lavers, 
and P. P. Biringer . 

































A Model for Impedance of Planar RF Inductors Based on Magnetic Films — A. Gromov, V. Korenivski, K. V. Rao, 

R. B. van Dover, and P. M. Mankiewich . 

Numerical Study of Electric Diffusion Effect Due to Imperfect Electrical Contacts — B.-K. Kim and K.-T. Hsieh . 

Crack Size and Shape Determination by Moving Magnetic Field Type Sensor — M. Enokizono, Y. Tsuchida, 

and T. Chady . 

Ohmic Losses Calculation in SMPS Transformers; Numerical Study of Dowell’s Approach Accuracy — F. Robert, 

P. Mathys, andJ.-P. Schauwers . 

Analysis of Isotropic Materials with Vector Hysteresis — O. Bottauscio, D. Chiarabaglio, C. Ragusa, M. Chiampi, 

andM. Repetto . 

Eddy Current Hysteresis and the Preisach Model — I. D. Mayergoyz . 

Simulation of Field-Temperature Effects in Magnetic Media using Anisotropic Preisach Models — A. A. Adly 

and I. D. Mayergoyz . 

Eddy Current and Hysteresis Losses in Ferromagnetic Media — V. Maid Machado and A. Lopes Ribeiro . 

Hysteretic Energy Losses in Media Described by Vector Preisach Model — G. Friedman and 1. D. Mayergoyz . 

On the Role of the Statistics in the Applicability of the Preisach Transformation — K. Metlov, I. Tomas, G. Vertesy, 

andM. Pardavi-Horvath . 

A Preisach Model for Aftereffect — E. Della Torre and L. H. Bennett . 

Identification of the Preisach Parameters of a Three Quadrant Medium —J. Lou, L. H. Bennett, and E. Della Torre . 

Interaction Effects in Cr02 Audio Tape: AC Versus Thermal Demagnetization — P. D. Mitchler, R. M. Roshko, 

and E. D. Dahlberg . 

A New Algorithm for Thermal Decay Simulations — /. Klik and Y. D. Yao . 

1/f Nyquist Magnetic Noise, Magnetic Viscosity and Hysteresis — A. Maraner, S. Vitale, and G. Bertotti . 

Modeling of Magnetic Properties of Heat Treated Dy-Doped NdFeB Particles Bonded in Isotropic and Anisotropic 

Arrangements — X. Fang, Y. Shi, and D. C. Jiles . 

Modeling of Hysteresis Loops of Ferrite Cores Excited by a Transient Magnetic Field — N. L. Mi, R. Oruganti, 

and S. X. Chen . 

MAGNETIC SENSORS AND COMPONENTS 

Increased Field Sensitivity in Co/Cu Multilayers with Soft Adjacent Layers — D. B. Jardine, N. D. Mathur, 

M. G. Blamire, and J. E. Evetts . 

InAs/(Al,Ga)Sb Quantum Well Structures for Magnetic Sensors — M. Behet, J. Das, J. De Boeck, and G. Borghs . 

Fluxgate: Tuned vs. Untuned Output — P. Ripka and S. W. Billingsley . 

Pyro Photosensor Utilizing Thermally-Sensitive Magnetic Thin Film — T. Yoshida, Y. Ajishi, H. Osada, S. Chiba, 

N. Tayama, K. Seki, and H. Matsuki . 

Development of a Moving Magnetic Flux Type Sensor using Shading Coils for ECT — Y. Tsuchida, T. Chady, 

andM. Enokizono . 

Effect of Stress on the Bamboo Domains and Magnetization Process of CoSiB Amorphous Wire — J. N. Nderu, 

M. Takajo, J. Yamasaki, and F. B. Humphrey . 

A Remotely Interrogatable Sensor for Chemical Monitoring — P. G. Stoyanov, S. A. Doherty, C. A. Grimes, 

and W. R. Seitz . 

Dependence of Large Barkhausen Jump on Length of a Vicalloy Fine Wire with Torsion Stress — S. Abe, 

A. Matsushita, and M. Naoe . 

High Frequency Carrier Type Bridge-Connected Magnetic Field Sensor — M. Takezawa, H. Kikuchi, K. Suezawa, 

M. Yamaguchi, K. Jshiyama, and K. I. Arai . 

Preparation and Properties of Elastically Coupled Electro-Magnetic Elements with a Bonding Structure — K. H. Shin, 

M. Inoue, and K. I. Arai . 

Geometry Effects on Low Frequency Noise in Giant Magnetoresistance (GMR) Sensors — A. F. Md. Nor, E. W. Hill, 

and M. R. Parker . 

Thermal Activation of Spin Wave Modes in Co Based Multilayers — M. A. Wongsam andR. W. Chantrell . 

A New Bi-Directional Inductive Force Sensor — V. Lemarquand . 

Hard-Soft GMR Sensors with Co-Rh based Artificial Antiferromagnetic Subsystem — H. A. M. van den Berg, 

G. Rupp, W. Clemens, G. Gieres, M. Vieth, J. Wecker, and S. Zoll . 

A New G iant Magneto-Impedance Head using Magnetic Microstrip Lines — N. Jiang, K. Yamakawa, N. Honda, 

and K. Ouchi . 

New Multi-Chambered Power Magnetics Concepts — G. E. Bloom . 

Application and Analysis of Adjustable Profile High Frequency Switchmode Transformer Having a U-Shaped Winding 

Structure— J. Lu, F. P. Dawson, andS. Yamada . 

Analysis of Frequency Characteristics of Small-Sized Wide-Band Compound Transformers — N. Nishizuka, M. Sato, 
and Y. Li . 






































Design and Analysis of Noise-Reduction Transformer Based on Equivalent Circuit — T. Yanada, S. Minowa, 

O. Ichinokura, and S. Kikuchi . 

An Analytical Method of a Planar Parametric Transformer Based on the Magnetic Circuit Model — Y. Sakamoto, 

M. Ohta, M. Natsusaka, and K. Murakami . 

Design and Simulation of Film Transformer on Flexible Polyamide Film in Very High Frequency Range — H. Tsujimotc 

2D and 3D Simulation of Toroidal Type Thin Film Inductors — H. J. Ryu, S. D. Kim, J. Kim, J. J. Lee, J. Kim, 

S. H. Han, H. J. Kim, and C. H. Ahn . 

The Characteristics of Low Temperature Co-Fired Multilayer Chip LC Filters — /f. M. Sung, C.-J. Chen, L.-J. Wang, 

and W.-SKo . 

Packaging-Compatible Microinductors and Microtransformers with Screen-Printed Ferrite using Low Temperature 

Processes — J. Y. Park andM. G. Allen . 

A Microfabricated Transformer for High-Frequency Power or Signal Conversion—M Xu, T. M. Liakopoulos, 

C. H. Ahn, S. H. Han, and H. J. Kim . 

The Effect of Magnetic Film Structure on the Inductance of a Planar Inductor — T. Inoue, K. Nishijima, S. Yatabe, 

T. Mizoguchi, andT. Sato ... 

Design of High Frequency Inductors Based on Magnetic Films — V. Korenivski and R. B. van Dover . 

Inductive Microtransformer Exploiting the Magnetoelastic Effect — L. H Rissing, S. A. Zielke, and H H Gatzen . 

MICROWAVE MAGNETICS 

Mode Beating of Spin Wave Beams in Ferrimagnetic LuaxwBio ge FesOia Films — O. Biittner, M. Bauer, C. Mathieu, 

S. O. Demokritov, B. Hillebrands; P. A. Kolodin, M.P. Kostylev, S. Sure, H Ddtsch, V. Grimalsky, 

y. Rapoport, and A. N. Slavin . 

Ferromagnetic Resonance Damping in Garnets: Comparison Between Saturated and Unsaturated States — T. Taffary, 

D. Autissier, F. Boust, andH. Pascard . 

Enhanced Microwave Magnetic Properties in Nonstoichiometric Yttrium Iron Garnets for High Power Applications — 

y. S. Cho, V. L. Burdick, and V. R. W. Amarakoon . 

Shape-Optimized Ferromagnetic Particles with Maximum Theoretical Microwave Susceptibility — R. M. Walser, 

W. Win, andP.M. Valanju . . 

Parametric Frequency Conversion with Amplification of a Weak Spin Wave in a Ferrite Film — B. A. Kalinikos, 

N. G. Kovshikov, M. P. Kostylev, and H. Benner . 

Theory of MSFVW Excitation in a YIG Film by a Finite-Length Microstrip Transducer — L. P. Peng, J. P. Parekh, 

cmdH. S. Tuan ... 

Experimental Investigation of the Nonlinear Interaction Between Optical Guided Waves and Magnetostatic Forward 

Volume Waves in a Bi-YIG Film— J. Kurumida and N. S. Chang . 

Design Procedure for Ferrite Microstrip DC Blocks—M R. M. L. Albuquerque and A. G. dAssungdo . 

Axially Polarized Wiggler Radiation from a Toroidal Electron Beam Source — H. A. Leupold, A. S. Tilak, 

andM.M. Visa sky ;.;. 

Technical Characteristics of a Novel Helical-Groove Traveling-Wave Tube Structure — T. M. Wallett, K. R. Vaden, 

J. Freeman, and A. Haq Qureshi . 

MAGNETIC RECORDING HEADS 

Anisotropy Control in Fabrication Process for NiMn Spin-Valve Dual Element Heads — T. Ishi, T. Suzuki, N. Ishiwata, 

M. Nakada, K. Yamada, K Shimabayashi, and H. Urai . 

Effect of Seed Layer on the Magnetoresistance Characteristics in a-CoNbZr-Based Spin Valves — H. S. Cho, F. Ueda, 

C. Hou, and H. Fujiwara . 

Thermal Stability of CoFe, Co and NiFe/Co Spin Valves — A. M. Zeltser, K. Pentek, and M. Menyhdrd, and A. Sulyok 
Activation Energy of Interdiffusion and Interface Structure for CoFe/Cu Spin- Valves —A. T. Saito, H. Iwasaki, 

Y. Kamiguchi, H. N. Fuke, andM. Sahashi . 

Enhancement of Magnetoresistance Characteristics in Spin Valve Structures by Two-Step Sputter Deposition — 

C.-M. Park and K. H. Shin ... 

The Distribution of Blocking Temperature in NiFe-RuxRhyMn Bilayers — S. Araki, M. Sana, M. Ohta, Y. Tsuchiya, 

K. Noguchi, H. Morita, and M. Matsuzaki . 

Thermal and Magnetic Stability of Unidirectional Anisotropy in Spin-Valve Magnetoresistive Heads — N. Ohshima, 

M. Nakada, and Y. Tsukamoto . 

New Soft Magnetic CoNiFe Plated Films with High Bs= 2.0-2.1 T — T. Osaka, M. Takai, K. Hayashi, Y. Sogawa, 

K. Ohashi, Y. Yasue, M. Saito, and K. Yamada . 

Improved Magnetic Anisotropy and Magnetostriction by Laminating FeAl(N) with Permalloy to Multilayers — 

W. Maass and H. Rohrmann . 

High Frequency Initial Permeability of NiFe and FeAIN — W. P. Jayasekara, J. A. Bain, andM. H. Kryder . 
































Magnetostriction Constants of (110) Oriented Epitaxially Grown FeTaN Thin Films — L Varga, H. Jiang, 

T J. Klemmer, and W, D. Doyle . 

Texture and Magnetic Properties of FeTaN Films Bias-Sputtered on Sloping Surfaces — J. Hong, S, X. Wang, 

and K. Rook . 

Controlof Asymmetry of Spin-valve Heads Based on Micromagnetic Analysis — a:.-/. Yamada, H. Kanai, Y. Uehara, 

andJ. Toda ... 

A Study of Voltage Fluctuation, Noise and Magnetic Instability in Spin Valve GMR Recording Heads —A. Wallash .... 
Magnetic Domain Instability in MR Heads Due to Overlaid Structure of Permanent Magnet Film — C. Mitsumata, 

K. Kikuchi, and T Kobayashi . 

Crossfeed Response of DMR vs. SAL Multi-Track Heads — F. Z. Wang, L. N. He, D. J. Mapps, D. T. Wilton, 

W W. Clegg, and P. Robinson . 

Multitrack Thin Film Heads for the Digamax™ Tape Storage System — J. J. M. Ruigrok, H. W. van Kesteren, 

S. R. Cumpson, D. J. Adelerhof S. B. Luitjens, E. A. Draaisma, and A. Hoogendoorn . 

Newly Developed Inductive Write Head with Electroplated CoNiFe Film — K. Ohashi, Y. Yasue, M. Saito, 

K. Yamada, T. Osaka, M. Takai, and K. Hayashi . 

Two Dimensional Model of Eddy Currents and Saturation in Thin Film Write Heads —A. F. Torabi, M. L. Mallary, 

R. Perry, and G. Kimball . 

Off-track Performance of Thin Film Single Pole Head for Perpendicular Double-Layered Media — H. Yamada, 

H. Muraoka, Y. Sugita, and Y. Nakamura . 

A New Write Head Trimmed at Wafer Level by Focused Ion Beam — T. Koshikawa, A. Nagai, Y. Yokoyama, 

T. Hoshino, and Y. Ishizuki . 

Extremely Low Inductance Thin-Film Single-Pole Head on Flying Slider — H. Muraoka, K. Sato, Y. Nakamura, 

T. Katakura, and K. Yazawa . 

Active Caneellation of Mutual Inductanee in Split-Coil Thin-Film Heads — S. E. Stupp and G. R. Lovelace . 

Writer Performance Improvement in MR Head with Over-Sized Trailing Poles Technique — E. Leung, M. Hayashi, 

R. Leung, K. Ino, N. Matono, S. Takahashi, and M. Fujita . 

GMR-DMR Read-Element Characterization and Projections of Head Performance on High Areal Density Rigid 

Media — 1. G. Trindade, M. H. Kryder, P. P. Freitas, and N. Smith . 

Two Leg, Side by Side, 0.6 to 1.0 Micron Wide, High Output, Vertical, GMR, Head Sensors V. Pohm, 

J. M. Anderson, R. S. Beech, and J. M. Daughton . 

Three-Dimensional Analysis of Dual Track Complementary Type of Heads for Perpendicular Magnetic Recording — 

T. Ichihara, S. Nakagawa, H. Matsumiya, and M. Naoe . 

High-Density Recording using MR Heads in Helical-Scan Tape Systems — T. Ozue, T. Shirai, T. Saito, T. Ikegami, 

H. Kano, and S. Onodera . 

Fabrication and Characterization of Contiguous Permanent Magnet Junctions — M. Xiao, A. J. Devasahayam, 

andM. H. Kryder . 

Spin-Valves with Bias Compensation Layer — H. Kanai, K. Yamada, M. Kanamine, andJ. Toda . 

A Self-Biased Spin Valve Sensor with a Longitudinally Pinned Layer — T. Suzuki and H. Matsutera . 

Charcteristics of NiFe/CuNi Multilayer GMR Sensors For Vertical GMR Heads — T. Mizuguchi, S. Terada, 

T. Miyauchi, and A. Matsuzono . 

Planar, Contact, Yoke GMR Head vs. Conventional, Flying, Shielded GMR Head: A Comparative Study — Y. Yoshida, 

K. Araki, S. Sugano, and Y. Kaneta . 

Micromagnetic Analysis and Current Biasing of Dual-Stripe GMR and Dual-GMR Sensors for High Density 

Recording — P. P. Freitas, S. Cardoso, and N. J. Oliveira . 

A New Method of Calculating the Medium Field and the Demagnetizing Field for MR Heads — Y. Suzuki and 

C. Ishikawa . 

Read Sensitivity in Abutted-Junction Type Spin-Valve Head — K.-I. Takano, N. Yamanaka, andM. Matsuzaki . 

Magnetic Changes in GMR Heads Caused by Electrostatic Discharge — A. Wallash and Y. K. Kim . 

ESD Induced Pinned Layer Reversal in Spin-Valve GMR Heads — M. Takahashi, T. Maeda, K. Inage, M. Sakai, 

H. Morita, andM. Matsuzaki . 

Amplitude and Asymmetry Correlation Study Between Quasi-Static and Dynamic Electrical Testing of MR Sensors 

J. Zhu and M. Loera . 

MAGNETIC RECORDING MEDIA 

Thermal Aftereffects in Thin Film Magnetic Recording Media — Y. Hosoe, T. Kanbe, K Tanahashi, 1. Tamai, 

S. Matsunuma, and Y. Takahashi . 

Thermal Stability and Nanostructure of CoCrR Longitudinal Recording Media — M Yu, M. F. Doerner, and 

D. J. Sellmyer . 

Effects of Thin Cr Interlayer on Time Decay of Magnetization and Magnetization Reversal for CoCrTaPt 

Thin Film Media — J.-P. Wang, L.-P. Tan, T. F. Liew, E. Teng andP.-W. Wang . 


































Dynamic Coercivity Effects in Thin Film Media — H. J. Richter, S. Z. Wu, and R. Malmhall . 

Numerical Simulations of the Effect of Record Field Pulse Length On Medium Coercivity at Finite Temperatures — 

H. N. Bertram and Q. Peng . 

Coercivity and Frequency Dependence of Track Widths and Erase Bands in Thin Film Media — L. Mei, M. E. Schabes, 

andN.H.Yeh ... 

Quantitative MFM Study of the Global and Local Magnetic Roughness of the DC-Demagnetized State of 

Thin Film Media— X. Song, Q. Chen, C. Leu, andR. Ranjan . 

Under-Keepered Media with MR Heads — M Nichols, B. M. Lairson, T. M. Coughlin, B. Gooch, J. Kehl, 

and J. Perez . 

Recording Physics of Keepered Inductive Media — E. T. Yen, H. J. Richter, G.-L Chen, G. Rauch, 

and T. M. Coughlin . 

Temperature Dependence of Magnetocrystalline Anisotropy Energy Determined using Co-Cr-Ta Single Crystal 

Thin Films — N. Inaba, M. Eutamoto, and A. Nakamura . 

CrMn Underlayers for CoCrPt Thin Film Media — L.-L. Lee, D. E. Laughlin, andD. N. Lambeth . 

Chromium Segregation in CoCrTa/Cr and CoCrPt/Cr Thin Films for Longitudinal Recording Media- 1 E. Wittig, 

T. P. Nolan, C. A. Ross, M. E. Schabes, K. Tang, R. Sinclair, and J. Bentley . 

The Effect of Carbon Overcoat Difiusion on CoCrTa/Cr Thin-Film Media — J. J.-K. Chang, K. E. Johnson, 

H. Kawayoshi, P. Ling, andM. Strathman . 

Cr-Ta 205 Seedlayer for Recording Media on Alternative Substrates — W. Xiong and H.-L. Hoo . 

The Dependence of Media Noise on the Magnetic Cluster Size for Co Based Thin Film Media Fabricated under 

Ultra Clean Sputtering Process — M. Takahashi, A. Kikuchi, H. Hara, and H. Shoji . 

Effects of Ultra-High Vacuum on Crystallographic, Recording and Magnetic Properties of Thin Film Media — 

C. Gao, S. Wu, J.-P. Chen, R. Malmhall, C. Habermeier, R. Sinclair, H. Laidler, and K. O'Grady . 

The Effect of fee Grains on the Magnetic and Recording Properties of Thin Film Media — K. O'Grady, 

N. S. Walmsley, C. F. Wood, andR. W. Chantrell . 

CoCrTa Intermediate Layers on NiAl Underlayers for CoCrPt Longitudinal Thin Film Magnetic Media — J. Zhou, 

D. E. Laughlin, and D. N. Lambeth . 

Orientation Ratio Reduction Through Pre-Deposition Substrate Annealing — B. Y. Wong,J. Ying, andH. Tran . 

Recording Performance of Thin Film Media with Various Crystallographic Preferred Orientations on Glass Substrates — 

M. Mirzamaani, X. Bian, M. F. Doerner, J. Li, andM. Parker . 

Magnetic and RAV Properties of CoPt-SiOa Granular Media — Kaitsu, A. Inomata, I. Okamoto, andM. Shinohara ... 
Fabrication, Micromagnetic and Recording Properties of CoCrPt on Plastic Disks — B. R. Acharya, E. N. Abarra, 

G. N. Phillips, T. Suzuki, K. Adachi, N. Kitagaki andM. Aihara . 

Magnetic Interaction in Co-Cr-R-Ta-Nb Media: Utilization of Micromagnetic Simulation — H. Akimoto, 1. Okamoto, 

andM. Shinohara . 

Small -dHc/dT Characteristics of CoR Granular and Thin Film Recording Media — A. Kikitsu, K. Yusu, K. Ichihara, 

and T. Tanaka . 

High-Density Recording Capability of Granular Media Composed of Co-R Grains and SiOa Matrix — K. Ichihara, 

A. Kikitsu, K. Yusu, F. Nakamura, andH. Ogiwara . 

Time Decay of the Remanent Magnetization in Longitudinal Thin Film Recording Media as a Function of Distributions 

of Grain-Size and Easy-Axis Orientation — C. Yang, J. M. Sivertsen, andJ. H. Judy . 

Micromagnetic Study of Network Media — J.-G. Zhu andH. Fang . 

Thermal Stability of Ultra-Thin Co Recording Media — H. Gong, W. Yang, D. N. Lambeth, M. Rao, 

and D. E. Laughlin . 

Effects of ECR Ion Shower Treatment on the Magnetic and Recording Properties of CoCrTaR Thin Film Media — 

Y. Okumura, M. Yasui, T. Akita, M. Maeda, andX. B. Yang . 

Effect of Grain Size Dispersion on Read/Write Properties in Thin Film Recording Media Affected by 

Thermal Fluctuation — Y. Nakatani, N. Hayashi, Y. Uesaka, and H. Fukushima . 

DC Erasure and Demagnetizing Fields on Written Bits in High Density Longitudinal Media — E. N. Abarra, 

G. N. Phillips, 1. Okamoto, and T. Suzuki . 

Comparison of Time-Decay of Read-Back Signals in Keepered and Non-Keepered Media — J. Chen, J. H. Judy, 

and T. Coughlin . 

Effects of R addition on the magnetic and microstructural properties of CoC granular films — J.-J. Delaunay, 

T. Hayashi, M. Tomita, and S. Hirono . 

Read Write Characteristics of Hexagonal Barium Ferrite Sputtered Films Prepared by Post Deposition Annealing — 

A. Morisako, M. Matsumoto, andM. Naoe . 

Microscopic Magnetization Structures and Noise in Single-Layer Perpendicular Thin Film Media — Y. Honda, 

Y. Hirayama, K. Ito, andM. Eutamoto . 

Effect of Medium Thickness on the Signal-to-Noise Ratio of Perpendicular Media — Y. Ikeda, Y. Sonobe, 
andH. Uchida . 



































Preparation and Characteristics of Co-Zn Ferrite Rigid Disks without Protective Layers for High Density Recording — 

N. Matsushita, M Ichinose, S. Nakagawa, and M Naoe . 

Nano-size Magnetic Crystallite Formation in Co-Cr Thin Films For Perpendicular Recording Media — S. Kadokura, 

M Naoe, S. Nakagawa, and 7. Maeda . 

Thermal Relaxation in Perpendicular Double-Layered Media — W. H, Jiang, H. Muraoka, 7 Sugita, 

and 7 Nakamura . 

Barium Ferrite Thin Films Without a Dead-Layer — 7 Chen, M Rao, D. E. Laughlin, and M. H. Kryder . 

Low Noise Co-Cr-Nb Perpendicular Recording Media with High Squareness — N. Honda, J. Ariake, K. Ouchi, 

andS.-L Iwasaki . 

Barium Ferrite Films Grown by Laser Ablation — A. Lisfi, J. C. Ladder, P. de Haan, M. A. Smithers, and 

F. J. G. Roesthuis . 

MFM Observation of Localized Demagnetization in Magnetic Recordings — A. Jander, P. Dhagat, R, S. Indeck, 

and M, W, Muller . 

A Comparison between Different Methods for Evaluating the Particle Interactions in Magnetic Recording Systems — 

G. Bottom, D. Candolfo, and A, Cecchetti . 

Analytical Determination of the LLG Zero-Damping Critical Switching Field — D. G. Porter . 

Development of an Advanced Metal Particulate Tape — H Inaba, K. Ejiri, K. Masaki, and T Kitahara . 

Influence of Magnetic Interaction and Particle Length on MP Tape Noise — N Nagai and M. Inoue . 

Measurement of Vector Minor Loops — F. Vajda and E, D. Torre . 

Epitaxial Growth of NiZn Ferrite on Barium Ferrite Particles — H.-S. Jung and Y.-K, Hong . 

Non-Arrhenius Behavior in Single Domain Particles — E. D. Boerner and H. N Bertram . 

The Effect of Particle Size on the Thermal Switching Characteristics of Metal Particle Tapes — S. M. Stinnett 

and W. D. Doyle . 

Mechanical Orientation of Advanced Metal Particle Dispersions — L. S. Prichard, K, 0 Grady, and P, L Mayo . 

Self-Assembly in Model Magnetic Inks — P. P. Visscher and 7. Gunal . 

HEADS AND MEDIA INTERFACES IN MAGNETIC RECORDING 

A New Sub-Femto Slider for Mass Production Planar Silicon Heads — J.-P, Lazzari, C Pisella, and L Tosi . 

Take Off Measurement of Pico Sliders on Laser Zone Textured Media — D. Harris, S. Venkatesan and K. OBrien . 

A new Laser Interferometer System for Investigation of the Dynamics at the Head/Disk Interface — 

M Staudenmann, M. J. Donovan, and D. B. Bogy .. 

Head-Disc Dynamics of Low Resonance Laser Textures - A Spectrogram Analysis — W. H Yao, D. Kuo, R. Ku, 

B. Marchon, and R. Sundaram . 

Dual Stripe Sensor on a Picoslider for In-Contact Thermal Asperity Testing — H H Gatzen and M. K Schwahe . 

Variation of the Heat Flux Between a Slider and Air Bearing when the Slider Flies Over an Asperity — S. Zhang 

and D. B. Bogy . 

Effect of Lubricant Thickness and Viscosity and Rest Time on Long-Term Stiction in Magnetic Thin-Film Rigid Disks 

— Z Zhao and B, Bhushan . 

Potential Data Loss Due to Head/Disk Contacts During Dynamic Load/Unload — M. Suk and D. Jen . 

Assessment of Surface Damage Mechanisms of Head/Disk Interface using CSS and Drag Tests — K-H. Chung, 

S.-C. Lee, and D.~E. Kim . 

Ultrathin Protective Overcoats on Hard Magnetic Disks — E. V. Anoikin, G. S. Ng, M. M. Yang, J. L. Chao, 

J. R. Elings, and D. W. Brown . 

Nanomechanical Properties of CNx Overcoats and Cathodic Arc Carbon (CAC) Films — R. C Hsiao, D. B. Bogy, 

and C. S. Bhatia . 

Study of Clock Head/Disk Interface Failure Mechanism in Servo-Writing Process — B. Liu, G. Sheng, Q. Chen, 

Q. Leng, C. T Yeo, and S, G. Lu . 

Measurement of Non-elastic Asperity Compliance of Magnetic Tapes — S. Tan, E. Baugh, and F. E. Talke . 

High Wear Durability of ECR-Sputtered Carbon Films — S. Hirono, S. Umemura, 7. Andoh, T Hayashi, 

and R. Kaneko . 

Tribological Properties and Environmental Effects of Nano and Pico Sliders on Laser Textured Media — B. Knigge, 

Q. Zhao, F. E. Talke, and P. Baumgart . 

Tribological and Mechanical Properties of CN Ultra-Thin Overcoat Films — R. D. Ott, T W. Scharf, D. Yang, 

andJ. A. Barnard . 

The Structure of Nitrogenated Carbon and its Interaction with Lubricant Molecules — P, Dai and C, Gao . 

Material and Tribological Properties of a-C:H Film by Plasma CVD for a Disk Overcoat — T Toyoguchi 

and T Yamamoto . 

Investigation of Phosphazene Additive for Magnetic Recording Lubrication — C M. Mate, P, H Kasai, G. W. Tyndall, 

C. H Lee, V, Roman, D. J. Packer, and R. J. Waltman . 








































Tribology of a Solid Fluorocarbon Film on Magnetic Recording Media — T. E. Karis, G. W. Tyndall, 

and M. S. Crowder . 

Deposition of High-Durability Protective Layers with a Composite Structure of DLC and GLC by Facing-Targets 

Sputtering — K. Noda, T. Kawanabe, andM. Naoe . 

Stiction Free Slider for Lightly Textured Disks — T. Yamamoto, T. Yokohata, and Y. Kasamatsu . 

Vibration of Head Suspensions for Proximity Recording — H. Takahashi, D. B. Bogy, andM. Matsumoto . 

An Investigation of Wireless Suspensions — T. Ohwe, T. Watanabe, and S. Yoneoka ... 

Sensitive Magnetic Readback Head-Disk Spacing Measurements in Recording Drives — V.J. Novotny 

andM.-J. Hsiao .. 

Flying Height Measurement while Seeking in Hard Disk Drives — B. C. Schardt, E. Schreck, R. Sonnenfeld, 

Q. Haddock, and J. R. Haggis . 

A Double-Sideband and Transmitted Carrier Amplitude Modulation Method for Laser Texture Characterization — 

Y. Li ... 

In-Situ Alumina Recession and Protrusion Measurement on a Magnetic Head — Y. Li and G. Wang . 

Calibrating ESC A and Ellipsometry Measurements of Perfluoropolyether Lubricant Thickness— M. F. Toney, 

C. M. Mate, and D. Rocker . 

Magnetic Readback Microscopy Applied to Laser-Texture Characterization in Standard Desktop Disk Drives — 

E. Schreck, R. Kimball, and R. Sonnenfeld . 

Measurement of the Head-to-Disk Stiction Force in an Unmodified Hard Drive using External Hall-Effect Sensors — 

R. Milby, E. Schreck, and R. Sonnenfeld . 

Finite Element Based Head-Tape Interface Simulation Including Head-Tape Surface Asperity Contacts — Y. Wu 

and F. E. Talke . 

Bump Formation and Growth by Multiple Laser Pulses on Ni-P Disk Substrate — T. C. Strand, A. C. Tam, 

P. Baumgart, andJ. Colonia . 

A Study of Pulsed-Laser Bump Formation on Smooth Glass Substrates- 1 Brannon, R. White, A. C. Tam, 

and P. Baumgart . 

Manufacturability of Advanced Laser Texture Designs— J. J. Liu, W. Li, and K. E. Johnson . 

Design of Sombrero and Donut Shaped Bumps for Optimum Tribological Performance — S. Chilamakuri 

and B. Bhushan . 

Formation and CSS Performance of NiP Surface Textured by Argon Ion Laser — W. J. Wang, Y. F. Lu, T. Liew, 

A. Ravikiran, M.C. Chai, T.S. Low . 

Inertia Effects on Static Friction Measurements of Laser Textured Media — M. Sullivan andJ. Chao . 

Fly/Stiction: Mechanical Instability of a Head-Disc Interface — *-J. Gui and B. Marchon . 

Issues on High-Speed Laser Zone Texturing of Magnetic Disk Substrates with Improved Quality — *-H. K. Park, 

P. J. M. Kerstens, P. Baumgart, and A. C. Tam . 

An Investigation of a Slider Air Bearing with a Asperity Contact by a Three-Dimensional Direct Simulation Monte 

Carlo Method — *-W. Huang and D. B. Bogy . 

Acoustic Emission of Laser Textured Disks Influenced by Bump Excitation — S. Wang, K. V. Viswanathan, 

andH-L. Liu . 

Biquadratic Models for Slider Airbearing Surfaces — E. Baugh, S. Weissner, and F. E. Talke . 

Identification of Slider/Disk Contacts using the Energy of the Acoustic Emission Si gnal — *-T. C. McMillan, 

F. E. Talke, and J. C. Harrison . 

MAGNETIC RECORDING 

High Speed Magnetic Recording — K. B. Klaassen, R. G. Hirko, andJ. T. Contreras . 

High Speed Switching Measurements in Thin Film Disk Media — S. M. Stinnett, W. D. Doyle, P. J. Flanders, 

and C. Dawson .. 

Theory of the Magnetic Damping Constant — H. Suhl . 

Computational Approaches to Thermally Activated Fast Relaxation — R, W. Chantrell, J. D. Hannay, M. Wongsam, 

T. Schrefl, and H. J. Richter . 

Signal to Noise Ratio Scaling and Density Limit Estimates in Longitudinal Magnetic Recording — H. N. Bertram, 

H. Zhou, andR. Gustafson . 

Detection and Capacity Limits in Magnetic Media Noise — R. Wood . 

Bit Cell Aspect Ratio: an SNR and Detection Perspective — T. C. Amoldussen . 

Recording at 300 KFCI with Perpendicular Co-Alloy Multilayers — K. Ho, B. M. Lairson, Y. K. Kim, G. 1. Noyes, 

andS.-Y.Sun . 

Thermal Relaxation in the Strong-Demagnetizing Limit — N. D. Rizzo and T. J. Silva . 

Resonance Interaction of Grains as a Mechanism of Thermal Stability of Longitudinal Magnetic Medium — 

V. L. Safonov and T. Suzuki . 






































Identification of Magnetic Aftereffect Model Parameters: Temperature Dependence — P. Rugkwamsook 

and C. E. Korman . 

Advanced MR Read/Inductive Write Heads for High Performance, High Density Tape Applications — R. H. Dee 

andJ. C. Cates . 

Timing-Based Track-Following Servo for Linear Tape Systems — R. C. Barrett, E. H. Klaassen, T. R. Albrecht, 

G. A. Jaquette, andJ. H. Eaton . 

Key Issues in the Design of Magnetic Tapes for Linear Systems of High Track Density — D. B. Richards 

and M. P. Sharrock . 

Tribology in LFltra-High Density Tape Drive Systems; State of the Art and Future Challenges — B. Bhushan 

and S. T. Patton . 

Servo Loop Gain Identification and Compensation in Hard Disk Head-Positioning Ser\'o — C.-I. Kang andM. Abed .... 
A Novel Disturbance Observer Design for Magnetic Hard Drive Servo System with a Rotary Actuator — Y. Huang 

and W. Messner . 

A Novel Add-On Compensator for Cancellation of Pivot Nonlinearities In Hard Disk Drives — J. Ishikawa 

and M. Tomizuka . 

Optimal Multirate Control Design for Hard Disk Drive Servo Systems — R. Chen, G. Guo, T. Huang, T.-S. Low, 

and S. Weerasooriya . 

A Novel Method for Reduction of the Cross Track Profile Asymmetry of MR Head During Self-Servo-Writing — 

B. Liu, S.-B. Hu, andQ.-S. Chen . 

Multi-Tapped Magnetoresistive Heads for Magnetic Tape Tracking Servo — J. H. Steele, II, W. C. Messner, 

J. A. Bain, T. A. Schwarz, W. J. O’Kane, and M. P. Connolly . 

A High Bandwidth Piezoelectric Suspension for High Track Density Magnetic Data Storage Devices — W. Guo, 

Z. Wang, X. Yao, T. Huang, and C. Bi . 

Shear Mode Piezoelectric Microactuator for Magnetic Disk Drives — S. Koganezawa, Y. Uematsu, T. Yamada, 

H. Nakano, J. Inoue, and T. Suzuki . 

Experimental Investigation of Shock Responses of Cantilever-shaft Design Hydrodynamic Bearing Spindle Motors — 

C. -P. Roger Ku andM. Shumway . 

Patterned Media Recording: Noise and Channel Equalization — S. K. Nair and R. M. H. New . 

Performance Comparison of a Class of (1,7) DFE Detectors — G. Mathew, K. C. Indukumar, Y. X. Lee, 

and R. W. Wood . 

Byte Synchronization System and Method using an Error-Tolerant Synchronization Pattern for the PR IV Channel — 

T. Yasuda, M. Blaum, and D. D. Tang . 

High Speed Implementation of Signal Space Detectors — T. Jeon and J. Moon . 

Low Complexity Signal Space Detector for (l,7)-Coded Partial Response Channels — Y. Kim and J. Moon . 

Digital Detection with Asynchronous Sampling using Amplitude Error Prediction — T. Oenning and J. Moon . 

A New Nonlinear Multi-Filter Detection Concept for the High Density Magnetic Recording Channel — 

F. Obernosterer, A. Kratzert, and W. F. Oehme . 

An Error Rate Improvement of Decision Feedback Equalization by Extraordinary Level Detection — M. Umemoto . 

An Analysis of Frame Formats for Digital Tape Recording — A. D. Weathers . 

Performance of an 8/9 Rate Matched Spectral Null Code on the PR4 Magnetic Recording Channel — S. She, 

W. G. Bliss, and D. E. Reed . 

A High-Rate Matched Spectral Null Code — M. Noda . 

Two-Dimensional Coding for a Multi-Track Recording System to Combat Inter-Track Interference — P. J. Davey, 

T. Donnelly, D. J. Mapps, and N. Darragh . 

Sensor Saturation Effects on NETS Measurements — J. S. Feng . 

A Theoretical Study of Nonlinear Transition Shift — Y. Zhang and H. N. Bertram . 

TMR Window Measurements with Thin Film Write/MR Read Heads on Metal Particle Tape Including Erase Bands — 

K. D. McKinstry and R. H. Dee . 

An Off-Track Capability Model Including Noise — R. S. Beach and P. 1. Bonyhard . 

A Description of the Complete Off-track Capability Curve and its Special Application -T-.C. Yu . 

Empirical Determination of Areal Density Capability — D. Saunders, T. Madsen, R. Machelski, M. Roe, N. Curland, 

and P. Bonyhard ... 

Optimal Track-Width Design of AMR/GMR Heads for High-Track-Density Disk Drives — F. Tomiyama, H. Ide, 

T. Hamaguchi, H. Takano, T. Yamaguchi, andN. Kodama . 

Quantitative MFM Study on Partial Erasure Behavior of Longitudinal Recording — T. K. Taguchi, A. Takeo, 

and Y. Tanaka . 

Finite Element Simulation of Digital Recording on ME Tape and Comparison with Experimental Data— Werling, 

F. Ossart, J.-B. Albertini, andM. Aid . 

A Comparison of Longitudinal and Transverse Recording — J. Miles, P. Sivasamy, M. Wdowin, B. Middleton 

andS. Casey .-. 






































Keepered Media Reproduction with Dual MR Heads — F. Z. Wang, L N. He, D. J. Mapps, D. T Wilton, 

W. W. Clegg, and P. Robinson . 

A New Equalizing Experiment Applying to Perpendicular Digital VCR using FFT Analysis — K. Kamijo, R. Taguchi, 

E, Miyashita, and J. Numazawa . 

Gd/Fe Multilayers with an Anisotropy Changing from In-plane to Perpendicular for MSR Applications — E. Stavrou, 

H. Rohrmann, and K. Roll . 

Magnetic and Magneto-Optic Study of a Layered Co/Pt - Dysprosium-Iron-Garnet System — J. M Meldrim, 

R, D. Kirby, M. J. DeVries, J. A. Woo Ham, and D. J. Sellmyer . 

The Creation of Nanometer Magnetic Domain Structure in Artificially Pinning Hole of Magneto-optical Recording 

Material — T.-K Wu, J, C. Wu, B,-M. Chen, andH-P. D, Shieh . 

New MSR Method for High Density Read Only Memory Disks — M. Birukawa, T. Suzuki, and N. Miyatake . 

Estimation of the Resolution by Mammos Read-Out — N. Takagi, A. Yamaguchi, Y. Uchihara, S. Sumi, H Awano, 

H Shirai, H. Watanabe, and N. Ohta . 

Signal Enhancement of 0.2 |im Packed Domain in Magnetic Domain Expansion Readout Disk with Gating Layer — 

H, Awano, H Shirai, H Watanabe, K. Shimazaki, K Ohta, Y. Xiao, and K. V Rao . 

A Novel Flying Magnetic Readout Head Based on Magneto-optic Transfer — T. Terada, T. Nomura, R. Tsuchiya, 

K Honda, M. Tomita, T. Furuoya, T. Kakezawa, and S. Kato . 

New Magnetic Domain Expansion MO Phenomena using an In-Plane Magnetizing Layer — K Shimazaki, 

H. Watanabe, M Yoshihiro, H Takao, H Awano, S. Ohnuki, N Ohta, Y. Xiao, and K. V Rao . 

Imaging of Magnetic Domains in Thin Co/Pt and CoNi/Pt Multilayers by Near-Field Magneto-Optical Circular 

Dichroism — V Kottler, C Chappert, N. Essaidi, and 7. Chen . 

MAGNETIC MEASUREMENT AND IMAGING 

Magnetization; Magnetostriction and Film Stress of Fe Monolayers on W(IOO) — D. Sander, A. Enders, 

andJ. Kirschner ... 

A Bipolar Pulse-Type Hysteresis Loop Tracer for Rare Earth Based Permanent Magnets — J. R, Rhee, 7 H Lee, 

M. 7. Kim, J. M Lee, M. 7. Oh, D. G, Hwang, S. S Lee, and C M. Park .. 

Dependence of Magnetic Properties on Crack Size in Steels — 7. Bi and D, C. Jiles . 

Measurement of Oxygen Pressure Increase in Magnetic Field — J. Nakagawa, N Hirota, K Kitazawa, H Yokoi, 

7 Kakudate, and S. Fujiwara .... 

A Digital Sampling Technique for Amplitude and Pulse Width Measurement — J. Zhu, T. Carr, and D. Varsanofiev ... 
MFM Quantification of Magnetic Fields Generated by Ultra-Small Single Pole Perpendicular Heads — 

S. K Khizroev, W Jayasekara, J. A. Bain, R. E. Jones, Jr., andM. H Kryder . 

Thermal Wave Interactions in Magnetic Materials — R. Carey, D. M. Newman, andJ. Wiggins . 

Changes in Magnetic Properties of Neutron Irradiated RPV Steel — D.-G. Park, J.-H Hong, C.-L Ok, J.-W. Kim, 

HC. Kim . 

MAGNETICS APPLICATIONS 

A Vector Oriented Control for a Magnetically Levitated Shaft — J. De Miras and A. Charara . 

Prototype Microactuators Driven by Magnetostrictive Thin Films — S. H Lim, S. H Han, H J. Kim, 7 S. Choi, 

J W Choi, andCHAhn . 

Thrust Characteristics of a Linear Oscillatory Actuator at a Low Temperature — A. Aoki, M. Watada, S. Torii, 

K Yamane, and D. Ebihara .:... 

A Novel Numerical Method for Analyzing of Passive Fault Current Limiter Considering Hysteresis — A. Mukherjee, 

S. C. Mukhopadhyay, M. Iwahara, and S. Yamada . 

Planar Integrated Magnetic Component with Transformer and Inductor using Multilayer Printed Wiring Board — 

T. Fujiwara .:. 

Performance Characteristics of a New Type of Linear Parametric Motor with Double Driving Surfaces — K. Ishikawa, 

M. Ishizuka, and S. Kikuchi . 

A Magnetic Coupled Charger with No-Load Protection — H Sakamoto, K Harada, H. Abe, and S. Tokuomi . 

The Application of Halbach Cylinders to Brushless AC Servo Motors — K Atallah andD. Howe . 

Analysis of Linear Electromagnetic Motion Devices by Multiple-Reference Frame Theory — C.-T. Liu and S.-C. Hsu ... 
Development of 3-Phase 100kVa Orthogonal-Core Type Variable Inductor with Sinusoidal Output — O. Ichinokura, 

M. Maeda, M. Sakamoto, K Mitamura, T. Ito, and T. Saito . 

A New Meander Type Contactless Power Transmission System-Active Excitation with a Characteristics of Coil Shape — 

F. Sato, H. Matsuki, S. Kikuchi, T. Seto, T. Satoh, H Osada, and K Seki . 

Measuring System of Magnetostriction of Silicon Steel Sheet Under AC Excitation using Optical Methods — 

T. Nakase, M. Nakano, K. Fujiwara, and N Takahashi . 

Cogging Torque Reduction of a Single-Phase Brushless DC Motor — D.-R. Huang, T.-F. Ying, S-J. Wang, C. Zhou, 

Y.-K Lin, K-W. Su, andC-IG. Hsu . 

































A Novel Spherical Permanent Magnet Actuator with Three Degrees-Of-Freedom — J. Wang, W. Wang, G. W. Jewell, 

and D. Howe . 

Magnetostrictive Linear Motor Development — J. P. Teter, M. H. Sendaula, J. Vranish, and E. J. Crawford . 

A 42-Tesla Pulse Transformer with a Mechanically High Resistant Field Former — E. Steingroever and G. Ross . 

Fabrication of a Magnetic Drive Unit for that Moves in the Same Direction of the Exciting Magnetic Field — 

M Enokizono, E Tadoka, and K. Goto . 

Electromagnetic Optimization of EMS-MAGLEV Systems — M Andriollo, G. Martinelli, A, Morini, and A. Tortella .. 
A Novel Combined Lift and Propulsion System for a Steel Plate Conveyance by Electromagnets — H. Hayashiya, 

D. llzuka, H, Ohsaki, and E. Masada . 

A Theory for Analyzing the Flap Motion of Wings of Small Flying Elements Driven by a Magnetic Torque — 

K. Shimasaki, M. Inoue, K. L Aral, and T. Honda . 

Superconducting Permanent Magnets from Bulk YBa 2 Cu 307 ^ Samples — S. Gruss, G, Fuchs, G, Krabbes, P. Schdtzle, 

J. Fink, K. H Muller, and L Schultz . 

Fabrication and Testing of a Small Pump Composed of a Magnet and An Elastic Plate — T. Honda, J. Yamasaki, 

and K. L Arai . 

Design of an Actuator Being Both a Permanent Magnet Synchronous Motor and a Magnetic Suspension — C Barthod 

and G. Lemarquand . 

Optimal Design of Rotor Circuits in Induction Type Bearingless Motors — A. Chiba and T. Fukao . 

A Method to Compute the Shielding of a 3-D Conductor Array by a Semi-Infinite Permeable Layer — M Sharifi, 

J. D. Lavers, and M. Gyimesi . 

Magnetization Reversal Mechanisms in Colloidal Dispersions of Magnetite Particles — J. M. Gonzalez, M. L Montero, 

J. A. Lopez-Perez, J, Mira, M. A. Lopez-Quintela, J. Rivas, X Batlle, and A. Labarta . 

Inter-Particle Interactions in Biocompatible Magnetic Fluids — Q,-T. Bui, Q. A. Pankhurst, and K. Zulqarnain . 

Magnetohydrodynamic Calculation for Electromagnetic Stirring of Molten Metal — K. Fujisaki, T. Ueyama, T. Toh, 

M. Uehara, and S. Kobayashi . 

Magnetic Separation of Nanoparticles — D. R. Kelland . 

High Gradient Magnetic Separation of a Biologically Produced FeS Adsorbent using Sulphate Reducing Bacteria — 

B. T. Coe, R. Gerber and D. Witts . 

Optical Measurements of Magnetophoresis of Macromolecules — M. Iwasaka and S. Ueno . 

Three-Dimensional Field and Side-Force Design Analyses of a Transverse Flux Linear Switched-Reluctance Machine — 

C-T Liu, K,-S, Su, andM.-H. Lee . 

The Robust Design Approach for Reducing Cogging Torque in Permanent Magnet Motors — S. X. Chen, T. S. Low, 

and B. Bruhl . 

Optimization of a Magnetic Actuator with Taguchi Method and Multivariate Analysis Method — H. Fusayasu, 

Y. Yokota, Y. Iwata, and H Inoue . 

A Design Technique for Magnetostrictive Actuators with Laminated Active Material — F. Stillesjo, G. Engdahl, 

and A. Bergqvist . 

A Novel Design Approach for Grasping Broad Characteristics of Magnetic Shield Problem — S, Wakao, T, Onuki, 

J. W. Im, and T, Yamamura . 

Analysis of Dynamic Characteristics of Switched Reluctance Motor Based on SPICE — O. Ichinokura, E Onda, 

M. Kimura, E. Watanabe, E. Yanada, and H J. Guo . 

Investigation of the Performances of a Permanent Magnet Biased Fault Current Limiting Reactor with a Steel Core — 

S. C Mukhopadhyay, M. Iwahara, S. Yamada, and F, P, Dawson . 

Use of a Conductor Screen to Magnetize NdFeB Magnets — R. R. Wallace, V. D. Fierro, L. A. Moran, and E. A. Lipo . 
Finite Element Modeling of Creep Damage Effects on a Magnetic Detector Signal for a Seam Weld/HAZ-Region in a 

Steel Pipe — M. J. Sablik, D. C. Jiles, and M. R. Govindaraju . 

Design Optimization of Stimulation Coil System for Nerve Stimulation — T. Onuki, S. Wakao, E. Miyokawa, 

Y. Nishimura, K Ishikawa, and H Hosaka . 

Finite Size Bi-Planar Gradient Coil for MRI — H Liu ... 


CONFERENCE AUTHOR INDEX 































JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Magnetic Microscopy and Imaging I 


R. D. Gomez, Chairman 


Time-resolved scanning Kerr microscopy of ferromagnetic structures 
(invited) 

M. R. Freeman, W. K. Hiebert, and A. Stankiewicz 

Department of Physics, University of Alberta, Edmonton T6G2J1, Canada 

Time-resolved microscopy enables valuable new measurements of the dynamics of resonance and 
relaxation in a range of magnetic systems. An overview of the scope of applications to 
ferromagnetic microstructures is presented. These include observations of ferromagnetic resonance 
and spatially nonuniform modes of oscillation, studies of magnetization reversal, and 
characterizations of the speed of magnetic recording devices. © 1998 American Institute of 
Physics. [80021-8979(98)36511-1] 


I. INTRODUCTION 

Recently, novel experimental information concerning the 
dynamics of a variety of magnetic systems has been obtained 
using picosecond time-resolved laser techniques combined 
with diffraction-limited optical microscopy. Ultrafast optical 
methods have been in use for some time in the extraction of 
relaxation and resonance information from magnetic 
systems.^""^ The addition of microscopic spatial resolution 
powerfully extends the approach to much smaller specimens, 
enabling measurements of relaxation in micrometer-scale 
structures, as well as some imaging of spatially nonuniform 
dynamics.In this paper we describe the study of ferromag¬ 
netic dynamics in small permalloy structures using this tech¬ 
nique. A similar procedure applies to the time-domain char¬ 
acterization of devices such as high-speed magnetic 
recording heads. 

In addition to the good spatial and temporal resolution 
achieved using an optical technique, another key aspect is 
the ability to perform vector measurements of the magneti¬ 
zation. The component of magnetization parallel to the wave 
vector of the incident light is resolved in the experiments. A 
vector measurement is not crucial to paramagnetic relaxation 
measurements, but is essential in order to perform magnetic 
resonance and ferromagnetic relaxation studies. Controlling 
the optical configuration, we are able to track dynamical ex¬ 
cursions of the magnetization in three dimensions through 
polar and longitudinal Kerr effect measurements. 

II. EXPERIMENTAL DETAILS 

An example of an experimental geometry for spatially 
resolved time-domain ferromagnetic resonance measure¬ 
ments is shown in Fig. 1.^ The single turn lithographic coil is 
patterned from a gold film with a titanium adhesion layer. A 
fast electrical pulse generated using a photoconductive 
switch propagates around the coil, inducing a transient mag¬ 
netic field at the sample, perpendicular to the substrate (the 
tipping pulse). The rise time of this pulse at the sample is 
limited to '^20ps by dispersion of the coil leads, and the 


decay time constant is ~500ps. Peak tipping field ampli¬ 
tudes are limited to —30 Oe with this coil. The static mag¬ 
netic field is applied in the plane of the sample, and the polar 
Kerr effect is used to record the out-of-plane component of 
the magnetization. Resonant precession of the magnetization 
(about the static field) induced by the tipping pulse is re¬ 
flected in oscillations of the polar Kerr signal. 

The permalloy films used in this work are sputter depos¬ 
ited in a load-locked ultrahigh vacuum chamber pumped to a 
base pressure of — 5X 10“^ Torr. A permanent magnet as¬ 
sembly is used to apply an in situ static field of approxi¬ 
mately 150 Oe in the plane of the substrate to establish an 
easy axis. The resulting films have low coercivity (<2 Oe in 
the easy direction), and low resistivity ( — 20 jmCl cm) indi¬ 
cating very little oxidation. SIMS analysis of the films show 
the composition to be 83% Ni 17% Fe (by weight), fairly 
close to the 81/19 proportion of the target. Patterning of the 
films is accomplished through photolithography and wet 
chemical etching, yielding the very smooth edges with a 
slight undercut profile as seen in Fig. 1(b). 



FIG. 1. Electron micrographs of the 8 pm diameter permalloy disk sample. 
Left panel: plan view, showing the surrounding lithographic gold coil. Right 
panel: tilted close-up view, clearly showing the clean edge of the disk. 


0021 -8979/98/83(11 )/6217/6/$15.00 


6217 


© 1998 American Institute of Physics 



6218 


J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Freeman, Hiebert, and Stankiewicz 



0 1000 2000 


Time [ps] 

FIG. 2. Examples of the response to the pulsed field of the out-of-plane 
component of magnetization, measured at the center of the disk by the polar 
Kerr effect. The solid lines are fits to the data using the Landau-Lifshitz- 
Gilbert equation, using the same parameters for each value of the static field. 


III. RESULTS 
A. Resonance 

The modal resonance frequencies are determined by the 
maxima in the power spectra of Fourier transformed time- 
domain data. The in-plane magnetic field dependence of the 
characteristic frequency is well described by the Kittel rela¬ 
tion for an infinite plane, as may be expected for such a large 
(on the scale of the domain wall width) disk. Modeling the 
time-domain data in more detail through numerical integra¬ 
tion of the Landau-Lifshitz-Gilbert equation, we find very 
good agreement.^ Data are shown in Fig. 2 for a range of 
values of the in-plane field. The measurements (shown by 
the dotted lines in the figure) were made with the 0.7 fxm 
laser spot focused at the center of the particle. The t = 0 
position is arbitrary, corresponding to the initial position of 
the delay line at a location yielding a reasonable baseline 
determination before onset of the signal. Using a pulse shape 
determined from higher field data by the procedure estab¬ 
lished in Ref. 7, the curves are all fit using the same set of 



FIG. 3. A collection of full spatial images of the polar Kerr signal at times 
corresponding to the successive peaks in the signal at the center of the disk 
in a static field of 500 Oe. 


parameters. The results of the fit are shown by the solid lines. 
Only the dimensionless Gilbert damping parameter is adjust¬ 
able, and we find 0.008, in reasonable agreement with 
earlier careful microwave measurements of Patton and 
co-workers.^ Note that these results represent the response of 
the magnetization to a very broad-band excitation. The high 
frequency components associated with the rising edge of the 
pulse excite the resonant oscillations, which then ring-down 
according to their intrinsic damping rate. Meanwhile the 
magnetization vector parametrically follows the slowly de¬ 
caying tail of the field pulse (consisting of that part of the 
spectrum of the broad-band excitation below the resonance 
frequency), giving rise to the offset of the centerline through 
the envelope of the oscillations. 

Time-resolved images of the magnetization across the 
whole disk clearly show the presence of nonuniform modes 
of oscillation, however. At these dimensions we are in an 
intermediate size regime, where the modal frequencies are 
not yet strongly influenced by size effects but the spatial 
response definitely is.^ Figure 3 shows a set of time-resolved 
magnetic images of the particle. With the static bias field at 
500 Oe (horizontal), an image was taken for a series of time 
delays corresponding to successive peaks in the oscillations 
measured at the disk’s center. Strikingly apparent are the 
enhanced initial responses at the edges (dark corresponds to 







J. AppL Phys., Vol. 83, No. 11,1 June 1998 


Freeman, Hiebert, and Stankiewicz 6219 


higher signal), that subsequently seem to propagate toward 
the center as a kind of shock wave. The effective velocity is 
on the order of 10^ m/s, much faster than a domain wall 
velocity, for example. The observation of enhanced response 
at the edges along the field direction is qualitatively consis¬ 
tent with the fact that in static equilibrium these edges are 
already demagnetized, and should be able to respond to the 
tipping field more easily. In contrast, no such effects are seen 
at the edges one-quarter of a rotation around the disk from 
these points, where there are no free poles in the initial mag¬ 
netic configuration. In these data, a reflection in the electrical 
pulse induces a bit of additional structure after the fifth peak. 
At long time delays, the spatial mode of oscillation becomes 
more uniform again. To highlight the nonuniformity, the 
gray scale in each image is adjusted to span between the 
minimum and maximum levels of the signal. In the later 
frames (8,9,10) the signal becomes quite uniform across the 
disk, with variations not much greater than the noise level in 
the measurement. The scaling procedure then mainly high¬ 
lights the noise, which appears as graininess. 

From these images we can conclude that we should in 
fact expect discrepancies between the Landau-Lifshitz- 
Gilbert model and the time domain data for this sample. 
Consistently poorer agreement is found between the data and 
the model in Fig. 2 over a time interval that begins coinci¬ 
dent with the arrival of the nonuniform response at the center 
of the structure. A more detailed numerical model taking into 
account the initial magnetic configuration of the disk seems 
essential to further quantitative progress. 


B. Reversal 

In-plane dynamics of the magnetization, and most spe¬ 
cifically those aspects related to magnetization reversal, are 
also of great interest at the present time.^"^^ In order to ad¬ 
dress these questions using time-resolved microscopy, it is 
only necessary to reconfigure the “vector geometry.” We 
measure the in-plane components of the magnetization (par¬ 
allel and perpendicular to the static magnetic field) using the 
longitudinal Kerr effect implemented in the traditional man¬ 
ner by masking half of the beam. While this is the simplest 
approach, one must beware that a mix of polar and longitu¬ 
dinal signals is observed when there is also an out-of-plane 
magnetization present. In addition the effective numerical 
aperture in the masking direction is halved, resulting in an 
elongated focus and some loss of spatial resolution. 

The other important geometric change is to place the 
transient magnetic field in the plane of the sample. Placing 
the sample directly on top of a current carrying transmission 
line straightforwardly does this. A cross-sectional schematic 
of the arrangement used in this work is illustrated in Fig. 4. 
The transmission line is 300 nm by 40 fjm gold, relatively 
thick for high current carrying capacity, and broad for mag¬ 
netic field uniformity at the sample. The current pulses in 
this case are generated by an avalanche transistor pulser (Pi¬ 
cosecond Pulse Labs Model 2000D). An insulating spacer 
(25 nm Si02) on top of the gold electrically insulates the 
permalloy from the transmission line, and optimally posi¬ 
tions the magnetic sample in the in-plane field. The calcu- 




m) 


a) 


20 micrometers 


NiFe 


i_ 25 tun ■ 1 


i 

\.(t) ® Gold ® 

f 300 nm 

1 0 


40 micrometers 



20 


FIG. 4. (a) Cross-sectional geometry showing the configuration for applying 
transient fields in the plane of the sample, (b) Calculated cross-sectional 
transient field profile for the volume occupied by the samples. 


lated field distribution above the transmission line is shown 
in Fig. 4(b). 

The permalloy samples for this study are rectangular 
bars, again produced by sputtering in the UHV system fol¬ 
lowed by optical lithography and wet chemical etching. Ini¬ 
tial magnetic characterizations are performed optically, using 
a small electromagnet to apply in-plane field to the sample. 
Spot measurements of the hysteresis are performed, with the 
laser focused at specific locations. As these results are 
strongly position dependent (the bars are much easier to satu¬ 
rate near the center than near the ends) we also use an im¬ 
aging method to characterize the static magnetic properties 
of the samples. The synchronous response to low frequency 
(280 Hz) ac fields is measured, yielding a signal representing 
the difference of the magnetization between positive and 
negative fields. Magnetic images taken for different field am¬ 
plitudes show how the hysteresis varies as a function of po¬ 
sition. A typical result is shown in Fig. 5. This is the longi- 



FIG. 5. A longitudinal Kerr image showing the signal change due to mag¬ 
netization reversal of the 10X4 fjbm bar in a ±30 Oe field switching at 280 


Hz. 






6220 


J. Appl. Phys., VoL 83, No. 11, 1 June 1998 


Freeman, Hiebert, and Stankiewicz 




FIG. 6. Changes of the x component of magnetization (larger signals shown 
brighter) for a 20X 6 jum bar in a - 5 Oe static biasing field, (a) Shift of the 
domain wall after 5.5 ns in a small tipping field, (b) and (c) are typical y-t 
diagrams for small and large tipping fields, respectively, where a linear 
vertical spatial scan across the center of the bar is repeated for increasing 
delay times. Note the change in time scale between (b) and (c). 




0 20 40 60 80 100 


Tipping field [Oe] 


FIG. 7. (a) Wall shift as a function of time determined by integrating the 
reversed component along y in data as shown in Fig. 6(b). (b) The effective 
reversal speed as a function of tipping field amplitude, determined from the 
linear slope of curves as in (a). 


tudinal Kerr signal (x component of the magnetization, 
parallel to the static field) from a 4X 10 /im particle for a 
± 30 Oe square-wave field modulation, showing a uniformly 
magnetized and saturated central region. Recording the dif¬ 
ferent Kerr components reveals information about the mag¬ 
netic anisotropy at the ends (due mainly to demagnetizing 
effects). Such static images provide a direct point of com¬ 
parison for the dynamical studies. A very detailed portrait of 
static reversal in permalloy bars was developed much earlier 
through Bitter pattern images, which have higher spatial 
resolution than the present optical experiments.^'^ 

A first glimpse at the dynamical information accessible 
in time-resolved studies of magnetization reversal is seen in 
the following data of the response of a nonuniformly mag¬ 
netized permalloy rectangle to a pulsed field in the plane of 
the particle. We examine a 20 /xmX 6 /xm rectangle (50 nm 
thick) with the static bias magnetic field parallel to the long 
direction. This bar is oriented transverse to the current flow 
direction of the transmission line so that the transient mag¬ 
netic field is parallel (or antiparallel) to the bias field. In a 
field of - 5 Oe, the static configuration of the particle corre¬ 
sponds to two antialigned domains along most of the length 
of the bar, with the domain wall near the center, and some 
closure domains at the ends. Time-resolved measurements 
are then performed to study the approach to saturation in¬ 
duced by the (0.4 ns rise time, 1.5 ns fall time, 10 ns dura¬ 
tion, opposite polarity to the static field) pulsed magnetic 
fields, starting from this simple demagnetized state. 


As a function of the amplitude of the pulsed field, two 
distinct regimes are observed in the reversal dynamics of the 
initially antialigned domain. At smaller pulse amplitudes 
(less than '-60 Oe) the reversal proceeds via uniform motion 
of the central domain wall towards the edge of the bar. Char¬ 
acteristic data are shown in Fig. 6. Panel (a) is a snapshot of 
the magnetization change 5,5 ns after the onset of the pulse. 
The light area is the region that has been swept out by the 
moving domain wall. To see the progression in detail, the 
change in the longitudinal Kerr signal is shown in two di¬ 
mensional images in Figs. 6(b) and 6(c) where the vertical 
axis corresponds to position along a line section through the 
center of the bar (in the short direction, y), while the hori¬ 
zontal axis is time. The signal growing with time in Fig, 6(b) 
for a small tipping field arises from motion of the domain 
wall with nearly constant velocity. The initial displacements 
of the wall are well below the spatial resolution of the mi¬ 
croscope, so the rate of reversal is extracted by integrating 
the Kerr signal across the particle and plotting the integral as 
a function of time, as in Fig. 7(a). Normalizing the curve by 
the saturation signal divided by the width of the bar, the 
slope can be converted to a wall velocity. 

Reversal rates as a function of pulsed field amplitude are 
shown in Fig. 7(b). A couple of points are of particular note. 
First, we do not observe a linear region at low fields, indi¬ 
cating that the motion cannot properly be described using a 
wall mobility. This may be indicating that we cannot ignore 







J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 



0 10 20 30 40 50 


Time [ns] 

FIG. 8. Time dependence of the x component of magnetization measured at 
sample center for three different structures, 4X4, 10X4, and 20X4yctm 
(light, medium, heavy line, respectively). -35 Oe static field, tipping field 
amplitude + 140 Oe, The dashed line shows the shape of the pulse, and the 
inset shows the rising edge response in more detail. 


the influence of the closure domains at the ends of the bar on 
the motion of the wall. Second, at pulse amplitudes above 65 
Oe, there is a nearly linear region, possibly proceeded by a 
discontinuity in the curve. The images of the magnetization 
are qualitatively different in this regime, with the reversal 
proceeding not by movement of the domain wall but rather 
through a rotation process which propagates through the cen¬ 
ter of the domain after nucleating near the closure domain 
boundaries at the ends. This is clearly evident in Fig. 6(c), 
where change in the longitudinal Kerr signal is seen to begin 
not at the wall but closer to the center of the domain, and to 
develop symmetrically about this point. The distinct asym¬ 
metry arising from wall motion in Fig. 6(b) is notably absent. 
Therefore the reversal rates found at higher fields in Fig. 7 
cannot correctly be interpreted as velocities because of this 
change in reversal mechanism. Normalizing the data as de¬ 
scribed above, the maximum wall speed we find before this 
phenomenological change is 650 m/s at 60 Oe. 

A great richness of phenomena is observed upon pursuit 
of these investigations to higher fields. Beginning from an 
equilibrium state in which the centers of the bars are uni¬ 
formly magnetized (static field of - 35 Oe), we obtain a view 
of the speed of reversal by recording the time evolution of 
the magnetization change with the laser focussed at the cen¬ 
ter of the structure. Results are shown in Fig. 8 for 4 jmm 
wide samples of three different lengths, 4, 10, and 20 /mm. 
The 10 ns duration transient field has amplitude 140 Oe. The 
rising and falling transitions are markedly asymmetric, par¬ 
ticularly for the longest and shortest samples. It is clear from 
the expanded view of the initial switch in the inset that re¬ 
versal at the center occurs more rapidly for the shorter bars. 
The rise time of the pulse itself starts to become significant 
in limiting the speed for the 4 X 4 /im structure. 

Much more information is available in full time-resolved 
images of the magnetization. We 'observe that the reversal 
process starts with a wave-like spatial oscillation of the in¬ 
plane magnetization. Figure 9 has panels showing the three 
components of the magnetization (long, jc, long, y, polar) for 
the 10X4 /im particle at ns after the onset of the field 
(see the abscissa of Fig. 8). The oscillation is initially quite 


Freeman, Hiebert, and Stankiewicz 6221 



FIG. 9. The nonuniformity of response during the initial flip is shown in this 
set of magnetic images taken for the 10X4 /tm bar at r = + 3 ns, under the 
conditions of Fig. 8. (a) Longitudinal (j:) component, (b) Transverse (y) 
component, (c) Polar (z) component. 


symmetric about the equilibrium (jc) direction, and shows up 
most dramatically in the y component. One direction then 
grows at the expense of the other, culminating in reversal. 
The relative degree to which this behavior is related to the 
“concertina” structure seen in static reversal,or is induced 
by dynamics, remains to be sorted out. The wavelength of 
the spatial variation appears to be extremely stable and re¬ 
producible. At the same time these oscillations are clearly 
observed only on the rising edge of the pulses. Two effects 
may be at work to cause different behavior on the trailing 
edge. The time rate-of-change of the magnetic field is con¬ 
siderably less when the pulse shuts off relative to when it 
turns on, making it less effective at driving a dynamic insta¬ 
bility. In addition the switched state may be more uniformly 
magnetized because of the unequal amplitudes of the static 
and transient fields, although the bar may not have com¬ 
pletely relaxed into a switched equilibrium state by the end 
of the 10 ns pulse. 

Strong dependences on sample size are also found in 
imaging. Some results from a more detailed investigation of 
magnetization reversal in the longer bar are reported in a 
companion paper. 






6222 


J. AppL Phys., Vol. 83, No. 11, 1 June 1998 


Freeman, Hiebert, and Stankiewicz 


IV. DISCUSSION 

The present work only begins to scratch the surface of 
what is possible with these pulsed optical methods. Many 
other materials systems and geometries remain to be inves¬ 
tigated with our present set-up. Some of the choices will be 
guided by the desire for convergence between experiment 
and micromagnetic simulations, an obvious goal for the near 
term. The immediate goal is to study smaller particle sizes. 

The same experimental techniques are well suited to the 
characterization of devices and media for magnetic record¬ 
ing, particularly when high speed is an issue.^^ ’^ The utility 
of such measurements is further enhanced by time-domain 
magneto-optical measurements of currents, for direct com¬ 
parison between the response (e.g., of the magnetization at 
the pole tips of a recording head) and the input (e.g., the 
drive signal to the coil). A stroboscopic “movie” of the 
magnetization at the air bearing surface of a write head in 
response to a dibit input can be viewed on the internet. 

In terms of the experimental method, there are many 
potential improvements that would further broaden the range 
of significant applications. Although the speed of the tech¬ 
nique is more than adequate for our present studies, this is 
material dependent. Awschalom and co-workers'^ have stud¬ 
ied much faster dynamics in magnetic semiconductors using 
optical excitation of the sample. Substantial improvement of 
the speed of pulsed magnetic field generation is required be¬ 
fore our approach can enter the sub-picosecond regime. Of 
even more interest is increasing the amplitude of magnetic 
field pulses, to open the door to large tipping angle measure¬ 
ments and associated nonlinearities in resonance. Studies of 
reversal in magnetically harder materials would also be of 
interest, as in the case of studies of high-speed switching in 
media by Doyle and co-workers.At present we are unable 
to pass more than about 300 mA peak current through the 
photoconductive switches. The corresponding current densi¬ 
ties are very high and may be near to intrinsic damage 
thresholds of the materials, but the fact that the quantum 
efficiency of the devices is very low suggests that there may 
still be room for significant improvement here. 

It is also imperative to improve spatial resolution in or¬ 
der to investigate the detailed micromagnetic dynamics of 
much smaller ferromagnetic particles. In the present experi¬ 
ments some information is already lost below the limit of 
spatial resolution, especially near the edges of the particles. 
When we attempt to cleanly separate the vector components 
of the magnetization the demands on resolution increase still 
further. Because of unwanted “clipping” of the beam which 
occurs as the focus spot scans over an edge, a small focus 


also helps in keeping the entire laser spot on the particle as 
close to the edge as possible. We have developed a solid 
immersion lens capability for these experiments offering im¬ 
provements of a factor of three in spatial resolution over that 
achieved here.^® This is probably good enough to explore 
strong size effects and to be useful for the next few genera¬ 
tions of magnetic devices, but certainly not for superpara- 
magnetic particles or for such devices as seem certain to 
exist before the “endpoint” of magnetic recording is 
reached. In this regard the near-field and second harmonic 
generation methods of Silva, Rogers, and co-workers^’ are 
particularly exciting. 

ACKNOWLEDGMENTS 

The authors are indebted to the Alberta Microelectronics 
Centre for access to their deposition and patterning facilities, 
and to Professor Abdul Elezzabi for his assistance during the 
early stages of this project. We thank J. Giusti for pointing 
out Ref. 14. This work is supported by the Natural Sciences 
and Engineering Research Council, Canada. 

*D. D. Awschalom, J.-M. Halbout, S. von Molnar, T. Siegrist, and F. 
Holtzberg, Phys. Rev. Lett. 55, 1128 (1985). 

^M. R. Freeman, M. J. Brady, and J. F. Smyth, Appl. Phys. Lett. 60, 2555 
(1992). 

^A. Y. Elezzabi, M. R. Freeman, and M. Johnson, Phys. Rev. Lett. 77, 
3220 (1996). 

A. Crooker, J. J. Baumberg, F. Flack, N. Samarth, and D. D. Awscha- 
lom, Phys. Rev. Lett. 77, 2814 (1996). 

^J. Levy, V. Nikitin, J. M. Kikkawa, A, Cohen, N. Samarth, R. Garcia, and 
D. D. Awschalom, Phys. Rev. Lett. 76, 1948 (1996). 

^W. K. Hiebert, A. Stankiewicz, and M. R. Freeman, Phys. Rev. Lett. 79, 
1134 (1997). 

^A. Y. Elezzabi and M. R. Freeman, Appl. Phys. Lett. 68, 3546 (1996). 
^C. E. Patton, Z. Frait, and C. H. Wilts, J. Appl. Phys. 46, 5002 (1975). 
^M. Lederman, S. Schultz, and M. Ozaki, Phys. Rev. Lett. 73, 1986 (1994). 
'^J. Ding and J.-G. Zhu, J. Appl. Phys. 79, 5892 (1996). 

W. Wernsdorfer, K. Hasselbach, A. Sulpice, A. Benoit, J.-E. Wegrowe, L. 
Thomas, B. Barbara, and D. Mailly, Phys. Rev. B 53, 3341 (1996). 

^^W. Wernsdorfer, B. Doudin, D. Mailly, K. Hasselbach, A. Benoit, J. 

Meier, J.-Ph. Ansermet, and B. Barbara, Phys. Rev. Lett. 77, 1873 (1996). 
‘^S. T. Chui, Phys. Rev. B 55, 3688 (1997). 

^'^H. A. M. van den Berg and D. K. Vatvani, IEEE Trans. Magn. 18, 880 
(1982). 

^^A. Stankiewicz, W. K. Hiebert, G. E. Ballentine, K. W. Marsh, and M. R. 
Freeman, IEEE Trans. Magn. (7th Joint MMM-I Proceedings) (submit¬ 
ted). 

*^M. R. Freeman and J. F. Smyth, J. Appl. Phys. 79, 5898 (1996). 

*^M. R. Freeman, A. Y. Elezzabi, and J. A. H. Stotz, J. Appl. Phys. 81, 4516 
(1997). 

http://laser.phys.ualberta.ca/~freeman/maghead.mov 
*^L. He, W. E. Doyle, L. Varga, H. Fujiwara, and P. J. Flanders, J. Magn. 
Magn. Mater. 155, 6 (1996). 

^^J. A. H. Stotz and M. R. Freeman, Rev. Sci. Instrum. 68, 4468 (1997). 
^‘T. J. Silva, T. M. Crawford, and C. T. Rogers (these proceedings). 



JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER II 


1 JUNE 1998 


Magnetic force microscopy image restoration technique for removing 
tip dependence 

Jian-Gang Zhu, Xiangdong Lin,®* and Rick C. Shi 

Data Storage System Center, Department of Electrical and Computer Engineering, Carnegie Mellon 
University, Pittsburgh, Pennsylvania 15213 

Yansheng Luo 

IBM, SSD, San Jose, California 

Quantitative interpretation of a magnetic force microscopy (MFM) image usually requires detailed 
knowledge of the magnetization configuration of the sensing tip. Here, we demonstrated a technique 
that converts the obtained raw MFM image into the magnetic pole density distribution without 
explicitly knowing the tip magnetization orientation. By creating an approximate point source of 
magnetic poles in the same sample imaged, the impulse response function of the MFM tip is 
obtained for deconvolution of a raw image in the Fourier space. Experimental demonstrations with 
various tip magnetization orientations were performed on recorded magnetic transitions in a thin 
film longitudinal medium. © 1998 American Institute of Physics, [80021-8979(98)53811-X] 


I. INTRODUCTION 

Magnetic force microscopy (MFM) has been used exten¬ 
sively in imaging magnetic structure in magnetic materials 
and devices. However, any MFM image depends on magne¬ 
tization configuration of the sensing tip used, while the tip 
magnetization configuration can be very complicated. Lack 
of the knowledge of the tip magnetization orientation often 
results in difficulties in interpretation of the obtained images. 
Direct calculations on tip magnetization configuration have 
been undertaken, however, it is often intensive and requires 
detailed knowledge of the tip magnetic film micro- 
structure.^"^ 

A simple deconvolution technique has been proposed 
previously."^ However, using the ends of magnetized elon¬ 
gated narrow bar as an ideal magnetic pole point source pre¬ 
sents many difficulties in practice. In this paper, a point 
source is created on the same sample imaged. The technique 
to convert a raw MFM image to the corresponding magnetic 
pole density distribution is presented in detail and demon¬ 
strated experimentally. 


11. DESCRIPTION OF THE TECHNIQUE 

A magnetic force microscope senses the gradient of the 
magnetic force exerted on the sensing tip due to the stray 
field of the sample. Assuming the measurement response is 
linear (which requires the tip magnetization be rigid), the 
obtained image I{x,y) can be written as the convolution of 
the tip impulse response function and the magnetic pole den¬ 
sity distribution, from which the stray field originates, as 
follows:"^ 

J p{x\y')‘h{x~x\y-y')dx'dy\ (1) 

where p(x,y) is the magnetic pole density distribution in the 
sample and h{x~x\y—y') is the tip impulse response func- 


^^Electronic mail: lin@dilbert.ece.cmu.edu 


tion with tip at (A:,y) and point pole source at {x\y'). The 
image for a point pole source at the origin is the tip impulse 
response function: 

lp{x.y) = h{x,y). 

Using the impulse response function, a MFM image of a 
magnetic structure imaged with the same tip at the same 
imaging conditions, can be deconvolved in the Fourier space 
with a Wiener’s filter: 


p{k^,k) = 


lp{^x^ky) 


lp{K,ky)M;{k,,ky) 

. ^i-. (2) 

4(^x ^ky) • I^{k^ ,ky) + tiny(^^ ,ky) 

The final magnetic pole density distribution p(x,y) can be 
obtained by inverse Fourier transformation of p{k^,ky). In 
all the cases presented here, tiny(A:;,,A:^) is chosen to be a 
small constant, adjusted for each individual case. 


III. SIMULATION RESULTS 

In this section, computer simulation results are presented 
to demonstrate the technique. In corresponding to the experi¬ 
mental demonstration, which will be presented in the later 
section, recorded transitions in a longitudinal thin film me¬ 
dium were chosen to be an example, as shown in Fig. 1. 
According to the orientation of the tip magnetization, three 
cases were shown here: the magnetization of the tip is case 
A: vertical, case B: horizontal, and case C: canted. 

The track width is assumed to be w = 2.0 jam and the 
intertransition spacing B=l.O /am. For calculation simplic¬ 
ity, the tip is assumed to be a uniformly magnetized sphere 
with diameter Z) — 30 nm. The point source of the magnetic 
pole density is approximated by an isolated transition, i.e., 
B=16 jam, with W= 0.2 /am. MFM images were calculated 
by calculating the gradient of the magnetic force exerted on 
the tip due to the stray field generated from the recorded 
transitions. The left height of the tip is 60 nm. 


0021-8979/98/83(11 )/6223/3/$15.00 


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© 1998 American Institute of Physics 


6224 J. Appl. Phys., Vol. 83, No. 11,1 June 1998 


Zhu et al. 


ABC 





FIG. 1. Recorded transitions for MFM imaging. 

A. Case A: Tip magnetized vertically 

In this case, the calculated image of the recorded transi¬ 
tions with assuming tip magnetization orientation is perpen¬ 
dicular to the sample surface, as shown in Fig. 2(a). In the 
image, alternating black and white stripes indicate the loca¬ 
tions of the transitions. Since the magnetization in the tip is 
vertical, only the vertical component of the stray field con¬ 
tributes to the image. The image of the approximate point 
source is shown in Fig. 2(b). Using this image as the impulse 
function, the image shown in Fig. 2(a) was deconvolved in 
the Fourier space according to Eq. (2), shown in Fig. 2(c). 
The slight broadening of the images is due to the finite size 
effect of the approximated point source. 

B. Case B: Tip magnetized horizontally 

When the tip is magnetized horizontally, only the gradi¬ 
ent of the horizontal component of the stray field is sensed. 
The MFM image of the same recorded magnetization struc¬ 
ture becomes that shown in Fig. 3(a) as in contrast to that 



FIG. 2. Calculated images with tip magnetization vertical to the sample 
surface, (a) Transitions, (b) point source, (c) deconvolved image. 



FIG. 3. Calculated images with tip magnetization orientation horizontal, (a) 
Transitions, (b) point source, (c) deconvolved image. 

shown in Fig. 2(a). The image of the approximate point 
source, shown in Fig. 3(b), also becomes dipolelike instead 
of a bell-shaped intensity profile as that shown in Fig. 2(b). 
Using this image of the point source to deconvolve the tran¬ 
sition image in the Fourier space, the resulting magnetic pole 
density distribution is recovered, as shown in Fig. 3(c), al¬ 
most exactly the same as that shown in Fig. 2(c). 

C. Case C: Tip with magnetization canted 

Since in practice, it is difficult to assure that the magne¬ 
tization of the tip is either perfectly vertical or perfectly hori¬ 
zontal, the case of canted magnetization orientation was 
simulated. The canting angle in this case was set at 10° with 
respect to the horizontal. The calculated MFM image of the 
recorded transitions is shown in Fig. 4(a), which is essen¬ 
tially a mixture of Figs. 2(a) and 3(a). Figure 4(b) shows the 
image of the point source. The restored magnetic pole den¬ 
sity distribution is shown in Fig. 4(c). Indeed, it is the same 
as that shown in both Figs. 2(c) and 3(c). The slight differ¬ 
ences among the three restored pole density distributions are 
due to the finite size of the point source as well as the finite 
size of the sensing tip. 

IV. EXPERIMENTAL RESULTS 

Experimental demonstration was performed on a thin 
film longitudinal disk medium recorded with a thin film 
head. The track width was VF^4.5 fim and adjacent transi¬ 
tion separation was B — 2.5 yu-m. The point source was cre¬ 
ated by using the same thin film head used in the recording 
to dc erase the recorded isolated transitions from both sides 
of the track. For analysis on the effect of finite size point 
charge, the residual track width, i.e., the width of the point 





J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Zhu et al. 


6225 



FIG. 4. Calculated images with tip magnetization canted 10° with respect to 
horizontal, (a) Transitions, (b) point source, (c) deconvolved image. 

charge, has been varied. The MFM tip has a magnetic coat¬ 
ing thickness of 40 nm. The lift height of the tip during 
imaging was 60 nm. 

Figure 5(a) shows the raw image of the recorded transi¬ 
tions with a vertically magnetized tip. Approximated point 
charges with various widths were used for image deconvo¬ 
lution. Figures 5(b), 5(c), and 5(d) show the deconvolved 
images for point charges of image widths 0.3, 0.46, and 0.55 



FIG. 5. MFM images with tip magnetized vertically (a) raw image (b)-(d): 
deconvolved images with different size point charges; (b) 0.30 yum, (c) 
0.46/im, (d) 0.55 /nm. 



FIG. 6. MFM images with tip magnetized horizontally (a) raw image (b), 
(c): deconvolved images with different size point charges, (b) 0.30 /im, (c) 
0.55 fim. 


/xm, respectively. For the case with the narrowest point 
charge, the resolution of the features in the deconvolved im¬ 
age is very similar to that in the raw image. Clearly, the 
wider the point charge width, the broader the feature size in 
the deconvolved images. 

The same recorded transitions were imaged with the tip 
magnetized horizontally. The raw image is shown in Fig. 
6(a). The deconvolved images with two different point 
charges of widths 0.3 and 0.55 /xm (image widths), are 
shown as Figs. 5(b) and 5(c), respectively. The effect of 
finite size of the point charge is also evident. 

V. SUMMARY AND REMARKS 

We have experimentally demonstrated the deconvolution 
technique for removing tip dependence in MFM images and 
restoring the raw MFM image to the magnetic pole density 
distribution. By creating a point source on the same sample 
imaged, the impulse response function of the sensing tip can 
be obtained at the same imaging conditions. The technique 
does require that the magnetization of the tip is rigid during 
imaging. If the size of the point source is greater than the tip 
resolution, the resolution of the deconvolved pole density 
distribution will be degraded. 

Since the MFM only senses the stray field from a mag¬ 
netized sample, the formula by Madabhushi et al^ is not 
valid. The divergence free portion of the magnetization M 
could not be recovered by MFM technique. Only the charge 
distribution can be imaged. 

^R. P. Ferrier, S. McVitie, A. Gallagher, and W. Nicholson, IEEE Trans. 
Magn. 33, 4064 (1997). 

^G. P. Heydon, A. N. Farley, S. R. Hoon, M. S. Valera, and S. L. Tomlin¬ 
son, IEEE Trans. Magn. 33, 4059 (1997). 

^S. L. Tomlinson and A. N. Farley, J. Appl. Phys. 81, 5029 (1997). 

"^T. Chang, M. Lagerquist, J.-G. Zhu, J. Judy, P. Fischer, and S. Chou, 
IEEE Trans. Magn. 28, 3138 (1992). 

^R. Madabhushi, R. D. Gomez, E. R. Burke, and I. D. Mayergoyz, IEEE 
Trans. Magn. 32, 4147 (1996). 



JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Quantification of magnetic force microscopy images using combined 
electrostatic and magnetostatic imaging 

R. D. Gomez,®* A. O. Pak, A. J. Anderson, E. R. Burke, A. J. Leyendecker, 
and I. D. Mayergoyz 

Department of Electrical Engineering and Laboratory for Physical Sciences, University of Maryland, 

College Park, Maryland 20742 

A method for calibrating the force gradients and probe magnetic moment in phase-contrast magnetic 
force microscopy (MFM) is introduced. It is based upon the combined electrostatic force 
microscopy EFM and MFM images of a conducting non magnetic metal strip. The behavior of the 
phase contrast in EFM is analyzed and modeled as a finite area capacitor. This model is used in 
conjunction with the imaging data to derive the proportionality constant between the phase and the 
force gradient. This calibration is further used to relate the measured MFM images with the field 
gradient from the same conducting strip to derive the effective magnetic moment of the probe. The 
knowledge of the phase-force gradient proportionality constant and the probe’s effective moment is 
essential to directly quantify field derivatives in MFM images. © 1998 American Institute of 
Physics. [80021-8979(98)27711-5] 


I. INTRODUCTION 


Magnetic force microscopy (MFM) has become a stan¬ 
dard diagnostic workhorse in understanding surface magne¬ 
tism. In its basic implementation, the technique maps an im¬ 
age which is proportional to the local magnetostatic force 
gradient between a ferromagnetic sample and a magnetic 
probe. In an ideal case of a magnetic dipole probe, the force 
is the gradient of the magnetostatic energy, (m-5), and 
the force gradient can be expressed as,^ 


dF^jx^y) 

dz 


3 


= 2 

1=1 


d^Hi{x,y) 

dz^ 


( 1 ) 


The image depends upon the direction of the probe’s mag¬ 
netic moment, and contains the contribution of the different 
components of the surface stray field. In practice, it is cus¬ 
tomary to premagnetize the probe along the surface normal 
direction, £, which makes the contrast proportional to the 
second derivative of the normal magnetic field component. 
By using Eq. (1), it is possible to interpret the images and 
extract the values of some parameters, such as the transition 
lengths and zigzag deviation of recorded patterns, the width 
of the domain wall, and the direction of local surface mag¬ 
netization of ferromagnetic surfaces, as well as other quanti¬ 
ties that are dependent only on the spatial coordinates but are 
independent of the absolute magnitude of the interaction 
force.^ The difficulty in establishing the absolute values of 
the interaction force arises since the proportionality constant, 
Kp, between the measured oscillation phase, and the 
force gradient, 

dF 

(2) 

is dependent upon the specific mechanical characteristics of 
the probe and its environment, and is generally unknown. In 
addition, the probe’s effective magnetic moment, m appear- 


^^Electronic mail: rclgomez@eng.umd.edu 


ing in Eq. (1) is also undetermined. Thus, without the knowl¬ 
edge of these two important probe-dependent parameters, 
Eq. (1) and Eq. (2) can only be taken as qualitative descrip¬ 
tions of the imaging contrast. 

Several research groups have attempted to calibrate the 
probe and provide estimates for tip-sample interaction force. 
Unfortunately, due to space constraints in this article, we 
refer the reader to the literature. Previous approaches have 
involved the imaging of a standardized system, such as a 
metal strip^’"^ or single-crystal surfaces^ or the usage of so¬ 
phisticated methods to measure the magnetic moment of the 
probe and compare the acquired data with various models for 
the probe.^’^ There are, however, no methods that prescribe a 
self-contained calibration procedure of both the probe’s me¬ 
chanical and magnetic characteristics by utilizing only the 
measurements of the instrument itself. In this work, we pro¬ 
pose a straightforward method for estimating Kp and 
thereby allowing a direct quantification of the MFM re¬ 
sponse. The basic concept uses the equivalence of the elec¬ 
trostatic (EFM) and magnetic interactions in generating the 
force gradients on a conducting metal strip. This was accom¬ 
plished by imaging a test sample, an 11 />tm wide Au metal 
line on silicon, using EFM and MFM with the same probe. 

II. EXPERIMENTAL RESULTS AND DISCUSSION 

The relationship between the force gradient and phase in 
Eq. (2) with constant Kp is valid as long as the scanned 
probe microscope (SPM) operates in a linear regime, which 
is tacitly assumed in our analysis. The force, F, could be due 
to either electrostatic or magnetostatic interactions. To deter¬ 
mine Kp , we obtained an EFM image of the test sample by 
biasing the metal structure at voltage V relative to the probe 
at ground and examined the dependence of the phase contrast 
versus bias voltage and height. Note that a regular MFM 
probe was used for this experiment, since the magnetic coat¬ 
ing is also electrically conducting. A typical EFM image is 
shown in Fig. 1 (right), along with a representative cross 
sectional profile. The electrostatic forces are purely attractive 


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© 1998 American Institute of Physics 



J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Gomez, Anderson, and Mayergoyz 6227 



FIG. 1. Right: EFM image of a conducting 11 /urn wide metal strip at V 
= 2 V. Left: MFM image of the same strip with 11 mA current. Bottom: 
Average line profiles across the strip. 


SO that the EFM contrast appears dark in the regions where 
the energized metal structure is present. The electrostatic 
force is a function of the bias voltage, V, as well as its 
capacitance: 




dC 


( 3 ) 


and the force gradient appearing in Eq. (2) can be expressed 
as 


dFl{x,y) ^C(x,y) 

dz ~ '2 

Equation (4) shows that the electrostatic force gradients and 
consequently the EFM images should vary as and its 
curvature and spatial variations are dependent only on the 
capacitance. This is experimentally verified in Fig. 2, which 
shows the acquired images at different voltages and at a con¬ 
stant height. The contrast has been reversed using software in 
order to emphasize the changing magnitude of the force gra¬ 
dient. In this experiment, the same area of the sample was 
continuously scanned at a tip height of 50 nm, as the bias 
voltage was progressively incremented by 100 mV. The val¬ 
ues of the maximum phase contrast in the range from 100 
mV to 2 V is shown at the bottom of Fig. 2. The fit to a 
quadratic function convincingly shows the dependence. 
As mentioned previously, all of the spatial variation in the 
electrostatic contrast is contained in the capacitance term so 
that the coefficient of the quadratic term in the fit is propor¬ 
tional to the second derivative of the capacitance with re¬ 
spect to z. Furthermore, since there are no dielectric materi¬ 
als in the gap region, the capacitance of the system depends 
only upon the geometrical arrangement. 

To model the capacitance of the system, we considered 
the dependence of the image on the separation or the lift 
height, h, between the sample and probe. Figure 3 shows the 
variation of the image contrast at constant voltage, V= 1.8 V, 
as a function of the height, h. As in Fig. 2, the same region 
was imaged repeatedly, as the lift height was incremented to 
the labeled values. The glitch separating each increment is an 
instrumental artifact and arises due to the finite response time 



FIG. 2, EFM contrast dependence on bias voltage. Top: EFM image at a lift 
height of 50 nm with increasing voltage. Bottom: Plot of the maximum 
contrast as a function of voltage, fitted to a quadratic function A(^ 
= 0.19y^ 


of the feedback system. Nevertheless, the log-log plot of the 
maximum phase contrast versus h at the bottom of the image 
clearly shows the strong dependence of the phase image on 
h. The lines are various power law curves, and the best fit to 
the data is The nearly h~'^ dependence suggests 

that the interaction between the sample and probe can be 
modeled as a finite area parallel plate capacitor. 

III. ANALYSIS 

The capacitance for a square parallel plate capacitor can 
be solved using the Schwarz transformation technique^ and 
the second derivative with respect to the separation distance, 
h, is given by 

1 2 \ 

where A is the effective surface area and R is the tip radius. 
In order to relate Eq. (5) with the parameters of the instru¬ 
ment, we assume that the apex of the pyramidal probe can be 
approximated by a square cross section of width yfnR. The 
first term in Eq. (5) is identified with an infinite plate capaci¬ 
tor and the second term is due to the fringing effects 

of the field at the edges. It is clear that as the sample-probe 
separation, h tends to zero, Eq. (5) is dominated by the first 
term. However, the relative contribution of the fringe effects 
increases as 036(hlR), so that the fringing field contributes 
about 36% for R=^h and significantly more for h>R. This is 
precisely the reason why the phase contrast in Fig. 3 follows 
the power law rather than h~^. Substituting Eq. (5) into 


d^C 

-^ = 2€oAX 





6228 J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Gomez, Anderson, and Mayergoyz 



FIG. 3. EFM contrast dependence on lift height. Top: EFM image at a 
constant bias voltage of 1.8 V at varying lift heights. Bottom: Log-log plot 
of the maximum contrast as a function of height. Fit corresponds to 
log|phase|= “ 1.9 log(/i)+3.1; plots for \og{\/h), log(l//z^), and log(l//z^) 
are also shown for comparison. 


Eq. (4), and using the result into Eq. (2), yields the explicit 
expression for the calibration for the parameter, Kp . 

' ' meas' ' ' 

where the numerator is the coefficient of the quadratic term 
of the data in Fig. 2, and the denominator is calculated di¬ 
rectly from the parameters: /? = 40nm, related to the effec¬ 
tive tip curvature, and the lift height, /z = 50 nm. Inserting 
these numbers into Eq. (6) yields Kp = 369 degs/ 
Newtons/m. Using this derived calibration constant, we can 
then calculate the effective probe moment along the z direc¬ 
tion. In this case, we assume for convenience that the probe 
is nominally oriented along the z axis, so that only the z 
component of the surface stray fields contribute to the image. 
Again, we can make use of Eq. (1) and Eq. (2) to show that 


m 


z 




1^ ^Imeas 


/ 


d^Bz 


(7) 


We now image the same current strip at a specific current, 
and measure the change in phase. A representative image is 
shown in Fig. l(left), where the bright and dark contrasts are 
most pronounced at the edges of the strip as expected for the 
maximum normal field component. The field from this non¬ 
ferromagnetic current strip is well known and the field de¬ 
rivatives in Eq. (7) at a distance ofh-50 nm and at a current 
of 11 mA is 5.5X 10^® T/m^. Using this value with the maxi¬ 


mum measured phase of 0.045 degrees in Fig. 1 (left), we 
obtain the effective moment for the probe, m^ = 2.22 
X 10“^^ A m^ (2.22X 10”^^ emu). This value is consistent 
with previous estimates,albeit somewhat lower, which 
could be attributed to differences on the specific probes used. 
As a plausibility check, we can compute the magnetization 
of the probe by dividing with effective magnetic volume. 
If the effective volume is assumed to be that of a half-sphere 
(277/3/?^) with /? = 40 nm (film thickness at 40 nm as well) 
then the magnetization is in excess of 18 000 emu/cc, which 
is much larger than the 400-800 emu/cm^ remanent magne¬ 
tization of the CoCr thin film coating. However, as pointed 
out by previous authors,^ the actual magnetic volume can be 
considerably larger than the volume of the half sphere shell 
at the apex of tip. In this particular case, if the effective 
volume were to include magnetic material up to a distance of 
200 nm from the apex, then we obtain = 586 emu/cc 
which is closer to the expected saturation magnetization of 
the CoCr coating. 

In conclusion, the value of this calibration method is that 
the procedure is self-contained, and that all calibrations are 
derivable from the measurements themselves. It does not ne¬ 
cessitate other sophisticated external measurements nor as¬ 
sumptions about the specific mechanical properties of the 
system. This will save considerable time and effort, and 
avoid the ever present doubt of whether the externally mea¬ 
sured probe characteristics are invariant under actual opera¬ 
tion. The procedure outlined in this paper, however, should 
be considered as an initial step that could be improved con¬ 
siderably. One area for improvement is the replacement of 
the analytical expression for the finite square area capacitor 
model with a more accurate numerical calculation involving 
the actual geometry of the pyramidal apex. This must be 
accompanied by a deconvolution procedure that takes into 
account the vertical excursion of the oscillating in the height- 
dependence measurements. Finally, it should be pointed out 
that while the calibration procedure here is carried out for 
phase-detection, a similar procedure can be performed for 
frequency or amplitude modes of force gradient mapping. 

This work was partially supported by NSF MRSEC and 
ARO Physics Contract No. 36114 PH-RIP. We thank Profes¬ 
sor R. Webb for the samples used. 


^ P. Grutter, H. J. Mamin, and D. Rugar, in Scanning Tunneling Microscopy 
Vol. //, edited by R. Wiesendanger and H.-J. Guntherodt (Springer, Berlin, 
1992), p. 151. 

^R. D. Gomez, E. R. Burke, and I. D. Mayergoyz, J. Appl. Phys. 79, 6441 
(1996). 

^T. Goddenhenrich, H. Lemke, M. Muck, U. Hartmann, and C. Heiden, 
Appl. Phys. Lett. 57, 2612 (1990). 

Babcock, V. Elings, J. Shi, D. D. Awshalom, and M. Dugas, Appl. 
Phys. Lett. 69, 705 (1996). 

^S. Huo, J. E. Bishop, J. W. Tucker, W. M. Rainforth, and H. A. Davies, 
IEEE Trans. Magn. 33, 4056 (1997). 

^G. P. Heydon, A. N. Farley, S. R. Moon, M. S. Valera, and S. L. Tom¬ 
linson, IEEE Trans. Magn. 33, 4059 (1997). 

^R. Proksch, G. D. Skidmorem, E. D. Dahlberg, S. Foss, J. J. Schmidt, C. 
Merton, B. Walsh, and M. Dugas, Appl. Phys. Lett. 69, 2599 (1996). 

^See, for example, R. S. Elliot, Electromagnetics (McGraw-Hill, New 
York, 1996), p. 180. 

^K. Babcock, M. Dugas, V. Elings, and S. Loper, IEEE Trans. Magn. 30, 
4503 (1994). 





JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Magnetic force microscopy using nonopticai piezoeiectric quartz 
tuning fork detection design with applications to magnetic recording studies 

M. Todorovic and S. Schultz®^ 

Department of Physics and Center for Magnetic Recording Research, University of California, San Diego, 

La Jolla, California 92093-0401 

We have developed a novel form of magnetic force microscopy that uses a commercial piezoelectric 
quartz tuning fork to detect magnetic forces and force gradients. Such a detection system is 
extremely simple and inexpensive, compared to conventional optical methods of cantilever vibration 
detection. The setup is, in addition, characterized by small size, which makes it attractive for studies 
done in constrained spaces. The instrument is first described, then theoretical comparison of signal 
to noise ratio and resolution is made with the conventional optical detection techniques of cantilever 
vibration, and finally, first images of thin film media commercial hard disk magnetic bit transitions, 
point response of magnetoresistive elements, and field gradients above the write gap of a 
commercial hard disk head are presented. © 1998 American Institute of Physics. 

[80021-8979(98)28111-4] 


I. INTRODUCTION 

Magnetic force microscopy (MFM)^ has become one of 
the most attractive techniques for studies of microscopic 
magnetic phenomena, and has found especially wide use in 
the commercial hard disk industry.^ The simplicity of the 
technique and minimal sample preparation have furthered 
MFM popularity. In conventional MFM, the magnetic probe 
vibration is monitored by optical means, the most sensitive 
being the fiber optic interferometer.^ We have adapted piezo¬ 
electric quartz tuning forks (PQTF), first introduced by Kar- 
rai and Grober,"^ as inexpensive and simple, nonopticai exci¬ 
tation and detection devices. The design is similar to the 
recent reports for near-held optical microscopy distance 
control,"^"^ and dynamic AFM based on PQTF.^ We hnd 
PQTF are particularly effective for magnetic recording stud¬ 
ies when proper modihcations are made for detection of 
magnetic forces and force gradients. In Refs. 4-6, a tapered 
optical hber is attached to one leg of the piezoelectric tuning 
fork, the tuning fork vibrates parallel to the sample surface, 
and the shear forces between the hber end and the sample 
change the resonant properties of the fork. The signal is then 
mapped with respect to the position over the sample. This 
technique exploits the high Q of the PQTF, and the simplic¬ 
ity of the nonopticai, small sized, one component design. We 
have modihed this setup by attaching a sharp magnetic tip to 
the end face of one of the legs of the PQTF, but vibrating in 
direction perpendicular to the sample, such that magnetic 
forces and force gradients can be imaged. 

II. DESCRIPTION OF THE INSTRUMENT 

To obtain maximum sensitivity of the instrument, we 
used the smallest available quartz tuning forks (Digi-Key 
Corp., Thief River Falls, Mn). The fork legs are 2 mm long, 
200 /mm thick, and 100 /im wide. This corresponds to a value 
of the spring constant, k, of approximately 2000 N/m, which 


®^Electronic mail: sschultz@ucsd.edu 


is an order of magnitude smaller than in previously reported 
shear force or dynamic AFM instruments. The Q is around 
3000 in air and 35 000 in vacuum. To maintain the sensitiv¬ 
ity, the magnetic probe is mounted on the end face of one of 
the tuning fork legs. This serves two purposes: (1) The qual¬ 
ity factor, Q, of such a setup remains within a few percent of 
the initial Q of bare tuning fork, while the resonant fre¬ 
quency is reduced due to the added mass (see Fig. 1); and (2) 
This probe arrangement does not increase the spring constant 
of the tuning fork, thus keeping the sensitivity at a maxi¬ 
mum. In a shear force microscope, due to specific probe 
characteristics, the fiber attachment usually reduces the Q 
from 7000 to 1000 and increases the spring constant, k, due 
to additional stiffness of the glue. Both of these changes 
reduce the sensitivity of the instrument. 

In our tuning fork MFM, the magnetic probe is a sharp 
electrochemically etched nickel wire. Such probes are some¬ 
times used in MFM work after being mounted on a piezo¬ 
electric bimorph and bent with a pair of sharp razors.^ In this 
new method, there is no need for bending the tip, which is 
often the hardest part of making such probes. The probe is 



FIG. 1. Resonance curves for piezoelectric quartz tuning fork in air with and 
without mounted magnetic probe. 

© 1998 American Institute of Physics 


0021-8979/98/83(11 )/6229/3/$15.00 


6229 



6230 J. Appl. Phys., VoL 83, No. 11, 1 June 1998 



FIG. 2. Scanning electron microscope (SEM) images of (a) tuning fork 
MFM and (b) nickel probe. 


mounted, using micromanipulators under an optical micro¬ 
scope, on the end face of one of the legs of the tuning fork, 
which is initially covered with a small drop of glue. In addi¬ 
tion, a small amount of silver epoxy connects the tip to one 
of the gold electrodes of the tuning fork in order to avoid 
electrostatic forces. The probe protrudes 100 to 300 yttm from 
the edge of the tuning fork leg. In this completed form, 
shown in Fig. 2, the MFM sensor’s overall height above the 
sample surface is less than 1 mm, which makes it very con¬ 
venient for use in constrained spaces such as vacuum cham¬ 
bers, or under a lens of an optical or scanning electron mi¬ 
croscope. 

III. SENSITIVITY AND RESOLUTION 
CONSIDERATIONS 

In conventional MFM, the vibration of the cantilever is 
monitored by optical means, and the signal that is measured 
is the second derivative of the field in the vibration direction. 
As the probe is scanned over a surface, the magnetic force 
gradients change the resonant frequency of the cantilever, 
and such change is detected in amplitude, phase, or fre¬ 
quency modulation modes, the last one having the largest 
bandwidth.^ The same physical principles apply in the tuning 
fork MFM design. The tuning fork is driven at the resonant 
frequency of approximately 32 kHz and magnetic force gra¬ 
dients are detected by monitoring the phase change in the 
resonant circuit. The sensitivity of the instrument is limited 
by the thermal noise of the tuning fork oscillator. In such 
case, previous publications have shown that the minimum 
detectable force gradient is proportional to^^ 


M. Todorovic and S. Schultz 



FIG. 3. 5 /imX5 /im scan of hard disk magnetic transitions with 2.8-/Am- 
track width. 

yJk/Qo). 

Since conventional MFM cantilevers and PQTFs operate 
at similar frequencies, the differences between the two de¬ 
signs lie in spring constants and quality factors of the two 
respective mechanical oscillators. Regular MFM cantilevers 
have spring constants between 1 and 10 N/m and Q values of 
about 100 in air and 1000 in vacuum, while smallest tuning 
forks have k values of 2000 N/m and Q value of 3000 in air 
and 35 000 in vacuum. 

The resolution of the MFM is determined by the dimen¬ 
sions and magnetic moment value of the probe, as well as the 
height at which it is scanned. For the highest resolution, 
minimum height is required, and a trade off is made with the 
spring constant to avoid tip crashes during the scan.^^ These 
comparisons make the conventional MFM more sensitive by 
a factor of less than 10, but the tuning fork can be scanned 
closer to the surface due to the larger spring constant. 

IV. RESULTS AND DISCUSSION 

Several types of measurements were done to demon¬ 
strate the usefulness of the simple design of tuning fork 
MFM in magnetic recording studies. The commercial hard 
disk recorded transitions were imaged in air, as shown in 
Fig. 3. The tuning fork was positioned near the sample sur¬ 
face by a vertical mechanical translator. The fork tines were 
vibrating at amplitudes between 25 and 50 nm, as confirmed 
independently by the fiber-optic interferometer^ we use in 
conventional MFM work. The sample was scanned by a high 
precision, linearized piezoelectric stage. The image in Fig. 3 
was taken in the phase mode and the scan range is 5 /mm. As 
expected, the image shows equivalent resolution to the con¬ 
ventional MFM, since the dimensions of the tip are similar. 
The signal-to-noise ratio compared to conventional MFM 
image is lower by an order of magnitude, which is also ex¬ 
pected theoretically due to the larger spring constant of the 
tuning fork. 

In addition to imaging magnetic transitions on hard disk 
media, the tuning fork MFM has also been used for measur¬ 
ing the point response function of commercial magnetoresis¬ 
tive elements, and imaging field gradients above the write 
gaps of commercial heads. ^ The head was placed on the 



J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


M. Todorovic and S. Schultz 6231 




(b) 


FIG. 4. Block diagrams for (a) MR point response measurement, (b) write 
gap imaging. 


sample holder so that the MR element and write gap face the 
tip on the tuning fork as shown in Fig. 4. The tuning fork 
was first driven at resonant frequency while over the MR 
element, thereby providing a magnetic alternating point flux 
source. The driving signal to the tuning fork was used as a 
reference signal for the lock-in amplifier, which monitored 
the signal from the MR element. Simultaneous with monitor¬ 
ing the ac MR element signal, a second lock-in amplifier 
monitored the signal from the resonant tuning fork circuit in 
order to avoid tip crashes during scan. Figure 5 shows the 
resulting image. The specific features of the MR point re¬ 
sponse function were repeatable. 

Alternatively, the inductive write head was driven at the 
resonant frequency of the tuning fork, as shown in Fig. 4(b). 
Alternating field gradients from the gap exerted alternating 
forces on the tip, and the piezoelectric signal from the tuning 
fork was monitored with a lock-in amplifier. Figure 6 shows 
the field gradient gray scale image of the trimmed pole write 
gap. These techniques provide important information about 
MR sensor cross track response, field gradients above the 
gap, and could provide simple and inexpensive diagnosis 
during fabrication of MR heads. 

In conclusion, novel detection technique for magnetic 
force microscopy is described and applications to magnetic 



FIG. 5. 4 /xmX4 fjim scan of point response function of a MR element. 



FIG. 6. (a) SEM image of 3-/im-wide write gap of commercial head and (b) 
20 /LtmX20 fim image of field gradient above the gap. 

recording technology are presented. The technique provides 
an inexpensive, simple, and small sized alternative to con¬ 
ventional MFM. 

ACKNOWLEDGMENTS 

The authors thank George Kassabian, Sam Hobbs, Ray 
Descoteaux, and Mark Vojkovich for technical help, and 
Robert O’Barr and Steven Yamamoto for helpful discus¬ 
sions. This work was supported by the Center for Magnetic 
Recording Research and NSF-DMR-9400439 (MRSEC) 
grant. 

^Y. Martin and H. K. Wickramasinghe, Appl. Phys. Lett. 50, 20 (1987). 
^D. Rugar, H. J. Mamin, P. Guethner, S. E. Lambert, J. E. Stem, I. Mc- 
Fadyen, and T. Yogy, J. Appl. Phys. 68, 3 (1990). 

^D. Rugar, H. J. Mamin, and P. Guethner, Appl. Phys. Lett. 55, 25 (1989). 

Karrai and R. D. Grober, Appl. Phys. Lett. 66, 14 (1995). 

^Y. H. Chuang, C. J. Wang, J. Y. Huang, and C. L. Pan, Appl. Phys. Lett. 
69, 22 (1996). 

®W. A. Atia and C. C. Davis, Appl. Phys. Lett. 70, 4 (1997). 

^H. Edwards, L. Taylor, W. Duncan, and A. J. Melmed, J. Appl. Phys. 82, 
3 (1997). 

^H. J. Mamin, D. Rugar, J. E. Stern, B. D. Terris, and S. E. Lambert, Appl. 
Phys. Lett. 53, 1563 (1988). 

^T. R. Albrecht, P. Grutter, D. Horne, and D. Rugar, J. Appl. Phys. 69, 668 
(1991). 

^^Y. Martin, C. C. Williams, and H. K. Wickramashinghe, J. Appl. Phys. 61, 
4723 (1987). 

^'H. J. Hug, A. Moser, Th. Jung, 0. Fritz, A. Wadas, I. Parashikov, and H. 

J. Guntheridt, Rev. Sci. Instrum. 64, 10 (1993). 

^^G. A. Gibson, S. Schultz, T. Carr, and T. Jagielinski, IEEE Trans. Magn. 
MAG-28, 2310 (1992). 












JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Kerr effect enhancement by photon tunneling and possible application 
to a new scanning probe magnetic microscope 

A. Kikitsu®* and C. M. Falco 

ARUSurface Science Division, The University of Arizona, Tucson, Arizona 85721 

M. Mansuripur 

Optical Sciences Center, The University of Arizona, Tucson, Arizona 85721 

Magneto-optical effects are calculated for the film stack consisting of hemisphere glass/magnetic 
film (10 nm)/air gap (d nm)/glass plate. Polarized light (wave length=800 nm) is irradiated through 
the hemisphere glass in the total internal reflection configuration. A typical amorphous rare 
earth-transition metal alloy is used for the magnetic layer. We find a large monotonic change in the 
figure of merit (product of the reflected amplitude of light and the Kerr rotation angle) as a function 
of the air gap, ranging from 1 to 800 nm. Similar results are obtained for a magnetic film with a 10 
nm Si02 protective layer and for a 1-nm-thin magnetic film. This phenomenon is mostly caused by 
a change in the reflectivity at magnetic film/air interface due to photon tunneling. The difference in 
the figure of merit between perpendicular and longitudinal magnetization is about 0.6®. These results 
imply that it might be possible to obtain an image of perpendicular magnetic moment with photon 
scanning tunnel microscopy (STM). This method can be combined simultaneously with a 
conventional atomic force microscope or STM. © 1998 American Institute of Physics. 
[S0021-8979(98)53511-6] 


I. INTRODUCTION 

In the total internal reflection (TIR) mode, light irradi¬ 
ated from the first medium with refractive index n^ to the 
second medium with ^2 (^i^^a) is completely reflected at 
the boundary,^ and the electromagnetic field in the second 
medium, which is called an evanescent field, decreases ex¬ 
ponentially with the distance from the boundary. However, 
when a third medium with refractive index n i exists close to 
the first medium, the evanescent wave is converted to a 
propagating wave at the second boundary. This phenomenon 
is called photon tunneling.^ The photon scanning tunnel mi¬ 
croscope (STM)^ utilizes this phenomenon. A scanned fine 
tip is used as the third medium, and the morphology of the 
first boundary (distance form the tip) is detected as a change 
in the intensity of the converted light. 

When the incident light is linearly polarized and the first 
medium is a magnetic film, magneto-optical (MO) effect, 
that is, a rotation of the polarization angle, will be observed 
both in the reflected and the converted light and also will be 
changed with the distance from the tip. This leads to a scan¬ 
ning probe magnetic microscope, which has the advantages 
of being sensitive to low magnetization materials and having 
no magnetic interaction between probe and sample. Safarov 
et al reported such a microscope using a pulsed magnetic 
field to a Co thin film sample."^ However, no static magneti¬ 
zation image was reported. A weak MO signal in the con¬ 
verted light appears to be a problem in this microscope sys¬ 
tem. 

In this article, we calculate MO effects in a hemisphere 
glass/magnetic film/air gap/glass plate system in the TIR 


“^Permanent address: Materials and Devices Research Laboratories, Toshiba 
Corporation R&D Center, Kawasaki, Kanagawa 210, Japan. Electronic 
mail: akira.kikitsu@toshibaxo.jp 


condition and estimate them from the view point of the fig¬ 
ure of merit, which corresponds to the detected intensity. 
Then we discuss the possibility of a new scanning probe 
magnetic microscope using the photon tunneling phenom¬ 
enon. 

II. CALCULATION 

Numerical calculations were performed by the program 
MULTILAYER™'"’ with a configuration shown in Fig. 1. This 
program solves Maxwell’s equations at flat interfaces with¬ 
out any approximations. A linearly polarized light (wave¬ 
length 800 nm) irradiated through the hemisphere glass at an 
angle 6 greater than the critical angle. The values of the 
dielectric tensor of a typical amorphous rare earth-transition 
metal alloy with perpendicular and longitudinal magnetiza¬ 
tion were used for the magnetic layer. 

III. RESULTS AND DISCUSSION 

A change in the figure of merit [(FOM): EX E: am¬ 
plitude of light, Oj ^: Kerr rotation angle] of the reflected light 



FIG. 1. Configuration used for the calculations. 


0021 -8979/98/83(11 )/6232/3/$15.00 


6232 


© 1998 American Institute of Physics 



J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Kikitsu, Falco, and Mansuripur 6233 



FIG. 2. Figure of merit (=amplitude of the reflected light vs the air 

gap for glass/MO material (10 nm)/air {d nm)/glass plate. P-polarized in¬ 
cident light and perpendicular magnetization were assumed. 

against the air gap d for ^=60°, 70°, and 80° is shown in 
Fig. 2. The magnetic film is a perpendicular magnetizeid MO 
material with thickness of 10 nm. The incident beam has a 
unit intensity and is p polarized, that is, the direction of the 
polarization is perpendicular to the film surface. Although a 
large more than 2°, is obtained at a couple of specific 
conditions, E tends to be small in such cases, so the FOM is 
small. As can be seen, the FOM increases monotonically 
with decreasing d. For ^=60°, the change in the FOM is as 
large as 0.6°, which is larger than the FOM for the case of 
normal incidence of 0.13°. The result for the longitudinal 
magnetization is shown in Fig. 3. FOM has rather complex d 
dependence but the change in the FOM is less than 0.1. 

It is clear that the detected MO signal almost corre¬ 
sponds to the perpendicular magnetic moment from the re¬ 
sults of Figs. 2 and 3. A difference in the FOM between 
perpendicular and longitudinal magnetization cases is shown 
in Fig. 4, When the direction of an analyzer is set to be 
crossed to that of the polarization for large d case, the signal 
intensity becomes large with decreasing d. Therefore, it 
might be possible to utilize this phenomenon for a new scan¬ 
ning probe magnetic microscope by using a fine glass tip 
instead of the glass plate. 

The change in FOM is caused by the change in the re¬ 
flectivity at magnetic film/air interface according to the ex¬ 
tent of photon tunneling. That is, FOM changes from the 
value of glass/magnetic film/glass configuration {d = Q) to 
that of TIR configuration (J=oo). in the calculation of 
FOM, a contribution of multiple-beam interference within 
magnetic film and air gap is included. When a fine glass tip 
is used for the glass plate in Fig. 1, such an interference does 
not expect to occur. However, FOM change is not thought to 
decrease so much even when the tip completely scatters the 



evanescent wave. FOM from hemisphere glass/magnetic film 
interface is estimated to be +0.1° and that from magnetic 
film/glass interface (<7=0) is estimated to be more than 
0.03° for ^—60°. Since FOM for large d value is indepen¬ 
dent of the occurrence of the scattering, FOM change is ex¬ 
pected to be more than 0.57° for ^=60°. 

Though a possible problem is that almost all of the de¬ 
tected light comes from the area where the tip is not posi¬ 
tioned, this light can be eliminated when the direction of an 



FIG, 4. Difference in FOM between the perpendicular and longitudinal 
magnetization cases for glass/MO material (10 nm)/air {d nm)/glass. 





6234 


J. Appl. Phys., VoL 83, No. 11, 1 June 1998 


Kikitsu, Falco, and Mansuripur 



FIG. 5. The difference in FOM between the perpendicular and longitudinal 
magnetization cases for the case of X=633 nm, for magnetic film with 10 
nm Si02 protective layer and for 1 nm magnetic film. Conditions are 
p-polarized incident, ^=60° and perpendicular magnetization. 

analyzer is set as mentioned above. As for the case of col¬ 
lecting the evanescent wave, large FOM (about 0.3° at maxi¬ 
mum) is obtained but it includes much contribution of the 
multiple-beam interference in air gap and also this method 
has a problem of poor coupling efficiency between photon 
and glass probe. Moreover, our method could employ a 
couple of signal enhancement method such as an ac method 
with photoelastic modulation optics^ or by vibrating the tip. 

Since a tip need not collect the light, a metal tip can be 
used. A change in FOM with air gap for glass/magnetic film/ 
air/Pt is 0.5°. This means that simultaneous measurement of 


magnetization and morphology would be possible by com¬ 
bining our method with a conventional STM or atomic foce 
microscope. 

In order to examine the feasibility of this method, MO 
effects were calculated for various film configurations. Fig¬ 
ure 5 shows the results for 633 nm wavelength, for a mag¬ 
netic film with a 10 nm Si 02 protective layer and for 1 nm 
magnetic film. Similar results to that shown in Fig. 4 are 
obtained. This method is useful for magnetic film with a 
dielectric overcoat and might have the capability for ultrathin 
magnetic film. 

IV. SUMMARY AND CONCLUSION 

A magneto-optical effect for the film stack of hemi¬ 
sphere glass/magnetic film/air gap/glass plate is calculated in 
the total internal reflection condition. It is found that the 
figure of merit (FOM) of reflected light changes monotoni- 
cally as a function of the air gap. This phenomenon is caused 
by the change in the reflectivity at magnetic film/air interface 
due to photon tunneling through the air gap. The monotonic 
air gap dependence of FOM and a FOM difference as large 
as 0.6° between perpendicular and longitudinal magnetiza¬ 
tion are found, so it might be possible to apply this phenom¬ 
enon to a new scanning probe magnetic microscope. 

ACKNOWLEDGMENTS 

This research was supported in part by US DOE Grant 
No. DE-FG03-93ER45488. 

^M. Bom and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 
1993). 

^J. P. Fillard, Near Field Optics and Nanoscopy (World Scientific, Sin¬ 
gapore, 1996). 

^R. C. Reddick, R. J. Warmack, and T. L. Ferrell, Phys. Rev. B 39, 767 
(1989). 

“^V. I. Safarov, V. A. Kosobukin, C. Hermann, G. Lampel, C. Marliere, and 
J. Peretti, Ultramicroscopy 57, 270 (1995). 

^multilayer't^ is a product of MM Research Inc., Tucson, Arizona; also 
see M. Mansuripur, J. Appl. Phys. 67, 6466 (1990). 

^K. Sato, Jpn. J. Appl. Phys. , Part 1, 20, 2403 (1981). 





JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Design and construction of a sensitive nuclear magnetic resonance force 
microscope 

T. A. Barrett, C. R. Miers, H. A. Sommer, K. Mochizuki, and J. T. Markert®> 

Department of Physics, University of Texas, Austin, Texas 78712 

We report our progress in the design and construction of a sensitive and versatile nuclear magnetic 
resonance force microscope. Improvements over previous designs include the use of higher 
(2(12^10^-10'^), single-crystal double-torsional mechanical oscillators for force detection and the 
development of extremely convenient positioning and approach capabilities. We describe both a 
demonstration experiment using large (~1 cm) torsional oscillators and the micromachining of the 
small (~100 ^m) torsional oscillators. © 1998 American Institute of Physics. 

[80021-8979(98)49711-1] 


I. INTRODUCTION 

Recently, Rugar et al ^ have reported the force detection 
of nuclear magnetism. In such an experiment, shown sche¬ 
matically in Fig. 1, the nuclear spins, in a sample mounted 
on a mechanical oscillator, are first polarized in a large static 
magnetic field; the z component of the nuclear magnetism is 
cyclically inverted at the mechanical oscillator resonant fre¬ 
quency by a modulated radio-frequency field from a nearby 
coil. This time-dependent nuclear moment is coupled to the 
field gradient of a nearby permanent magnet, producing a 
resonant force on the mechanical oscillator; the oscillator 
motion is detected with a fiber-optic interferometer. Here, we 
first describe the probe that brings these elements together; 
we then discuss the design sensitivity of this probe. The 
function of the elements is demonstrated using large single¬ 
crystal silicon double-torsional oscillators; finally, the fabri¬ 
cation of the torsional micro-oscillators that will permit the 
ultimate design sensitivity is discussed. 

II. EXPERIMENT 

The experimental probe, contained in a vacuum can, fits 
in a 60-mm-diam variable-temperature cryostat which itself 
is inserted in the bore of an 8.2 T superconducting magnet. 
The bottom of the probe is shown in Fig. 2. Rotary motion 



Tor«loaal Oiclllator 
with Sample 


FIG. 1. Experimental setup for the NMR microscope, including static field 
5o, inhomogeneous field magnet, double-torsional oscillator, rf field coil, 
and fiber-optic interferometer. 


^^Electronic mail: markert@physics.utexas.edu 
0021 -8979/98/83(11 )/6235/3/$15.00 


from outside the probe drives the three mechanical transla¬ 
tors shown, one each for fiber coarse approach positioning, 
oscillator lateral movement, and permanent magnet position¬ 
ing. The piezoelectric elements provide finer adjustments: 
the piezoelectric bimorph swings the fiber optics in and out 



FIG. 2. Probe elements showing manipulation capabilities: three translators 
for coarse positioning, and piezoelectric bimorph, tube, and stack for fine 
positioning. 

© 1998 American Institute of Physics 


6235 















6236 J. Appl. Phys., Vol. 83, No. 11,1 June 1998 


Barrett et al. 



FIG. 3. The single-crystal silicon double-torsional oscillator. In the antisym¬ 
metric mode, most of the energy is in the motion of the head. 


of the plane of the figure, the stack piezo provides fiber optic 
fine positioning, and the tube piezo provides fine positioning 
for the permanent magnet. 

Fiber optic interferometers of similar design have been 
described elsewhere.^ Here, a 675 nm laser diode is coupled 
into one arm of a Gould directional coupler; reflections from 
the cleaved end of the fiber and from the nearby oscillator 
interfere and are sensed by a PAR photodiode, the output of 
which is detected by a lock-in amplifier. For this system, the 
output current at the photodiode is about 20 pA/A; the pho¬ 
todiode noise level is less than 0.2 pA/^/Hz, thus providing a 
motion sensitivity of better than 0.01 A/VHz- 

We refer to Ref. 1 for a discussion of detailed relations 
between the relevant quantities. Here, we specify the param¬ 
eters used in our demonstration experiment: the static field 
was varied (as the permanent magnet approached a paraffin 
sample at the edge of the oscillator) over the range of 8.50- 
8.55 T (8.20 T from the superconducting magnet, and 0.30- 
0.35 T from an iron-wire permanent magnet). An approxi¬ 
mately 20 G rf field was turned on 400 kHz off resonance, 
swept to the NMR frequency of 363.5 MHz over a 0.5 ms 
period, and then frequency modulated at the oscillator 10.3 
kHz frequency with an amplitude of 50 kHz. The static field 
gradient at the sample was approximately 300 T/m. 

For both the demonstration experiment and for the ulti¬ 
mate microscope design, single-crystal double-torsional os¬ 
cillators are used. To understand why, refer to Fig. 3. Re¬ 
sidual losses in single-crystal oscillators occur through 
coupling to the base; typical cantilever modes have a 
<2^ 10^. For a double-torsional oscillator in the antisymmet¬ 
ric mode with a small moment of inertia at the top (the head), 
most of the energy is stored in the head, effectively isolating 
its Q, We routinely obtain Q’s of10^ at room temperature, 
~ 10^ at 77 K, and '^10^ at 4.2 K. For any mechanical os¬ 
cillator, the_theOTe^l sensitivity from thermal noise is 
\l4kksTA v/Qo), where a> and k are the frequency and 
effective spring constant of the oscillator. For our large os- 



FIG. 4. Amplitude of motion of oscillator head during the NMR experiment 
described in the text. 


dilators at room temperature, the measured parameters indi¬ 
cate Fjnin=3X 10“^^ N. However, this produces a motion a 
factor of five smaller than our photodiode detection limit of 
0.01 A/>/Hz; thus the latter sets the noise level. For our small 
oscillators, we predict 2 X 10“ N at 4.2 K; this, how¬ 
ever, will result in a motional amplitude of 0.2 A, well above 
our photodiode limit; thus for the small oscillators, the noise 
is thermally limited. 

In the one-dimensional experiment using the large oscil¬ 
lators, no signal is observed at the lock-in output when the 
spins in the sample are far from resonance. As the magnet 
approaches the sample, there reaches a point where a slice of 
the spins are resonant, of thickness Az = ABI{dB^Idz)} 
where AB^IOG is determined by the frequency modulation 
and the amplitude of the rf field. For our dB^ldz^300 T/m, 
we have Az^7 /xm. Thus for our 2-mm-diam sample, a 
volume of 0.02 mm^ was resonant, corresponding to 
6X 10^^ spins and a moment (via Curie’s law) of 6X 10“^"^ 
J/T, and thus a force of F^MidB^ldz) = 2X 10“^^ N, well 
above our photodiode noise floor. Figure 4 shows a plot of 
the lock-in output as a function of time for a 1.3 s rf pulse; 
the oscillator is seen to ring up to an amplitude of approxi¬ 
mately 0.25 A before decaying back to the noise level of 
approximately 0.01 A, indicating a force of about 3X 10“^^ 
N, quite close to the predicted value. 

For the small oscillators, the moment sensitivity will be 
greatly enhanced, both because of the increased force sensi¬ 
tivity and because much larger field gradients can be used 
(the maximum field gradient simply scales inversely with the 
diameter of the wire). For example, a 100-yum-diam wire will 
produce a field gradient of about 10"^ T/m, implying a resolv¬ 
able moment of 10"^* J/T, or about 10^ proton moments at 
4.2 K. Such NMR sensitivity is unprecendented. 

III. OSCILLATOR FABRICATION 

The oscillators were fabricated by standard photolitho¬ 
graphic and micromachining techniques. The large oscilla¬ 
tors have been described elsewhere.^’^ The small oscillators 
were fabricated as follows: a silicon wafer was masked with 




J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Barrett et al. 


6237 



min to 4 h to recrystallize the damaged silicon and spread the 
profile to any desired thickness up to about 4000 A. The 
annealed wafers were placed in an anisotropic silicon etch 
consisting of 48% H 2 O, 32% ethanol, and 20% KOH for 
about two days. Once the oscillators were fully undercut 
from the substrate, a great impediment to completing the 
fabrication is the drying (surface tension tends to pull the 
oscillators to the substrate). To overcome this, a freeze¬ 
drying technique^ was successfully employed, eliminating 
the surface tension problem completely. Figure 5 shows an 
scanning electron microscopy (SEM) micrograph of the free¬ 
standing single-crystal double-torsional micro-oscillator at¬ 
tached only at the base. Such oscillators are now undergoing 
characterization and testing for use in the NMR microscope. 

ACKNOWLEDGMENTS 

This work was supported by the National Science Foun¬ 
dation under Grant No. DMR-9705414, The Welch Founda¬ 
tion under Grant No. F-1191, and the Texas Advanced Tech¬ 
nology Program under Project No. 003658-339. 


FIG. 5. Scanning electron micrograph of one of the micro-oscillators. 

! 

rows of various sizes of micro-oscillators, typically 150 />tm 
high, and implanted with 134 keV boron ions at a dose of at 
least 1.4X10^^/cm^ to provide an etch stop for the final 
structures. This implant was chosen for a target depth of 
4000 A and initial profile thickness of approximately 1000 
A. The implanted wafers are then annealed at 1000 °C for 15 


^D. Rugar, 0. Ziiger, S. Hoen, C. S. Yannoni, H.-M. Vieth, and R. D. 
Kendrick, Nature (London) 264, 1560 (1994). 

^T. R. Albrecht, P. Griitter, D. Rugar, and D. P. E. Smith, Ultramicroscopy 
42-44, 1638 (1992). 

^A. L. Barr and J. T. Markert, Phys. Rev. Lett. 77, 731 (1996). 

^G. Kaminsky, J. Vac. Sci. Technol. B 3, 1015 (1985); R. N. Kleiman, G. 
K. Kaminsky, J. D. Reppy, R. Pindak, and D. J. Bishop, Rev. Sci. Instnim. 
56, 2088 (1985). 

^H. Guckel, J. J. Sniegowski, and T. R. Christenson, Sens. Actuators 20, 
117 (1989). 











JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Nanocomposite and Film Hard Magnets Fred J. Cadieu, Chairman 


Exchange-spring behavior in epitaxial hard/soft magnetic bilayer films 

J. S. Jiang,Eric E. Fullerton,M. Grimsditch, C. H. Sowers, and S. D. Bader 

Materials Science Division, Argonne National Laboratory^ Argonne, Illinois 60439 

We present results on the magnetic reversal process in epitaxial Sm-Co(lT00)/TM (TM=Fe, Co) 
bilayer films prepared via magnetron sputtering onto Cr-buffered single-crystal MgO substrates. The 
magnetically hard Sm-Co films have 20 T uniaxial anisotropy and coercivities >3 T at room 
temperature. The magnetization of the soft layer is pinned at the interface to the hard-magnet layer 
and switches reversibly as expected for an exchange-spring magnet. With increasing soft layer 
thickness, the coercive field of the hard layer becomes significantly less than that of a single layer. 

We also present numerical solutions to a one-dimensional model that provide the spin configuration 
for each atomic layer. Comparison of the experimental results with the model simulations indicates 
that the exchange-spring behavior of our bilayer films can be understood from the intrinsic 
parameters of the hard and soft layers. © 1998 American Institute of Physics. 

[80021-8979(98)42611-2] 


The exchange-spring magnets, which are composed of 
suitably nano-dispersed hard and soft magnetic phases, have 
been the subject of many recent studies.Exchange inter¬ 
action between the two magnetic phases results in enhance¬ 
ment of the remanence and the energy-product. Although 
future application of exchange-spring magnets will most 
likely be based on nano-dispersed composite geometries,^ to 
obtain greater insights into the coercivity mechanism and 
magnetization reversal process in these materials, it is advan¬ 
tageous to devise a simpler structure with well-defined prop¬ 
erties to isolate the various contributions that are often 
masked by the structural complexities of a random two- 
phase system. Theoretical calculations by Skomski and 
Coey^’^ predicted that, in superlattice structures consisting of 
exchange coupled soft layers and aligned hard-magnet lay¬ 
ers, a giant energy-product of 120 MGOe (about three times 
that of commercially available permanent magnets) is attain¬ 
able. 

It is now possible to fabricate high-quality permanent 
magnet thin films with well-defined crystallographic orienta¬ 
tion and close-to-intrinsic magnetic properties.^ For example, 
epitaxially grown Sm-Co films can have the c axis of the 
hep structure lying in-plane, giving rise to strong uniaxial 
in-plane anisotropy.These films, when incorporated into 
the bilayer structure with transition metal (TM) soft-magnet 
layers, provide a model system in which the magnetization 
rotation process of the exchange-coupled TM layers can be 
studied with the applied field both parallel and perpendicular 
to the anisotropy axis of the hard layer. In this article we 
examine the magnetization reversal processes in epitaxial 
hard/soft Sm-Co(lT00)/TM bilayers (TM=Fe and Co). We 
also use a simple one-dimensional atomic model to simulate 

“taectronic mail: jiang@anl.gov 

'’^Present address: IBM Almaden Research Center, 650 Harry Rd,, San Jose, 
CA 95120-6099. 


the spin profile and the magnetization hysteresis loops. Com¬ 
parison of the experimental results with the model simula¬ 
tions indicates that the exchange-spring behavior can be un¬ 
derstood from the intrinsic parameters of the hard and soft 
layers. 

The Sm-Co(lT 00 )/TM bilayers are grown via dc mag¬ 
netron sputtering onto single-crystal MgO(llO) substrates 
coated with an epitaxial 200 A Cr( 211 ) buffer layer. The 200 
A Sm-Co layers are deposited by co-sputtering from sepa¬ 
rate Sm and Co sources with a nominally Sm 2 Co 7 concen¬ 
tration at a substrate temperature 75=600 ®C as outlined in 
Refs. 9 and 10. The TM layers are then grown at ^5 
= 300-400 °C with thicknesses of 25-200 A and capped 
with a 50 A Cr layer. The magnetic properties were mea¬ 
sured using a 7 T superconducting quantum interference de¬ 
vice (SQUID) magnetometer equipped with both longitudi¬ 
nal and transverse coils, and the longitudinal magneto-optic 
Kerr effect (MOKE) using -polarized, 633 nm light. 

The structural and magnetic characterization of 
Sm-Co(irOO) films grown onto Cr(211) buffer layers are 
described in detail in Ref. 10. The epitaxial relation for the 
Sm-Co(irOO) films is Sm-Co[0001]l|Cr[0lT]|lMgO[001], 
resulting in a uniaxial in-plane structure with the magnetic 
easy axis parallel to the Sm-Co c axis. The films exhibit 
strong uniaxial in-plane anisotropy consistent with the ex¬ 
pected c-axis anisotropy. For H parallel to the Sm-Co easy 
axis (MgO[001]), a square loop is observed with a coercive 
field He of 3.4 T. The coercivity increases to 7.3 T at 25 K. 
For H applied in the orthogonal in-plane direction, a sheared 
hard-axis loop is measured. The anisotropy field, estimated 
from extrapolating the hard-axis loop to saturation, is ^20 T, 
close to the known anisotropy value of bulk Sm-Co. These 
high-quality hard magnetic layers form the basis of this 
study. 

Shown in Fig. 1 are room-temperature easy-axis hyster¬ 
esis loops of the Sm-Co (200 A)/Fe bilayers with different 


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Jiang et al. 6239 



H (T) 

FIG. 1. Room-temperature magnetic hysteresis loops for single layer 
Sm-Co and Sm-Co/Fe bilayer films with different Fe thickness with H 
parallel to the easy-axis directions. The loops are offset vertically for clarity. 


Fe layer thicknesses. For a 25 A Fe layer, a square easy-axis 
loop is measured, indicating that the Fe layer is strongly 
coupled to the underlying Sm-Co film and that the two lay¬ 
ers switch as a unit. As the result of coupling between the 
layers, the coercivity 1.7 T is only '--50% of that of the 
isolated Sm-Co film. For the 100 and 200 A Fe layers the 
loops change shape quite significantly, and separate switch¬ 
ing transitions for the Fe and Sm-Co layers are observed. 
This is similar to that observed in Refs. 11-14 but with 
much thinner soft layers in the present samples. The switch¬ 
ing fields for the Sm-Co layers (0.6-0.7 T) are similar for 
the 100 and 200 A Fe layers and are only 20% of that of the 
isolated Sm-Co film value. The saturation magnetization 
increases with increasing Fe layer thickness. 



FIG. 2. Room-temperature magnetic properties of Sm-Co/Fe bilayer films 
measured by MOKE, (a) Hysteresis loop (solid curve) and recoil curves 
(open circle) measured with H parallel to the easy-axis directions for the 
100 A Fe film, (c) The irreversible magnetization AMj^. vs reverse field 
measured with H parallel to the easy axis. 


Shown in Fig. 2(a) are the hysteresis loop and recoil 
curves for the 100 A Fe layer film measured using the 
MOKE technique. As a result of the finite penetration of the 
light, the MOKE measurements are dominated by the top Fe 
layer. At low reverse fields, the Fe layer is pinned by the 
underlying Sm-Co layer. The Fe layer starts to switch at the 
exchange field T. Above a sharp drop in the 

magnetization occurs as the Fe layer starts to rotate away 
from alignment with the hard layer. The rotation is fully 
reversible since the recoil curves coincide with the demag¬ 
netization curve. At reverse fields >0.5 T, the recoil curves 
deviate from the demagnetization curve as the hard layer 
begins to switch irreversibly and the Fe does not recover full 
remanence on recoil. A quantitative assessment of the irre¬ 
versibility is the irreversible magnetization change AMjn. 
= Mj.—M^{H) where is the remanent magnetization and 
M^{H) the field-demagnetization remanence after recoiling 
from the reversal field H. Shown in Fig. 2(b) is 
as a function of the reverse field. The magnetization is fully 
reversible (AMirj.= 0) up to 0.5 T, where the Sm-Co layer 
switches and AMi^- begins to increase sharply. 

To obtain greater insight into the switching of both the 
soft and hard layers, we use a one-dimensional atomic model 
where the bilayer is treated as a chain of spins normal to the 
layers and each spin is the sum of total moments in an 
atomic layer.^^’^^’^^ The total energy of the system is given 
by: 

A-. "" 

E=-^ cos( - e,- + 1 )- E Ki cos^C (9,) 

1=1 « /=1 

N 

- 2 HMi cos( di-O h), (1) 

i=\ 

where the rotation angle for the iih layer <9, is measured 
relative to the easy-axis direction of the hard layer, is the 
angle between the field and the easy axis, , Kf, Mi, d are 
the exchange constants, uniaxial anisotropy constants, mag¬ 
netic moments, and inter-plane distance (=2 A), respec¬ 
tively. The equilibrium spin configuration for a given field is 
determined by minimizing Eq. (1). To calculate this configu¬ 
ration we employ an iterative approach outlined by 
Camley.^^ Details of the modeling will be published 
elsewhere. 

Shown in Fig. 3(a) is a comparison of the calculated 
Sm-Co/Fe(200 A) demagnetization curves to the ones mea¬ 
sured at 25 K. Included are both the longitudinal and trans¬ 
verse magnetization with respect to the applied field. The 
parameters used in the calculation are, for the hard layer, 
1.2X 10“^ ergs/cm, Kh = 5X 10^ ergs/cm^ 

= 550 emu/cm^; for the soft layer, A^=2.8X 10“^ ergs/cm, 
K^= 10^ ergs/cm^, M^= 1700 emu/cm^, the interface ex¬ 
change constant Aint= 1.8X10“^ergs/cm, and 0ff=3'^. The 
values of and M/j were estimated from magnetization 
measurements on the Sm-Co films. The calculation repro¬ 
duces the Hex value, the field dependence of both the longi¬ 
tudinal and transverse magnetization, as well as the switch¬ 
ing field of the Sm-Co layer at ^1.5 T. The value of 
which is intermediate to the exchange coupling of the hard 
and soft layers, reflects the strong interfacial exchange cou- 






6240 J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Jiang et al. 



FIG. 3. (a) Low-temperature (25 K) demagnetization curves for the Sm- 
Co/Fe(200 A) film compared to the model calculation (solid line). The lon¬ 
gitudinal and transverse components of the magnetization are given by the 
circles and triangles, respectively, (b) Representative spin configuration de¬ 
termined from the model calculation shown in (a). Open circles are Fe spins 
and filled circles are Sm-Co spins. The free Fe surface is located at zero and 
the Sm-Co/Fe interface is at 200 A. 


pling between the layers. With a large interfacial exchange 
energy, the moments in the soft layer near the interface are 
pinned by the hard layer. Shown in Fig. 3(b) is the spin 
configuration at various fields for the calculated magnetiza¬ 
tion in Fig. 3(a). As expected, the distribution of moments is 
consistent with the expectation that the Fe located away from 
the interface rotates more. As H increases, the interfacial 
Sm-Co spin is also increasingly rotated and a domain wall is 
slowly introduced into the hard layer. At a field such that the 
domain wall energy density in the soft layer becomes greater 
than that in the hard layer, the domain wall in the soft layer 
moves into, and switches, the hard layer. ^ 

The temperature dependence of the Sm-Co(200 A)/ 
Co(100 A) bilayer is shown in Fig. 4. At low temperatures, 
separate switching transitions are observed for the Sm-Co 
and Co layers at and respectively. The exchange 
field for the bilayer structure with Co layers is significantly 
higher than that with Fe layers of comparable thickness. This 
behavior arises from the intrinsic magnetic anisotropy of the 
Co layer. The c-axis Co anisotropy stabilizes the Co layer 
either parallel or antiparallel to the Sm-Co film and results 
in an enhanced Co switching field. The Co layer reverses by 
nucleating a 180°-domain wall. As long as the Sm-Co does 
not switch, the is given by the requirement that the en¬ 
ergy cost (y) in creating a domain wall be balanced by the 
gain in Zeeman energy i.e., //ex“ where t is 

the Co layer thickness. A rough estimate gives T, 

in reasonable agreement with the experiment. The exchange 
field //ex remains rather temperature-insensitive whereas the 
//jn- decreases with increasing temperature, suggesting that 
the hard layer switches via some thermally assisted reverse 
domain nucleation and wall de-pinning. At temperatures 
above 250 K, square easy-axis loops are observed as the 
Sm-Co and Co layers switch simultaneously a nucleation 
field 



I ■ ■ I _I_I I 

- 3 - 2-10 1 2 3 

H (T) 



FIG. 4. (a) Easy-axis hysteresis loops for the Sm-Co(200 A)/Co(]00 A) 
measured at different temperatures, (b) The switching fields plotted as a 
function of temperature. 


In conclusion, we have presented the experimental re¬ 
sults on strongly exchange-coupled Sm-Co(l 100)/TM bi¬ 
layer films. The magnetically hard Sm-Co layers have an 
in-plane uniaxial anisotropy field as large as 20 T. The mag¬ 
netization of the soft TM layer is pinned at the interface to 
the hard-magnet layer and switches reversibly as expected 
for an exchange-spring magnet. Our model calculation using 
intrinsic parameters gives quantitative agreement with the 
experimental data. 

This work was supported by the U.S. Department of En¬ 
ergy, Basic Energy Sciences-Materials Science, under Con¬ 
tract No. W-31-109-ENG-38. 


^E. F. Kneller and R. Hawig, IEEE Trans. Magn. 27, 3588 (1991). 

^J. Ding, P. G. McCormick, and R. Street, J. Magn. Magn. Mater. 124, LI 
(1993). 

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75, 6646 (1994). 

^I. A. Al-Omari and D. J. Sellmyer, Phys. Rev. B 52, 3441 (1995). 

^T. Schrefl, H. F. Schmidts, J. Fidler, and H. Kronmuller, IEEE Trans. 
Magn. 29, 2878 (1993). 

^R. Skomski and J. M. D. Coey, Phys. Rev. B 48, 15 812 (1993). 

^R. Skomski, J. Appl. Phys. 76, 7059 (1994). 

^J. M. D. Coey, Solid State Commun. 102, 101 (1997). 

^E. E. Fullerton, C. H. Sowers, J. Pearson, S. D. Bader, X. Z. Wu, and D. 
Lederman, Appl. Phys. Lett. 69, 2438 (1996). 

^^E. E. Fullerton, J. S. Jiang, C. Rehm, C. H. Sowers, S. D. Bader, J. B. 
Patel, and X. Z. Wu, Appl. Phys. Lett. 71, 1579 (1997). 

Mibu, T. Nagahama, and T. Shinjo, J. Magn. Magn. Mater. 163, 75 
(1996). 

'^D. Givord, J. Betz, K. Mackay, J. C. Toussaint, J. Voiron, and S. Wiich- 
ner, J. Magn. Magn. Mater. 159, 71 (1996). 

^^S. Wiichner, J. C. Toussaint, and J. Voiron, Phys. Rev. B 55, 11 576 
(1997). 

Suzuki, R. B. van Dover, E. M. Gyorgy, J. M. Phillips, and R. J. 
Felder, Phys. Rev. B 53, 14 016 (1996). 

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2951 (1965). 

’^R. E. Camley, Phys. Rev. B 35, 3608 (1987). 

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Phys. Rev. B (submitted). 







JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Magnetization reversal of Nd(Dy)-Fe-B thin films on Si(111) or Ta/Si(111) 

J. L. Tsai, T. S. Chin,®* and E. Y. Huang 

Department of Materials Science & Engineerings Tsing Hua University, Hsinchu 300, Taiwan, 

Republic of China 

S, K. Chen 

Department of Materials Science, Feng Chia University, Taichung 407, Taiwan, Republic of China 

Nd(Dy)-Fe-B films were prepared by dc magnetron sputtering on a Si(l 11) wafer with or without 
a Ta underlayer. The reversal magnetization process of Nd-Fe-B/Ta bilayer was found to be 
dominated by nucleation control model with the magnetic inhomogeneity coefficient a^=0.32 
defined by Kjonmuller’s formulation of micromagnetic theory. But the coercivity mechanism of 
Nd(Dy)-Fe-B single layer was fitted well to domain wall pinning behavior. The range factor (half 
width between pinning sites) tq is equal to 6.9 nm as rf>dg, the width of the domain wall. The 
magnetization phenomena of the two films are also manifest from initial magnetization curves. 

© 1998 American Institute of Physics. [80021-8979(98)42711-7] 


L INTRODUCTION 

Nd”Fe-B films have been prepared by thin film pro¬ 
cesses such as magnetron sputtering, molecular beam epi¬ 
taxy, and pulsed laser deposition. These films have poten¬ 
tial applications in microelectronics or the micro¬ 
electromechanical system (MEMS) due to the high energy 
product possible even down to a nanometer scale. The mag¬ 
netic properties depend mainly on microstructure, thus the 
growth technologies, texture control, and microstructure 
studies of Nd-Fe-B films have attracted much attention.^" 

Magnetization reversal of Ndi 5 Fe 77 B 8 sintered magnets 
and Nd-Fe-B melt spun ribbons has been studied in detail 
by Kronmuller using the micromagnetic model,and by 
Hadjipanayis using the Gaunt model, respectively. But that 
of Nd-Fe-B thin films has not been studied in-depth so far 
due mainly to the difficulty in structure control and the in¬ 
terface problems. 

In this article we applied Kronmuller’s formulation to 
study the coercive mechanism of the sputtered Nd(Dy)- 
Fe-B films with or without the Ta underlayer, which has 
been reported to exhibit exchange interaction between the 
interface. 

II. EXPERIMENT 

Nd(Dy)-Fe“B films, with a thickness of 324 nm, with 
or without a Ta underlayer (30 nm) were prepared by dc 
magnetron sputtering carried out in a vacuum chamber with 
a background pressure of 5X10“^ Torr. A commercial 
Ndi 2 Dy 3 Fe 77 B 8 target and a pure Ta foil, with a diameter of 
3.3 cm each, were used. The distance between the target and 
the substrate was 10 cm. High purity argon (99.999%) was 
used as a sputtering gas and the working pressure was 8 
X10“^Torr during sputtering. The Nd(Dy)-Fe-B films 
were deposited at room temperature and post annealed in a 
high vacuum (1X10“^ Torr) with a temperature between 
480 and 600 °C. The phases of films were analyzed by x-ray 


^^Electronic mail: tschin@mse.nthu.edu.tw 


diffraction (XRD). The thickness of each film was measured 
using an a-step thickness probe. The surface roughness of 
the films was measured with an atomic force microscope 
(AFM). The initial magnetization curves and magnetic hys¬ 
teresis loops with different applied fields were measured 
with a vibrating sample magnetometer (VSM) at room tem¬ 
perature. The magnetic properties of the films were also mea¬ 
sured at 5-400 K by a superconducting quantum interference 
device (SQUID) magnetometer under a maximum field of 55 
kOe. 

The coercive mechanism was studied by using the modi¬ 
fied Brown’s micromagnetic theory. 

III. RESULTS AND DISCUSSION 

A. Microstructure study 

Figure 1 shows the x-ray diffraction patterns of Nd(Dy)- 
Fe-B films with or without Ta underlayer. All peaks are 
attributed to R 2 Fei 4 B single phase (refer to JCPDS file 39- 
0473, where R is the rare-earths) for both the (Nd,Dy) 2 Fei 4 B 
single layer and the (Nd,Dy) 2 Fei 4 B/Ta bilayer. The Ta dif¬ 
fraction cannot be found because of its extreme thinness, 
about 30 nm. The (Nd,Dy) 2 Fei 4 B peaks are rough and broad¬ 
ened due to the fine grain structure resulting from the lower 
annealing temperatures at 480-520 °C for 10 min. 

To make a quantitative surface morphology, the root 
mean square surface roughness was taken by an AFM to be 
4.8 and 8.9 nm, respectively, for the films with or without Ta 
underlayer. Samples with roughness below 10 nm appear to 
have a mirrorlike smoothness which is good for application 
in lithography. 

B. Initial magnetization curves 

Figure 2 shows magnetic hysteresis loops of films with 
or without the Ta underlayer measured parallel to the film 
plane. The coercive force of the (Nd,Dy) 2 Fei 4 B single layer 
and the (Nd,Dy) 2 Fei 4 B/Ta bilayer are 14.0 and 11.3 kOe, 
respectively, while the squareness ratio of the bilayer, 0.72, 
is higher than that of the single layer, 0.62. The shape of 


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26 


FIG. 1. X-ray diffraction patterns of sputtered (Nd,Dy) 2 Fei 4 B films on 
Si(III). 


hysteresis loops changes as the magnetization field is in¬ 
creased. Initial magnetization curves of the (Nd,Dy) 2 Fei 4 B 
film with or without the Ta underlayer exhibit two different 
magnetization reversal processes; that of 
(Nd,Dy) 2 Fei 4 B/Si(lll) film, sustaining nearly the same 
width before a sharp ascent, is dominated by the domain- 
wall pinning,while that of the bilayer shows neither a 
nucleation nor a wall-pinning control process, as shown in 
Fig. 2(a). Thus further testimony was carried out by the mi¬ 
cromagnetics approach. 


C. Testimony of the magnetization reversal model 

According to the well-known micromagnetic approach, 
the relationship between coercivity {He) and the ideal nucle¬ 
ation field {Hn) is given by Brown’s formula^^ 

(i) 

Here a is a form factor and //„ equals correspond¬ 

ing to the ratio between the first anisotropy constant and 
spontaneous magnetization, respectively. A^gff means effec¬ 
tive local demagnetization factor. A modified relationship 
about form factor a has been derived from the micromagnet¬ 
ics theory by Kronmuller,^^’^"^’^^ describing the reduction in 
nucleation field due to (1) the misalignment of grains ; 
and (2) the magnetic inhomogeneity coefficient ajt i.e., a 

IM ,-. (2) 

For the studied Ndi 2 Dy 3 Fe 77 B 8 films, the R 2 Fei 4 B hard mag¬ 
netic phase possesses Ki values from negative to positive in 
the temperature range 5-400 K. The temperature dependent 
coercive force of the films could be delineated in two parts: 



Ha(kOe) 

FIG. 2. Hysteresis loops of (Nd,Dy) 2 Fej 4 B films at different applied fields. 


one below the spin reorientation temperature (T^r—135K) 
and the other above it. Three temperature ranges are 
distinguishable:^^ 

(i) In the temperature range of 5-135 K: {Ki<0,K2>0) 



0 1 2 3 4 5 6 

2K, a 

FIG. 3. He!Ms vs for the sputtered (Nd,Dy) 2 Fei 4 B film with 

Ta underlayer. 







J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Tsai et al. 


6243 



FIG. 4. HcIMg vs for the sputtered (Nd,Dy) 2 Fei 4 B film with¬ 

out Ta underlayer. 


1 (^ ^ SisTjCtan <5)“ ^ 

cos (5[ 1 + (tan \ ^ J5r,[ 1 + (tan S )^^]/ ’ 

where S is replaced by ^=^+0 for /sri<0. Without the ex¬ 
ternal field, the easy magnetization direction deviates from 
the c axis by an angle 0 =arcsin(-Ari/ 2 ^ 2 )^^. if spin reori¬ 
entation occurs for ^i<0/^ 

In the temperature range of 135-298 K: 

{K,>0,K2>0-K2<K^<AK2) 

_ A{K, + K^) 11 K, 

” 3M, \?> eK^] * 

In the temperature range of 298-400 K: 

{K,>K2.K2>0) 

H, = 2K,IM, (4) 

_ 1 / 2>K2{i^vi \ 

cos 9 [H-(tan \ A^i[l + (tan 

where (p is the angle between the c axis of neighboring 
grains. The is equal to 0.5 for isotropic Nd(Dy)-Fe-B 
thin films. 

As indicated in Eqs. (3) and (4), in both case 
vs He!Ms should be fitted in a straight line for a nucleation 
control magnet. The plot of HnCx^/Ms vs /M^ is shown in 

Fig. 3. The linearized slope is the value of , which in this 
case is measured to be 0.32, being larger than the critical 
value of 0.30. The effective demagnetization field N^ff is 
obtained as 0.45. This means that the coercive mechanism of 


Nd(Dy)-Fe-B film with the Ta underlayer is dominated by 
the nucleation control model. By using Eq. (2'), the fitting of 
//„ /Ms vs He /Ms is also a line but with a negative N^ff that 
is out of physical meaning. The data of Nd(Dy)-Fe-B film 
without the Ta underlayer were also fitted by Eqs. (3) and 
(4). 

By measuring magnetic properties of Nd(Dy)-Fe-B 
single layer film from 5 to 400 K, a linear plot of H^/Ms vs 
IKa^/M] was obtained as shown in Fig. 4. The magnetic 
inhomogeneity coefficient is measured to be 0.12. This 
value is less than the critical value of 0.3. Therefore, the 
magnetization reversal of the Nd(Dy)-Fe~B single layer 
film is determined by domain-wall pinning. A magnet with a 
thick pinning region of (ro>^ 5 ) should have an a value of 
(2^5/37rro), where Tq is a range factor (half-width between 
pinning sites). The reported data of domain wall width 
was equal to 3.9 nm for the Ndi 5 Fe 77 Bg sintered magnet.^^ 
The calculated value of Tq is 6.9 nm. 

ACKNOWLEDGMENT 

The authors are grateful for the partial support of this 
project by the National Science Council of the Republic of 
China under Grant No. NSC87-2216-E007-043. 

^D. J. Keavney, E. E. Fullerton, J. E. Pearson, and S. D. Bader, IEEE 
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J. Magn. Magn. Mater. 127, 289 (1993). 

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Magn. Magn. Mater. 82, 48 (1989). 

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Mater. 148, 426 (1995). 

Hu, X. C. Kou, and H. Kronmuller, Phys. Status Solidi B 188, 807 
(1995). 

Hu, X. C. Kou, and H. Kronmuller, Phys. Status Solidi A 138, K41 
(1993). 

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Phys. Status Solidi A 137, 227 (1993). 

^^G. C. Hadjipanayis, J. Appl. Phys. 63, 3310 (1988). 

J. L. Tsai, E. Y. Huang, S. K. Chen, and T. S. Chin, IEEE Trans. Magn. 
33, 3646 (1997). 

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291 (1988). 

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JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Phase formation and magnetic properties of Co-rare earth magnetic films 

Y. Liu 

Center for Materials Research and Analysis, and Department of Mechanical Engineering, 

University of Nebraska, Lincoln, Nebraska 68588-0656 

Richard A. Thomas, S. S. Malhotra, Z. S. Shan, S. H. Liou, and D. J. Sellmyer 

Center for Materials Research and Analysis, and Behlen Laboratory of Physics, University of Nebraska, 

Lincoln, Nebraska 68588-0111 

Co-Sm and Co-Pr films were deposited by dc magnetron sputtering. Transmission electron 
microscopy and magnetic measurement were used to study the micro structure and magnetic 
property relationship. The nanostructure of the as-deposited Co 19 at. % Sm films consists of two 
phases: the amorphous phase and the crystallite phase. Upon annealing at 600 °C, the Co 5 Sm phase 
with the CusCa structure, having grain size of about 20 nm, is obtained along with high coercivity 
(45 kOe). The as-deposited Co 22 at. % Sm films also have nanostructure similar to the Co 19 at. % 
films except the volume fraction of the crystallite is reduced. This is related to the concentration of 
Sm which promotes the formation of the amorphous phase. A new metastable phase Co 3 Sm is 
formed upon annealing of the Co 22 at. % Sm film at 500 °C. This phase has the DO 19 structure in 
which the Sm atoms take ordered positions of a triangular pattern in the close-packed planes. A 
relatively high coercivity value of 29 kOe was obtained from this phase. The as-deposited Co-Pr 
films show mainly an amorphous phase. Upon annealing at 500 °C for 20 min, Co 2 Pr with the 
Mg 2 Cu-type structure was identified in the Co 35 at. % Pr film. Two phases were identified in the 
Co 16 at. % Pr films. Coercivities up to 3.1 kOe were achieved in these films. © 1998 American 
Institute of Physics. [S0021-8979(98)30611-8] 


I. INTRODUCTION 

Hard and semihard Co rare earth films are of increasing 
interest for magneto-electronic and magnetic-recording ap¬ 
plications. The Co-Sm and Co-Pr systems also have high 
Tc suitable for high temperature magnets. A number of ar¬ 
ticles on the Co-Sm and Co-Pr systems have been 
presented. The magnetic properties of materials can be 
divided into intrinsic properties and extrinsic properties. The 
intrinsic properties such as magnetization are related to the 
crystal structure of the magnetic phase while the extrinsic 
properties such as coercivity are affected by the microstruc¬ 
ture. Development of new magnetic materials involves the 
search for new magnetic phases and the design of micro¬ 
structure. In this article we report our detailed study on phase 
formation, micro structure, and magnetic properties relation¬ 
ship in films based on the Co-Sm system and Co-Pr system 
heat treated at different temperatures. 

II. EXPERIMENTAL PROCEDURE 

For the Co-Sm system, the films were deposited by dc 
magnetron sputtering. Two compositions near the Co 5 Sm 
and Co 7 Sm 2 were selected. All films have a Cr underlayer of 
about 90 nm except the one with the composition of Co 19 
at. % Sm annealed at 600 °C which is deposited on a quartz 
substrate. All the films have a Cr cover layer of about 10 nm. 
For the Co-Pr system multilayers of Co-Pr/Co films were 
deposited using a multiple-gun dc and rf sputtering chamber. 
The multilayer microstructure is designed to promote mag¬ 
netic hard phase and soft phase coupling in order to gain 
maximum energy product. A 50 nm underlayer and a 10 nm 


cover layer of Cr were used for film seeding and protection. 
Plan-view transmission electron microscopy (TEM) samples 
were prepared by dimpling and ion milling process. TEM 
study was conducted using a JEOL 2010 transmission elec¬ 
tron microscope. 

III. RESULTS AND DISCUSSION 

The deposition parameters, film thickness, coercivity, 
and phase identification results are summarized in Table I. 


D 



2 


0.004 > 

^ ^ ^ 

Cr(80nm)/SmCo( 

* "" 1 ■ 1 

264nm)/Cr(10nm) . 

0.002 - 

■ ■ 

■ 

■ 

■ 

■ 

■ 

■ 

-1->- 

■ 

■ 

■ 

. 


■ 

■ 

1 

■ 


! 

■ 

■ 

-0.002 - 

■ 

■ 


■ 

■ 

B 



. ■ 

.0 004 - 

-1---^---1 

H=45kOe - 
c 

L——'- \ -^ n - 


H(kOe) 


FIG. 1. Magnetization loop of the CojSm film annealed at 600 ®C. 


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© 1998 American Institute of Physics 






J. AppL Phys., Vol. 83, No. 11, 1 June 1998 


Liu et a/. 


6245 


TABLE I. Composition, deposition condition, nanostructure, and magnetic properties relation in Co-Sm and 
Co-Pr films. C indicates crystallite phase and A amorphous phase. Vc is the volume fraction of the crystallite 
phase against the amorphous phase. 


Film com. 

(at. %) 

Ar pressure 
(mTorr) 

Film thickness 
(nm) 

Phases 

-Vc 

(%) 

Grain size 
(nm) 

Coercivity 

(kOe) 

Co 19 at. % Sm 

5 

24 

C+A 

91 

5 

0.61 

Co 19 at. % Sm 

12 

24 

C+A 

65 

5 

2.58 

Co 19 at. % Sm 

30 

24 

C+A 

54 

5 

0.92 

Co 19 at. % Sm 







Annealed at 600 °C 

20 

360 

Co5Sm 

(CusCa) 

100 

20 

45 

Co 22 at. % Sm 

5 

30 

C+A 

81 

5 

1.2 

Co 22 at. % Sm 

17 

30 

C+A 

57 

5 

4.1 

Co 22 at. % Sm 

30 

30 

C+A 

48 

5 

3.4 

Co 22 at. % Sm 







Annealed at 500 °C 


394 

DOi9 

100 

15 

29 

I 2 T 1 I 


a 

100 


12021 



100 
90 J 



FIG. 2. (a) Comparison of SAD pattern and calculated intensity distribution FIG. 3. (a) Comparison of SAD pattern and calculated intensity distribution 

for the film described in Fig. 1. (b) TEM image of the microstructure. for the Co 22 at. % Sm film, (b) TEM image of the microstructure. 







6246 J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 

The nanostructure of the as-deposited Co 19 at. % Sm films 
has been studied in earlier work^ and is included here for 
comparison. Upon annealing at 600 the equilibrium 
phase Co 5 Sm with the Cu 5 Ca structure is obtained along 
with high coercivity. Figure 1 shows the magnetization loop. 
Coercivities up to 45 kOe were achieved. Figure 2 shows the 
selected area diffraction (SAD) pattern and TEM micro¬ 
graph. The diffraction shows perfect match with the calcu¬ 
lated intensity. The grain size is about 20 nm. 

The Co 22 at. % Sm films also have a nanostructure 
similar to the Co 19 at. % films except the volume fraction of 
the crystalline against amorphous phase is reduced. This is 
related to the concentration of Sm which promotes the for¬ 
mation of the amorphous phase. Figure 3 shows the SAD 
pattern and the TEM image of the Co 22 at. % Sm film 
annealed at 500 °C. A new phase Co 3 Sm is formed as indi¬ 
cated by the matching of the TEM pattern and calculation. 
This phase has the DO 19 structure in which the Sm atoms 
taking the ordering positions of a triangular pattern in the 
close-packed planes. The close-packed planes are stacked by 
the sequence of ABAB in the c direction. A relatively high 
coercivity value of 29 kOe was obtained from this phase. 

The appearance of the DO 19 structure is not a surprise 
but rather easy to comprehend. In the as-deposited Co-Sm 
films, the structure of the crystallite is the close-packed struc¬ 
ture with Sm atoms randomly distributed in the close-packed 
planes and short range packing order in the c direction. Upon 
annealing, two things happened: one is that the Sm atoms 
within each close-packed plane form a triangular ordering 
pattern, and the second is that the packing in the c direction 
takes the long range ABAB packing. The lattice parameters 
deduced from this phase are a - 0.256 nm c — 0.419 nm com¬ 
pared to the lattice parameters of Co = 0.2505 nm, 0.4065 
nm. It is interesting to note that the lattice parameters be¬ 
tween the DOi 9 phase and the Co phase are close to each 
other, suggesting a low energy state at the interphase. It is 
suggested that two-phase structure composed of Co and 
DOi 9 phase could be stable up to 500 ''C. 


Liu et al. 

The as-deposited Co-Pr films show largely amorphous 
phase. Upon annealing at 500 ®C for 20 min, Co 2 pr of the 
Mg 2 Cu-type structure was identified in the Co 35 at. % Pr 
film. Two phases were identified in the Co 16 at. % Pr films. 
Coercivities up to 3.1 kOe were achieved in these films. 

IV. CONCLUSIONS 

Three metastable phases were found in the sputtered 
Co-Sm films: the amorphous phase, the close-packed hex¬ 
agonal phase with different stacking mode in the as- 
deposited film, and the DO 19 structure phase in the film an¬ 
nealed at 500 °C. 

Corresponding to the different phases and microstruc¬ 
ture, the coercivities change from about 1-42 kOe. Maxi¬ 
mum coercivity was achieved from the Co 5 Sm phase with 
the Cu^Csl structure. The new metastable phase of DO 19 
structure found in the Co 22 at. % Sm film also showed 
relatively high coercivity of 29 kOe. 

ACKNOWLEDGMENTS 

The authors wish to thank Xueli Zhao for preparing the 
TEM samples. The TEM work was performed at the Central 
Facility for Electron Microscopy operated by CMRA. This 
research is sponsored by the U.S. Department of Energy, 
Grant No. DE-FG-02-86ER45262, National Science Founda¬ 
tion, Grant No. DMR-9623992, National Storage Industry 
Consortium, and CMRA. S. H. Liou is supported by the U.S. 
Army Research Office, Grant No. DAAG55-98-1-0014. 

‘ Y. Liu, B. W. Robertson, Z. S. Shan, S. Malhotra, M. J. Yu, S. K. Renuku- 
nta, S. H. Liou, and D. J. Sellmyer, IEEE Trans. Magn. 6, 4035 (1994). 

^Y. Liu, D. J. Sellmyer, B. W. Robertson, Z. S. Shan, and S. H. Liou, IEEE 
Trans. Magn. 31, 2740 (1995). 

^S. S. Malhotra, Y. Liu, Z. S. Shan, S. H. Liou, D. C. Stanford, and D. J. 
Sellmyer, J. Magn. Magn. Mater. 161, 316 (1996). 

^E. M. T. Velu and D. N. Lambeth, IEEE Trans. Magn. 28, 3249 (1992). 

^K. Chen, H. Hegde, S. U. Jen, and F. J. Cadieu, J. Appl. Phys. 73, 5923 
(1993). 



JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


High coercivity SmCo based films made by pulsed laser deposition 

F. J. Cadieu R. Rani, X. R. Qian, and Li Chen 

Department of Physics, Queens College of CUNY, Flushing, New York 11367 

Films of SmCo based materials exhibiting high intrinsic coercivities and smooth hysteresis loops 
have been prepared by pulsed laser deposition (PLD) onto moderately heated substrates. Films 
directly crystallized from SmCo 5 targets onto 375 °C substrates exhibited a maximum 
= 11.3 kOe at a pulse repetition rate of 10 Hz with lower coercivities for both lower and higher 
pulse repetition rates. In the present case the films were deposited onto polycrystalline substrates. 

The films exhibited a very small grain size of less than 1 ^tm diameter, were mirrorlike, and shadow 
deposited films were relatively particulate free under scanning electron microscope examination. 
Shadowed PLD deposition was used for the best films. Laser wavelengths of 193 and 248 nm were 
used with pulse repetition rates from 5 to 50 Hz. Films grown without shadowing exhibited a great 
deal of particulate contamination. The hysteresis loops of such nonshadowed films were constricted 
and exhibited drops in the 477M values upon demagnetization. To our knowledge this is the first 
reporting of high coercive force SmCo based films deposited by PLD exhibiting single phase type 
hysteresis loops. © 1998 American Institute of Physics, [S0021-8979(98)42811-l] 


INTRODUCTION 

High coercivity films of SmCo based systems have been 
deposited by sputtering by several distinct variants. Highly 
textured polycrystalline films have been made by using sput¬ 
ter process control to grow films at thicknesses out to at least 
120 Such films have the crystalline c axes nearly 

randomly aligned onto the substrate plane. Buffer layers are 
j necessary to grow relatively thick films but in principle ar¬ 
bitrarily thick films of highly aligned SmCo deposits can be 
grown by this method. In contrast to this, highly aligned thin 
films with thicknesses of less than 0.1 /mm have been grown 
by using substrate film epitaxy.^’^ The thicker films as grown 
by sputter process control are generally more suited to device 
applications. Such relatively thicker films as grown by sput¬ 
ter process control have been used to bias to saturation YIG 
substrates,"^ to bias permalloy films,^ and in the construction 
of a film based magneto-optic waveguide isolator.^ In this 
latter device the textured SmCo films were grown directly 
onto compliant layers directly deposited onto a Bi-YIG op¬ 
tical waveguide so that epitaxy could not have been used to 
grow such films. Film scale magnetic devices generally em¬ 
ploy a magnetically sensitive material such as a magnetore¬ 
sistive material, a superconducting film element, or a mag¬ 
netic field sensitive optical material. In addition soft 
magnetic films are used as flux paths with permanent magnet 
films used as magnetic biasing elements. Many of the mag¬ 
netically sensitive types of materials have been readily de¬ 
posited by pulsed laser deposition (PLD). Such films include 
high oxide superconductors, ferrites, and magnetoresis¬ 
tive materials such as the La manganites. It should be noted 
that these are oxide materials which are generally difficult to 
sputter deposit with controlled texturing and at appreciable 
deposition rates. To illustrate the differences in PLD and 
sputter deposition we have made SmCo based magnetic films 
by PLD. Although the time averaged deposition rates of 


^^Electronic mail: Fred_Cadieu@QC.EDU 


Sputter and PLD deposited films are comparable, material is 
ejected in PLD only during a series of pulses of very short 
time duration compared to the time between pulses.^ This 
means that the relative mobility of deposited surface atoms is 
very much less for PLD than for sputtering since a complete 
monolayer can be deposited per pulse. The growth of PLD 
deposited permanent magnet films also has direct impact on 
the fabrication of film scale magnetic devices. There have 
been only a few reportings of rare earth transition metal films 
as grown by PLD and mostly confined to Nd 2 Fei 4 B.^^ 

EXPERIMENT 

PLD, utilizing a Lambda Physik 305Fi excimer laser, 
has been used to deposit SmCo based films from a set of 
bulk compound targets. Films have been deposited using 
wavelengths of 248 and 193 nm, pulse energies of 500-650 
mJ at 5-50 Hz with an estimated pulse width of 15 ns. A 
shadow mask has been used to shield part of the substrate 
during the PLD process. In this manner the magnetic prop¬ 
erties, as well as the number of particulates reaching the 
substrate in and out of the shadow region, could be observed. 
Most of the films discussed here have been grown using a 
substrate temperature ranging from 100 to 750 °C in argon 
pressures from 100 to 240 mTorr. Film compositions were 
determined using electron excited x-ray analysis in a scan¬ 
ning electron microscope (SEM). The film composition mea¬ 
surements were calibrated against known bulk composition 
standards. 

RESULTS AND DISCUSSION 

SmCo based films deposited by PLD in the absence of 
any shadowing onto heated alumina substrates exhibited a 
strong dependence of Sm concentration on the argon back¬ 
ground gas pressure in the deposition chamber. Figure 1 
shows the Sm concentration for a series of films deposited 
onto polished alumina substrates at 375 °C from SmCo 5 tar¬ 
gets, and at 500 °C from SmCo “2-17” targets, as a func- 


0021 -8979/98/83(11 )/6247/3/$15.00 


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© 1998 American Institute of Physics 


6248 


J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Cadieu et al. 


24 


20 

on 

16 


12 

0 20 40 60 80 100 

Ar Pressure (mTorr) 

FIG. 1. The Sm at % for a series of PLD films made on to 375 °C substrates 
from bulk SmCos targets, and films made on to 500 °C substrates from bulk 
SmCo “2-17” targets, for different Ar pressures during the deposition is 
shown. 


SmCo^ Target T. Sub. 375 



/ 

/"2-ir Target T. Sub. 500 “C 



tion of Ar gas pressure. The targets in the latter case con¬ 
sisted of normal bulk type “2-17” magnet material with a 
composition of Sm 13 at %, Co 58%, Fe 20%, Cu 7%, and 
Zr 2%. Under vacuum conditions the film Sm concentration 
corresponded to that of the targets. Films made under 
vacuum, however, exhibited a large number of particulates 
causing such films to be unattractive for film device applica¬ 
tions. During sputtering large concentration changes can also 
be effected by using increased sputtering gas pressures and 
in particular admixtures of Xe as a part of the sputtering 
gas.^ Changes in the sputtering gas pressure could be used to 
vary the film composition from 12 to 18 at %.^^ Higher pres¬ 
sures tend to preferentially scatter the lower mass transition 
metal atom components relative to the more massive Sm 
atoms. The net effect is that the lighter transition metal atoms 
are on the average scattered through larger angles and effec¬ 
tively removed from the deposition beam. Higher pressures 
in the deposition chamber tend to enrich the Sm concentra¬ 
tion in the films. 

Room temperature hysteresis loops measured in plane 
and perpendicular to the plane are shown in Fig. 2 for a 
shadow region film deposited at 375 °C and 100 mTorr Ar at 
a laser wavelength of 193 nm with a pulse rate of 14 Hz. The 
PLD target was bulk SmCos. The in plane was 9.7 kOe 
and the loop shape was characteristic of single phase mate¬ 
rial. It should be noted that there is no retracing of the in 
plane hysteresis loop to the highest measurement magnetic 
field of 18 kOe. An x-ray diffraction pattern for the film of 
Fig. 2 is shown in Fig. 3. The evident CaCu 5 -type structure 
(110) dominant texturing and (111) secondary CaCu 5 -type 
shoulder are consistent with the relative shapes of the in 
plane and perpendicular to the plane hysteresis loops. 

Films of SmCo based materials made without the use of 
a shadow mask exhibited an appreciable density of particu¬ 
lates on the substrate. Films made in vacuum, 1.8 
X 10~^ Torr, on to 550 °C substrates exhibited a small grain 
size of 0.17-0.30 /xm diameter. The particulates tended to be 
of two principal sizes, ^0.33 /xm diameter for the small 
ones, and ^0.83 ytxm diameter for the larger ones. The par¬ 
ticulate density for nonshadowed films increased with pres¬ 
sure even though the number density of the larger sized par- 



FIG. 2. Room temperature hysteresis loops for a shadow deposited PLD 
film made from SmCo 5 target at 375 °C on to alumina substrate, pressure 
100 mTorr Ar, pulse rate 14 Hz arc shown. The key items to note are that 
the intrinsic coercivity is 9.7 kOe and that the loop shape is smooth. 


ticulates remained nearly constant. Nonshadowed films made 
at 500 °C and 30 mTorr Ar exhibited an average particulate 
density of 0.21//xm^, similar films except at 75 mTorr Ar 
exhibited 0.33//xm^. In order to limit the number of particu¬ 
lates arriving at the substrate a stainless steel sheet metal 
shadow was located in the deposition plume to block the 
direct transport of particulates to the substrate. A higher 
background gas pressure of argon was then required to scat¬ 
ter the atoms to reach the substrate. The shadow mask strip 
was arranged midway between the target and substrate so 
that the shadow blocked a 13X50 mm substrate region. 

Figure 4 shows hysteresis loops for a SmCo based film 
shadow deposited at a substrate temperature of 375 °C in 100 
mTorr Ar at a laser pulse rate of 10 Hz. The in film plane ///^ 
was 11.3 kOe. The film surface was mirrorlike which is dif¬ 
ferent from directly crystallized textured SmCo films grown 
onto alumina films by sputtering. The smooth mirrorlike sur¬ 
face was consistent with a small average grain size. The 



FIG. 3. An x-ray diffraction trace for the film of Fig. 2 is shown which 
indicates (110) dominant and (111) secondary texturing. The x ray is in¬ 
dexed as CaCus-type structure film. The substrate lines from the polycrys¬ 
talline AI 2 O 3 are indicated by S in the figure. 






J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Cadieu et al. 


6249 



FIG. 4. Room temperature hysteresis loops are shown for a PLD film de¬ 
posited from bulk SmCos target at 375 °C, pressure 100 mTorr Ar, shad¬ 
owed deposition. The laser settings were 193 nm, 600 mJ pulses, 10 ns pulse 
width, and 10 Hz. 


shadow deposited films replicated polish marks on the under¬ 
lying substrate that made it difficult to determine a film grain 
size. The deposit in the shadow region was particulate free. 

To study the effects of surface atom mobility a series of 
films were deposited from bulk SmCos targets in 100 mTorr 
Ar onto substrates held at 375 using X==193 nm for dif¬ 
fering pulse repetition rates from 5 to 50 Hz. This is shown 
in Fig. 5 where the jH^ values versus laser pulse rate are 
shown for a series of films shadow deposited under the same 
conditions except for the laser pulse repetition rate. The 
higher pulse rates result in low coercivities due to insuffi¬ 
cient time between pulses for surface atom site adjustments. 



FIG. 5. The coercivity vs laser pulse rate is shown for a series of films 
shadow deposited from SmCos bulk targets using \=193 nm, T substrate 
= 375 °C, and F= 100 mTorr Ar. The values shown were measured at room 
temperature on as deposited films. 


In this series the highest coercivity of 11.3 kOe was obtained 
for a pulse rate of 10 Hz. The hysteresis loops for films made 
at laser pulse rates between 10 and 20 Hz were offset in the 
initial magnetization direction since the maximum applied 
field of 18 kOe was insufficient to achieve saturation. Lower 
pulse rates resulted in low coercivities believed to be caused 
by surface gas contamination due to the longer times be¬ 
tween successive pulses. 

A key result of this article is that it has been possible to 
produce SmCo films directly by shadowed PLD onto slightly 
heated substrates with coercivities up to 11.3 kOe at 10 Hz 
as a function of the laser pulse repetition rate. Higher laser 
pulse rates did not allow sufficient site relaxation between 
pulses, while lower pulse rates lead to film contamination 
because of the longer time between deposition pulses. An 
operative deposition condition is that ^ItIR —const-d, where 
T is the absolute substrate temperature with the surface atom 
speed proportional to ^JT, d is the site relaxation distance, 
and l/R is the time between laser pulses for the pulse rate R. 
Higher laser pulse rates can then only be fruitfully used at 
higher substrate temperatures where the surface atom mobil¬ 
ity is increased to provide site relaxation before the surface is 
buried by the deposit from the next laser pulse. At higher 
substrate temperatures the film reactivity with contaminating 
background gases is expected to increase so that higher sub¬ 
strate temperatures would require lower background gas 
pressures. 

ACKNOWLEDGMENTS 

The PLD system was purchased with NSF-ARI Grant 
No. STI-9512308, and with partial support from the NYS 
Graduate Research Initiative. This work was supported in 
part by the U.S. Army Research Office, Grant No. DAAH04- 
94-G-0079, and in part by the Office of Naval Research, 
Grant No. ONR N00014-96-1-0767. Some support was also 
derived from the PSC-CUNY Faculty Research Award Pro¬ 
gram of CUNY. 

^F. J. Cadieu, H. Hegde, and K. Chen, IEEE Trans. Magn. MAG-25, 3788 
(1989). 

^F. J. Cadieu, “Permanent Magnet Thin Films,” in Physics of Thin Films 
(Academic, San Diego, 1992), Vol. 16. 

^ F. J. Cadieu, in Magnetic Materials, Processes, and Devices IV, edited by 
L. T. Romankiw and D. A. Herman, Jr., Proc. Electrochem. Soc. (Elec¬ 
trochemical Society, Pennington, NJ, 1996), paper PV 95-18, pp. 319- 
335. 

"^F. J. Cadieu, H. Hegde, E. Schloemann, and H. J. Van Hook, J. Appl. 
Phys. 76, 6059 (1994). 

^E. E. Fullerton, C. H. Sowers, J. P. Pearson, S. D. Bader, X. Z. Wu, and 
D. Lederman, Appl. Phys. Lett. 69, 2438 (1996). 

^E. E. Fullerton, J. S. Jiang, C. Rehm, C. H. Sowers, S. D. Bader, J. B. 
Patel, and X. Z. Wu, Appl. Phys. Lett. 71, 1579 (1997). 

^H. Hegde, S. U. Jen, K. Chen, and F. J. Cadieu, J. Appl. Phys. 73, 5926 
(1993). 

*M. Levy, R. M. Osgood, Jr., H. Hegde, F. J. Cadieu, R. Wolfe, and V. J. 
Fratello, Photonics Technol. Lett. 8, 903 (1996). 

^D. H. Lowndes, D. B. Geohegan, A. A. Puretzky, D. P. Norton, and C. M. 
Rouleau, Science 273, 898 (1996). 

’‘^H. Lemke, C. Echer, and G. Thomas, IEEE Trans. Magn. 32,4404 (1996). 
^^E, J. Cadieu, H. Hegde, and K. Chen, Thin Solid Films 193/194, 857 
(1990). 





JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Mechanism of composition change in sputter deposition 
of barium ferrite films with sputtering gas pressure 

E. Suzuki and Y. Hoshi®> 

Faculty of Engineering, Tokyo Institute of Polytechnics, Atsugi, Kanagawa 243-02, Japan 

M. Naoe 

Tokyo Institute of Technology, Meguro-ku, Tokyo 152 Japan 

In this study, we used computer simulation to investigate changes in the composition of hexagonal 
barium ferrite films with sputtering gas pressure obtained by the sputter-deposition processes. The 
iron content in the film deposited by facing target sputtering increased as the sputtering gas pressure 
increased and reached a maximum value at a certain gas pressure. These changes in the film 
composition were explained as follows: sputtered particles scatter when they collide with sputtering 
gas atoms, and this scattering changes the ratio of the particles reaching the substrate. When the 
substrate was located to the side of the target, as in a facing target sputtering system, this scattering 
resulted in an increase in the amount of sputtered particles arriving at the substrate, although too 
much scattering caused the amount to decrease. When a magnetron sputtering system is used for the 
film preparation, this gas scattering leads to a decrease in the amount of sputtered particles arriving 
at the substrate which is located opposite the target. Since this gas scattering depends significantly 
on the atomic mass of the sputtered particles, the gas pressure dependence of the amount of iron 
atoms arriving differs considerably from that of the amount of barium atoms arriving. This 
difference leads to the changes in film composition, © 1998 American Institute of Physics. 
[80021-8979(98)46311-4] 

I. INTRODUCTION 

A hexagonal barium ferrite (BaM) thin film with excel¬ 
lent magnetic properties cannot be obtained unless the film 
composition is controlled precisely.^ In the sputter deposition 
of barium ferrite films, however, the film composition 
changed significantly when the deposition conditions 
change,^ mainly because high-energy particles, produced 
from negative oxygen ions emitted from the target, bombard¬ 
ing the film surface caused the composition of the film to 
differ from that of the target material.This high-energy 
particle bombardment of the film surface was eliminated in 
facing target sputtering (FTS), which resulted in only a small 
change in film composition.^ 

The iron content in a BaM film deposited by a FTS 
system, however, increases with an increase in sputtering gas 
pressure, reaches a maximum at a certain gas pressure, and 
decreases with further increases in the gas pressure. To ex¬ 
plain these changes in the film composition with sputtering 
gas pressure, we carried out a computer simulation of the 
sputter deposition processes and found that changes in the 
film composition with sputtering gas pressure were mainly 
caused by the scattering that occurs when sputtered particles 
in the space between the target and substrate collide with the 
atoms of the sputtering gas. 

In this article, we will show the mechanisms of the com¬ 
position changes caused by the scattering of sputtered par¬ 
ticles through the collisions with sputtering gas atoms in FTS 
and in conventional magnetron sputtering. 


“taectronic mail: hoshi@ee.t-kougei.ac.jp 


II. SIMULATION OF TRANSPORT PROCESS IN 
SPUTTERING 

A facing target sputtering system and a magnetron sput¬ 
tering system were assumed to be used for the film deposi¬ 
tion (Fig. 1). The trajectory of each of the sputtered particles 
emitted from the target was calculated and the amount of 
sputtered particles deposited on the substrate was estimated. 
This transportation of the sputtered particles was calculated 
according to the model reported by Motohiro^ and Turner.^ 
The emission angles of sputtered particles from the target 



Magnetron sputtering system 


10cm 


Target 



Center 


Substrate 


Facing target sputtering system 


FIG. 1. Target-substrate arrangement in the sputtering systems simulated in 
this study. 


0021 -8979/98/83(11 )/6250/3/$15.00 


6250 


© 1998 American Institute of Physics 





J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Suzuki, Hoshi, and Naoe 


6251 



(a) facing target sputtering (FT^ 



Ar gas pressure [mTorr] 

(b) magnetron sputtering 

FIG. 2. Relation between sputtering gas pressure and the amounts of iron 
and barium atoms arriving at the substrate, (a) is obtained for the FTS, and 
(b) is obtained for the magnetron sputtering system. 



(a) facing target sputtering (FTS) 



(b) magnetron sputtaing system 

FIG. 3. Changes in the arrival ratio of iron atoms to barium atoms with 
sputtering gas pressure, (a) is obtained for FTS, and (b) is obtained for the 
magnetron sputtering. 


were assumed to follow cosine law. The energy distributions 
of iron atoms emitted from the target were assumed to be 
emitted from pure metal iron, and calculated by using Tomp¬ 
son’s model.^ The energy of primary ion which bombards 
the target surface was assumed to be 780 eV. For barium 
atoms, the following parameters were used in calculating the 
energy distribution; atomic number, 56; atomic mass, 137.3; 
atomic radius, 2.22 A; length between atoms, 4,35 A; bond¬ 
ing energy (Ba02), 8.4 eV in the Tompson’s model.^ Gas 
temperature during sputtering was assumed to be 673 K. In 
the simulation, one million atoms were emitted from the tar¬ 
get and the amount of particles incident on the substrate was 
calculated at various sputtering gas pressures. It should be 
noted that the sputtering gas, iron, and barium, differ consid¬ 
erably in terms of both atomic radius and atomic mass. 

III. RESULTS AND DISCUSSIONS 

Figure 2 shows simulated examples of the amount of 
iron atoms and barium atoms arriving at the substrate in the 
magnetron sputtering and in the FTS. The amount of atoms 
arriving in Fig. 2 was normalized by the value obtained with¬ 


out gas scattering. It should be noted that the amount of 
atoms arriving in the FTS increases as the sputtering gas 
pressure increases. On the contrary, the amount of atoms 
arriving in magnetron sputtering decreases as the sputtering 
gas pressure increases. This increase in the FTS and decrease 
in the magnetron sputtering are explained as follows: in a 
facing target sputtering system, the substrate is located to the 
side of the target as shown in Fig. 1. In this target-substrate 
arrangement, scattering of the sputtered particles because of 
collisions with sputtering gases leads to an increase in the 
amount of sputtered particles arriving at the substrate. Too 
much scattering which will occur at a higher gas pressure, 
however, causing the amount to decrease. 

In the magnetron sputtering system, the scattering causes 
a decrease in the amount of both iron and barium arriving at 
the substrate as the sputtering gas pressure increases, since 
the substrate is located opposite the target. 

It should also be noted that the gas pressure dependence 
of the amount of iron atoms arriving at the substrate differs 
remarkably from that of barium atoms. This is mainly due to 
the different atomic masses of iron and barium. These differ- 





6252 J. AppL Phys., Vol. 83, No. 11, 1 June 1998 


Suzuki, Hoshi, and Naoe 



FIG. 4. The amount of iron atoms arriving during sputtering in Ar, Kr, and 
Xe in FTS. 

ences in the amount of deposition particles arriving should 
cause the film composition to change. The ratio of the 
amount of the iron atoms to barium atoms arriving at the 
substrate (arrival ratio) is equivalent to the composition of 
the deposited film, when the sticking probability is unity. 
Figure 3 shows the changes in the arrival ratio with sputter¬ 
ing gas pressure in the FTS Fig. 3(a) and in the magnetron 
sputtering system Fig. 3(b). The arrival ratio of iron to 
barium estimated from the composition of barium ferrite 
films deposited by the FTS is also shown in Fig. 3(a). The 
arrival ratio at 2 mTorr was assumed to be 1. The iron con¬ 
tent in the film deposited by FTS increases as the sputtering 
gas pressure increases, and reaches a maximum at a certain 
gas pressure. It is clear from the figure that these changes in 
the arrival ratio obtained from the simulation qualitatively 
agree with experimental results. 

On the other hand, the arrival ratio of iron to barium in 
the magnetron sputtering system decreases monotonically as 
the sputtering gas pressure increases, since the amount of 
arriving iron atoms decreased more steeply than did the 
amount of barium atoms. This indicates that the iron content 
in the film should decrease as the sputtering gas pressure 



FIG. 5. The amount of barium atoms arriving during sputtering in Ar, Kr, 
and Xe in FTS. 



Sputtering gas pressure(mTorr) 

FIG. 6. Arrival ratio of iron atoms to barium atoms sputtered in Ar, Kr, and 
Xe in FTS. 

increases, if the high-energy particle bombardment of the 
film surface is eliminated during deposition. However, dis¬ 
tinguishing the composition change due to the gas scattering 
of sputtered atoms was difficult, since the high-energy par¬ 
ticle bombardment of the film surface during deposition was 
not eliminated in this sputtering system. 

When other sputtering gases (such as Kr and Xe) are 
used in place of Ar, the gas pressure dependence of the 
amount of iron and barium atom arriving will differ signifi¬ 
cantly from that observed in sputtering using argon gas. This 
difference will result in changes in the pressure dependence 
of the film composition. Figures 4 and 5 show examples of 
the amounts of iron and barium atoms arriving during sput¬ 
tering in various gases in the FTS. It is clear from the figure 
that the gas pressure where the amount of atoms arriving 
takes a maximum value shifts to a lower gas pressure area as 
the mass of sputtering gas increases. From these results, the 
changes in film composition with the changes in sputtering 
gas pressure, shown in Fig. 6, can be derived. The 
sputtering-gas-dependent changes in film composition should 
thus be taken into consideration to obtain a film with the 
desired composition. 

IV. CONCLUSIONS 

The transportation of sputtered particles from the target 
to the substrate was investigated. The scattering of sputtered 
particles by collision with the sputtering gas was found to 
play an important role in changing the film composition. In 
addition, it should be noted that this gas scattering effect will 
lead to a quite different gas pressure dependence of the film 
composition when the arrangement of target and substrate in 
the sputtering systems is changed. 

^M. Matsuoka, Y. Hoshi, M. Naoe, and S. Yamanaka, IEEE Trans. Magn. 

18, 1119 (1982). 

^M. Naoe, S. Hasunuma, Y. Hoshi, and Y. Yamanaka, IEEE Trans. Magn. 

17, 3184 (1981). 

^T. Motohiro, J. Vac. Sci. Techno). 4, 189 (1986). 

"^G. M. Turner, I. S. Falconer, B. W. James, and D. R. McKenzie, J. Appl. 

Phys. 65, 3671 (1989). 

^M. W. Thompson, Philos. Mag. 18, 377 (1968). 







JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Magnetic and structural properties of high coercivity Sm(Co, Ni, Cu) 
sputtered thin films 

C. Prados®' and G. C. Hadjipanayis 

Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716 

The effects of heat treatments on the structural and magnetic properties of Sm(Co, Ni, Cu) sputtered 
thin films were investigated. Crystallization of the initially amorphous magnetic films produces a 
huge enhancement of coercivity (from 100 Oe to more than 40 kOe). The crystallized structure 
consists of exchange coupled precipitates in the nanometers range. The pinning of the magnetization 
reversal at the high anisotropy grains is proposed as the origin of such a magnetic behavior. By 
tuning the coercivity through the annealing conditions, these systems could be used in a number of 
applications, from longitudinal recording media to thin film permanent magnet. © 1998 American 
Institute of Physics, [80021-8979(98)46411-9] 


I, INTRODUCTION 

In the last years, SmCo/Cr bilayers films have been pro¬ 
posed as an attractive candidate for ultrahigh density record¬ 
ing media. The main driving force for the use of rare-earth 
based alloys is to attain a recording density as high as 10-20 
Gb/in^. In general, modifications of the SmCos composition 
have been used due to its high coercivity and large magnetic 
anisotropy. In order to obtain appropriate microstructure and 
crystallographic orientation in these films, extensive studies 
have been carried out using different deposition conditions 
and underlayer materials."^ 

On the other hand, the CaCu 5 type compounds, 
SmCo 5 _;^.Ni;f and SmCo 5 _;fCu^ are known to exhibit huge 
values of coercivity due to the so-called giant intrinsic mag¬ 
netic hardness.In spite of the number of studies related to 
the properties of the bulks alloys, only a few are reported on 
thin films. In this article, the structural and magnetic proper¬ 
ties of SmCo 5 , SmCo 2 Cu 3 , and SmCo 2 Ni 3 thin films depos¬ 
ited by dc magnetron sputtering on a Cr underlayer are stud¬ 
ied in the as-deposited state and after subsequent heat 
treatments. The different microstructures which have been 
obtained lead to a wide range of coercivity values, which 
make these compounds suitable for a variety of applications, 
from longitudinal recording media to thin film permanent 
magnets. 

II. EXPERIMENT 

Sm(Co, Ni, Cu)/Cr bilayers were deposited on water 
cooled Si substrates with a dc magnetron sputtering system. 
Ar at a pressure of 5 mTorr was used as discharge gas. The 
Cr underlayers were deposited from a pure (99.9%) solid Cr 
target. The Sm(Co, Ni, Cu) targets were pressed powder type 
with nominal compositions SmCo 5 , SmCo 2 Cu 3 , and 
SmCo 2 Ni 3 . The deposition rates were 1.25 A/s for Cr and 6 
A/s for Sm(Co, Ni, Cu) and were calibrated by low angle 
x-ray diffractometry (XRD). The thickness of the Cr under¬ 
layer and the Sm(Co, Ni, Cu) film were 300 and 500 nm, 
respectively. The role of the Cr underlayer is to promote a 


^^Electronic mail: celso@fresno.csic.es 


c-axis texture along in plane directions in the Sm-Co film in 
order to increase its in-plane magnetic anisotropy."^ The bi¬ 
layers were annealed in a vacuum of better than 10“^ Torr at 
a constant temperature for 30 min. Different pieces of the 
same as-deposited sample where submitted to this heat treat¬ 
ment, ranging the annealing temperature for each piece from 
400 to 650 ®C. Each heat treatment has been labelled with 
the characteristic annealing temperature. The structural prop¬ 
erties were determined by XRD. Room temperature hyster¬ 
esis loops were measured with a superconducting quantum 
interference device (SQUID) magnetometer at a maximum 
applied magnetic field of 55 kOe. Principal remanence 
curves were measured at room temperature using a vibrating 
sample magnetometer. 

III. RESULTS AND DISCUSSION 

The high angle XRD diagrams of the samples showed 
the (110) peak as the single line from the Cr, and revealed 
that the Sm(Co, Ni, Cu) layers were amorphous in the as 
deposited state. After subsequent heat treatments, the amor¬ 
phous hallow around the position corresponding to the 
SmCo 5 (111) line started to evolve into a broad nanocrystal¬ 
line peak with an increasing relative intensity. Figure 1 
shows the crystalline grain size for the layers of composi¬ 
tions SmCo 2 Cu 3 and SmCo 2 Ni 3 as a function of the anneal¬ 
ing temperature. Grain size has been determined from the 
full width at half maximum through the Scherrer’s formula. 
The values are around 20 nm for SmCo 2 Ni 3 and 10 nm for 
SmCo 2 Cu 3 . The effect of the increasing annealing tempera¬ 
ture was to increase the Sm-Co crystallized fraction rather 
than change the grain size, which slightly grew with the an¬ 
nealing temperature. Preliminary transmission electronic mi¬ 
croscopy studies showed that the nanocrystallites are embed¬ 
ded in an amorphous matrix. 

Figure 2(a) shows the evolution of coercivity with the 
annealing temperature for the three compositions. All of 
them exhibit low coercivity in the as deposited state, because 
of their amorphous structure, which increases more than two 
orders of magnitude with the heat treatment. The hardening 
starts at 515 °C for the case of SmCo 5 and at 450 ®C for 
SmCo 2 Ni 3 and SmCo 2 Cu 3 . The highest value of coercivity 


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(D 

N 

U) 

• S 

cd 

cl5 


20 A 


12 H 


SmCo Ni 

2 3 


SmCo Cu 

2 3 


-a 


T («C) 

ami 



FIG. 1. SmCo 2 Cu 3 and SmCo 2 Ni 3 grain size as a function of the annealing 
temperature. Grain size has been determined from the width of the (111) 
SmCo 5 line using Scherrer’s formula. 


has been of 42 kOe for the SmCo 2 Cu 3 composition, annealed 
at 550 °C for 30 min (note that coercivity has been deter¬ 
mined at room temperature and with a maximum applied 
field of only 55 kOe). Coercive fields larger than 20 kOe 
have been obtained for the other two compositions. These 
values are comparable, and even much larger in the case of 
SmCo 2 Cu 3 , than those reported in epitaxial oriented Sm-Co 



FIG. 2. Evolution of coercivity (a) and relative remanence (b) with the 
annealing temperature in the films SmCo 2 Cu 3 , SmCo 2 Ni 3 , and SmCos. 
Both coercivity and relative remanence have been obtained measuring hys¬ 
teresis loops with a maximum applied field of 55 kOe. 


FIG. 3. SM plots of the sample with composition SmCos at two represen¬ 
tative annealing conditions, 535 (low coercivity) and 550 °C (high coerciv¬ 
ity). SM(H) has been obtained from the isothermal magnetization curve, 
My{H) and the dc demagnetization Mj{H) through the expression dM 


films measured along the hard axis.^ Relative remanence 
(remanent moment divided by the magnetic moment at the 
maximum applied field) is displayed in Fig. 2(b) for the three 
compositions at the different annealing temperatures. In the 
highest coercivity range the relative remanence is around 
0 . 8 . 

No steps are observed in the measured hysteresis loops 
over the range of annealing conditions and subsequent struc¬ 
tures. This is indicating that, in spite of the different amor¬ 
phous and crystalline phases present in the films, they be¬ 
have magnetically coupled. This point is more deeply 
analyzed through the principal remanence curves. 

SM plots have been constructed from the principal re¬ 
manence curves measured for the three compositions at dif¬ 
ferent annealing conditions (for the definition of the principal 
remanence curves and SM plots see, for instance, Ref. 8). 
Figure 3 shows SM plots for the SmCo 5 sample at two rep¬ 
resentative annealing conditions, 535 °C where the sample 
still exhibits a low coercivity, and 550 °C in the high coer¬ 
civity range. The positive values of the SM are interpreted to 
result from magnetizing interaction between the particles 
(exchange coupling). The maximum value of the SM plot 
does not change substantially with the annealing tempera¬ 
ture, indicating that the strength of the interaction between 
particles is independent of the coercivity. Similar behavior is 
observed in the other two compositions, intergrain interac¬ 
tion is always magnetizing and of the same order for the 
different crystallization stages. 

The structural and magnetic characterization described 
above provides insight on the outstanding magnetic proper¬ 
ties exhibited by these samples. In the as deposited and low 
temperature annealing stages, the magnetic layers are basi¬ 
cally amorphous with low coercivity. A nanocrystalline 
structure is developed with the higher temperature heat treat¬ 
ments, with the grain size being rather independent of the 
annealing temperature. The particles are exchange coupled 





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C. Prados and G. C. Hadjipanayis 6255 


through the remaining ferromagnetic matrix. The huge en¬ 
hancement of coercivity may be related to the strong hin¬ 
drances of the magnetization reversal due to domain wall 
pinning at the high anisotropy Sm-Co precipitates. The pin¬ 
ning effectiveness improves with the density of crystallites 
giving rise to such an enhancement of coercivity at annealing 
temperatures around 500-550 °C. 

IV. CONCLUSION 

SmCo 5 /Cr and giant intrinsic magnetic hardness com¬ 
pounds Sm(Co, Ni, Cu) 5 /Cr have been fabricated by dc 
magnetron sputtering deposition. Heat treatment of the ini¬ 
tially amorphous magnetic films results in a refined grain 
structure with high anisotropy Sm-Co precipitates in the na¬ 
nometric scale. At the same time, a huge coercivity enhance¬ 
ment (from 100 Oe to 42 kOe in the case of SmCo 2 Cu 3 ) is 
observed. The nondependence of the strength on the positive 
magnetic interaction between particles and the average grain 
size on the crystallization stage, indicated that the coercivity 


is related to domain wall pinning at the high anisotropy pre¬ 
cipitates. The possibility of tuning the coercivity over a 
range of more than two orders of magnitude through the 
annealing conditions, make these films suitable for a variety 
of applications, from longitudinal recording media to thin 
film permanent magnets. 

‘E. M. T. Velu and D. N. Lambeth, J. Appl. Phys. 69, 5175 (1991). 

^S. S. Malhotra, Y. Liu, Z. S. Shan, S. H. Liou, D. C. Stafford, and D. J. 
Sellmyer, J. Appl, Phys. 79, 5958 (1996). 

^S. Takei, S. Shomura, A. Morisako, and M. Matsumoto, J. Appl. Phys. 81, 
4674 (1997). 

Okumura, H. Fujimori, O. Suzuki, N. Hosoya, X. B. Yang, and H. 
Morita, IEEE Trans. Magn. 30, 4038 (1994). 

^S. Foner, E. J. McNiff, H. Oesterreicher, F. T. Parker, and M. Misroch, J. 
Appl. Phys. 49, 2061 (1979). 

Oesterricher, F. T. Parker, and M. Misroch, J. Appl. Phys. 50, 4273 
(1979). 

^E. Fullerton, J. S. Jiang, C. Rehm, C. H. Sowers, S. D. Bader, J. B. Patel, 
and X. Z. Wu, Appl. Phys. Lett. 71, 1579 (1997). 

^R. W. Chatrell, in Nanomagnetism, edited by G. C. Hadjipanayis (Kluwer 
Academic, Dordrecht, 1994), p. 21. 


JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


I JUNE 1998 


Mechanically alloyed nanocomposite magnets (invited) 

P. G. McCormick®* 

Special Research Centre for Advanced Mineral and Materials Processing, University of Western Australia, 
Nedlands 6907, Australia 

W. F. Miao 

Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 

P. A. I. Smith 

Department of Physics, Trinity College, Dublin 2, Ireland 

J. Ding 

Department of Materials Science, National University of Singapore, 119260 Singapore 

R. Street 

Special Research Centre for Advanced Mineral and Materials Processing, University of Western Australia, 
Nedlands 6907, Australia 

Nanocomposites, consisting of a hard magnetic rare earth-transition metal phase exchange coupled 
to soft magnetic of-Fe or a-(Fe,Co), exhibit enhancement of the remanent magnetization due to 
exchange coupling across interfaces between grains. Modeling studies have shown that crystallite 
sizes of less than 20 nm are generally required for significant remanence enhancement and values 
of remanent magnetization equal to 70%-80% of saturation magnetization have been reported in 
mechanically alloyed two phase mixtures of a-¥c and a hard magnetic phase, such as Nd 2 Fei 4 B. 
Studies of microstructural evolution during mechanical alloying have shown that as-milled 
structures consist of a magnetically soft two phase mixture of a-Fe and an amorphous phase. Similar 
microstructures are observed regardless of whether mechanical milling or mechanical alloying has 
been carried out. Heat treatment above a critical temperature is required to crystallize grains of the 
hard magnetic phase. The formation of metastable intermediate phases with interesting magnetic 
properties may precede formation of the equilibrium phase. It is found that the crystallization 
temperature is an important parameter determining the grain size of the soft magnetic phase and, 
hence, magnetic properties. Recent measurements of the reversible and irreversible magnetization 
behavior of this novel class of permanent magnet are also discussed. © 1998 American Institute 
of Physics. [80021-8979(98)42911-6] 


L INTRODUCTION 

Nanocomposite permanent magnetic materials have at¬ 
tracted considerable interest since 1991, when it was 
recognized^ that exchange coupled, nanoscale mixtures of a 
hard magnetic phase such as Nd 2 Fei 4 B and a soft magnetic 
phase such as a-Fe could potentially provide maximum en¬ 
ergy products, excess of 200 kJ/m'^.^ In addition 

to the high values of that may be achieved, nano¬ 

composite magnets are of commercial interest because the 
costly magnetic alignment step is not required to obtain 
maximum performance and the alloys require less of the ex¬ 
pensive rare earth element. 

Remanence enhancement is associated with exchange 
coupling at interfaces separating nanocrystalline hard and 
soft magnetic phases, which causes the magnetization vector 
of the soft phase to be rotated toward that of the hard phase, 
thus increasing the remanent magnetization in the direction 
of initial magnetization. As a consequence, the material, al¬ 
though crystallographically isotropic, can exhibit remanence 
values significantly higher than the isotropic value of 0.5 of 
the saturation magnetization, M^, for a material with 


®taectronic mail: pgm@mech.uwa,edu.au 


uniaxial magnetocrystalline anisotropy, without the necessity 
of crystallographic alignment. 

The basic concepts of exchange coupling and remanence 
enhancement date back to the studies of Meiklejohn and 
Bean.^ McCallum, et al.^ first reported remanence enhance¬ 
ment in single phase nanocrystalline melt spun Nd 2 Fej 4 B 
containing small amounts of Si and Al. The phenomenon 
was attributed to exchange coupling between ~20 nm 
Nd 2 Fei 4 B grains. Remanence enhancement in nanocrystal¬ 
line composites of magnetically hard and soft phases was 
first reported by Coehoorn and co-workers.Remanence 
values of up to 0.8 were measured in a melt-spun 
Nd 4 Fe 78 B|g alloy consisting of Nd 2 Fei 4 B, Fe 3 B, and a-Fe. 
Ding et alJ'^ first reported remanence enhancement in me¬ 
chanically alloyed two phase a-Fe/Sm 2 Fei 7 N 2.6 alloys con¬ 
taining 5-11 at % Sm. The as-milled structures consisted of 
two phase mixtures of a-Fe and an amorphous phase. Crys¬ 
tallization at temperatures above 773 K resulted in two phase 
a-Fe/Sm 2 Fei 7 mixtures which were subsequently nitrided at 
673 K to form a-Fe/Sm 2 Fei 7 N 2 . 6 - The crystallite size was 
— 15-20 nm in samples heat treated at 873 K. Remanence 
enhancement has now been observed in a number of me¬ 
chanically alloyed and heat treated nanocomposite alloys. 


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Micromagnetic modeling studies have shown that the 
magnetic properties of nanocomposite magnets depend 
strongly on both the microstructure developed during pro¬ 
cessing and the intrinsic magnetic properties of the indi¬ 
vidual phases.^"^^ Of particular importance, the grain size of 
the soft phase should be less than the exchange length of the 
soft magnetic phase,The calculations of Fischer et al}^ 
predict that should increase logarithmically with increas¬ 
ing grain size and that the magnetic properties are degraded 
by a nonuniform microstructure. The values of M ^., and 
predicted by modeling studies exceed experimental 
values and it is clear that greater attention needs to be placed 
on the development of optimum microstructures and phase 
constitutions during processing to enable property improve¬ 
ments to be realized. In this article recent studies of 
microstructure-property relationships in mechanically al¬ 
loyed and heat treated rare-earth nanocomposite magnetic 
materials are reviewed. 

II. STRUCTURAL EVOLUTION DURING MECHANICAL 
ALLOYING 

Mechanical alloying and the related processes of me¬ 
chanical milling and mechanochemical processing have been 
applied to the synthesis of a wide range of amorphous and 
nanocrystalline materials.The application of mechanical 
alloying to the synthesis of magnetic materials was first re¬ 
ported by Schultz and co-workers in and subse¬ 

quently has been applied to a wide range of rare-earth per¬ 
manent magnet alloys. 

The metastable nanocrystalline and/or amorphous struc¬ 
tures which are inherently obtained in mechanically alloyed 
powder are developed from the repeated processes of defor¬ 
mation and fracture which accompany ball/powder collision 
events. Plastic deformation of the powder particles initially 
occurs by the development of shear bands. When sufficiently 
high dislocation densities are reached the shear bands de¬ 
compose into sub-grains separated by low-angle grain 
boundaries. With further milling the sub-grain size is re¬ 
duced and the sub-grains become randomly oriented and 
separated by high angle boundaries. The large surface energy 
of the nanocrystalline grains has been shown to provide the 
driving force for a crystalline-^amorphous phase 
transition. The rate of diffusion is also important as the 
diffusion coefficients may be increased by the deformation 
induced defect density and high local collision temperatures. 
In many systems the final structure reflects the competition 
between deformation induced disorder and diffusion limited 
recovery processes and is independent of whether the starting 
material is pre-alloyed or a mixture of elemental powders. 

The as-milled structures of a wide range of rare-earth 
permanent magnet alloys are characterized by nanoscale 
mixtures of crystalline and amorphous phases. For ex¬ 
ample, both mechanically alloyed and mechanically milled 
FeNdB alloys consist of a mixture of nanocrystalline a-Fe 
and amorphous NdFe phases.^"^’^^ Mechanical milling of the 
Nd 2 Fei 4 B phase has been shown to result in disproportion¬ 
ation into a mixture of a-Fe and amorphous NdFe.^^ The 
same final phases are formed regardless of whether the start¬ 
ing material has been pre-alloyed.^^’^^ 



Microstructure evolution in single phase Nd 2 Fei 4 B and 
two phase a-Fe/Nd 2 Fei 4 B composites during mechanical 
milling has been studied in detail using x-ray diffraction, 
Mossbauer spectroscopy, and transmission election micros¬ 
copy (TEM) measurements.^^ Figure 1 shows the effect of 
milling time on the volume fraction of the phases present in 
initially single phase Nd 2 Fei 4 B. The phase compositions 
were determined from Mossbauer measurements.^^ In the 
early stage of milling, the fraction of the amorphous phase 
increased rapidly at the expense of the Nd 2 Fei 4 B phase. Af¬ 
ter milling for 12 h the microstructure consisted of '~80% 
amorphous phase and ^20% Nd 2 Fei 4 B. For longer milling 
times the a-Fe phase began to form, while the fraction of 
amorphous phase remained approximately constant. For 
milling times exceeding 40 h the fraction of a-Fe reached a 
constant value of nearly 0.20. A small fraction of Nd 2 Fei 4 B 
was still present after milling for 80 h. Miao and 
co-workers suggested that the a-Fe phase forms from the 
amorphous phase, thus giving a two-stage reaction 
Nd 2 Fei 4 B—»al^a-Fe+a 2 , where a\ and al refer to the 
two amorphous phases. A similar two-stage process has also 
been observed in two phase a-Fe/Nd 2 Fei 4 B composites.^^ 

In Sm-Co alloys a single amorphous phase is formed 
during mechanical alloying.^The partial substitution of 
Fe for Co leads to a mixture of a Sm-Co-Fe amorphous 
phase and nanocrystalline a-(Fe-Co) in milled samples.^^ As 
shown in Fig. 2, the formation of a-(Fe-Co) was observed 
when the Fe content exceeded the Sm concentration. A 
bright field TEM image and selected area diffraction pattern 
of an as-milled Sm 9 2 C 049 8 Fe 4 o particle are shown in Fig. 3. 
The distinct diffraction rings are associated with the a-(Fe- 
Co) phase. The broad diffuse rings which are also evident are 
consistent with the presence of an amorphous Sm-Co-Fe 
phase. 

III. EFFECT OF HEAT TREATMENT 

In all rare earth-transition metal magnetic alloys studied 
to date the as-milled structure is magnetically soft and a 
post-milling heat treatment must be carried out to form the 


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McCormick et al. 



FIG. 2. X-ray diffraction patterns showing effect of Fe content, x, on the 
phases present in as-milled Sm ,0 5 Cog 9 5 _^Fe^ (Ref. 33). 


hard magnetic phase and thus obtain hard magnetic proper¬ 
ties. The crystallization temperature in NdFeB alloys has 
been shown to be a function of the Fe content, increasing 
from 550 °C to over 600 °C as the equilibrium volume frac¬ 
tion of a-Fe increased from 15% to 15%?^ A two stage 
crystallization process has been observed to occur in both 
NdFeB (Ref. 18) and SmCoFe alloys.^^'^'* With NdFeB al- 
loys the first stage involves the crystallization of the amor¬ 
phous phase with no change in the volume fraction of a-Fe 
as shown in Fig. 4. No solid state reaction occurred between 
the amorphous and a-Fe phases during the first stage of crys- 



FIG. 3. TEM micrograph of as-milled Smg |Co 49 8 Fe 4 o particle (Ref. 22). 



Milled Temperature CC) 

FIG. 4. Phase changes accompanying crystallization in NdioFeg 4 B 6 (Ref. 
18). 


tallization. At higher temperatures a decrease in the fraction 
of a-Fe accompanied further crystallization of Nd 2 Fe| 4 B. 
The temperatures required for complete crystallization of the 
Nd 2 Fei 4 B phase are sufficiently high for grain growth of the 
a-Fe phase to occur. Minimum grain sizes of 20 nm have 
been reported for crystallized a-Fe/Nd 2 Fei 4 B nanocompos¬ 
ite structures, as compared to 5-10 nm in the as-milled 
powders.^® 

Similar observations have been reported for SmFeCo 
alloys.^On annealing, the amorphous phase formed dur¬ 
ing milling initially crystallized to a metastable intermetallic 
phase or a mixture of intermetallics having the same compo¬ 
sition as the amorphous phase. As with a:-Fe/Nd 2 Fei 4 B, no 
solid state reaction occurred between the amorphous phase 
and the nanocrystalline a-(Fe-Co) phase during crystalliza¬ 
tion. The initial crystallization reaction occurred between 
430 and 530 °C, with the crystallization temperature decreas¬ 
ing with increasing Sm and Fe content of the amorphous 
phase. A solid state reaction occurs at higher temperatures 
between the initially crystallized phase and a-(Fe-Co) to 
form the equilibrium 2-17 phase. It has been found that the 
intermetallic phase initially crystallized in 
Smio. 5 Co 49 5 Fe 4 o[Sm(Co,Fe) 7 ] has better magnetic properties 
that formed by solid state reaction at higher temperatures. 
Since the structure of the initial intermetallic phase is deter¬ 
mined by the composition of the amorphous phase, it is clear 
that control of the as-milled structure is vital for producing a 
particular combination of soft and hard phases. 

IV. MAGNETIC PROPERTIES OF NANOCOMPOSITE 
MAGNETS 

The magnetic properties of nanocomposite magnets 
characteristically exhibit high values of remanent magnetiza¬ 
tion and reversible susceptibility. Figure 5 compares the 
magnetization curves and recoil loops for mechanically al¬ 
loyed single phase Sm 2 Fei 4 Ga 3 C 2 and exchange coupled 
Sm2Fei4Ga3C2+40% a-Fe samples, respectively.As 
shown in Fig. 5, the single phase material exhibits a rema¬ 
nent magnetization equal to 0.5 M, and relatively flat recoil 
loops associated with a low reversible component of the total 






J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


McCormick et al. 


6259 




FIG. 5. Magnetization curves and recoil loops for: (a) single phase 
Sm 2 Fei 4 Ga 3 C 2 and (b) a-Fe/Sm 2 Fei 4 Ga 3 C 2 nanocomposite (Ref. 25). 

magnetization. In comparison, the two phase material exhib¬ 
its a higher remanent magnetization (Mr^O.65 M^) and a 
lower coercivity. The recoil curves exhibit large reversible 
magnetization. 

The high reversible magnetization of exchange coupled 
nanocomposites is associated with the rotation of the mag¬ 
netic moments within soft phase grains towards the direction 
of easy magnetization in neighboring hard grains to which 
they are exchange coupled. It is important to note that the 
reversible magnetization changes in the two phase material 
occur at fields significantly higher than the coercivity of the 
uncoupled soft phase. This behavior is a clear indication of 
exchange coupling between nanosized grains of hard and 
soft phases. Without such exchange coupling irreversible 
magnetization reversal of the soft phase (a-Fe) would occur 
at fields of a few Oe, resulting in a reduced remanence and a 
step in the magnetization curve. The reversible magnetiza¬ 
tion of the two phase sample is associated almost entirely 
with the soft phase. Feutrill, McCormick and Street^^ have 
shown that the reversible magnetization in the nanocompos¬ 
ite is limited by the onset of reversal of the hard phase. It is 
also noted in Fig. 5 that the irreversible relaxation observed 
at the start of the recoil loops (magnetic viscosity) is signifi¬ 
cantly reduced in the two phase material as compared with 
the single phase material. It has been shown that the time 
dependent magnetic viscosity behavior in exchange coupled 
magnets is associated with time dependent reversal of the 
hard phase.^^ 

The nature of the interface between the hard and soft 
phases in exchange coupled nanocomposites is not well un¬ 
derstood. Kneller and Hawig^ determined that crystallo¬ 


graphic coherence across the interface between hard and soft 
phases was a necessary condition for exchange coupling and 
hence remanence enhancement. High resolution TEM studies 
on nanostructured materials indicate that, while the inter¬ 
faces take on low energy, highly ordered configurations, 
there is no crystallographic coherence across interface 
boundaries.Exchange coupled behavior has been ob¬ 
served in mechanically milled Nd 2 Fei 4 B which consisted of 
a nanocomposite mixture of Nd 2 Fei 4 B and an amorphous 
phase.Similar behavior has also been reported in 
Sm 2 Fei 7 N 3 , partially disproportionated by mechanical mill¬ 
ing to contain a mixture of an amorphous phase and 
Sm2Fei7N3.^* 

Since crystallographic coherence does not exist between 
the hard and soft phases in these materials, coherence cannot 
be a necessary condition for exchange coupling and rema¬ 
nence enhancement in nanocomposite magnets. Indeed, sig¬ 
nificant remanence enhancement has been reported in the 
melt-spun Nd 2 Fei 4 B/a:-Fe system containing an amorphous 
intergranular phase.Exchange effects between metallic 
hard and soft magnetic phase components rely on the distrib¬ 
uted nature of the electrons involved in cooperative behavior. 
The range of interaction of collective electrons is of the order 
of a few interatomic distances. In these circumstances ex¬ 
change coupling between grains is not critically dependent 
on crystallographic coherence. 

V. FACTORS LIMITING MAGNETIC PROPERTIES 

The main factors limiting the performance of mechani¬ 
cally alloyed nanocomposite magnets are microstructure re¬ 
lated. The values of a maximum energy product obtained to 
date are limited by low coercivity, and it is clear that increas¬ 
ing He will rely on optimizing the microstructure. In particu¬ 
lar, the average grain size and grain size distribution are 
important parameters determining the magnetic properties. 
The values of M^, and all decrease with in¬ 

creasing grain size. A number of studies have now shown 
that the grain size in mechanically alloyed and heat treated 
nanocomposites exhibiting optimum magnetic properties is 
typically —20 nm, which is larger than the optimum grain 
size of —10 nm predicted by modeling studies.^’^’^ 

As discussed previously, the minimum grain size that 
can be achieved in mechanically alloyed nanocomposites is 
limited by the heat treatment conditions employed in the 
crystallization of the hard magnetic phase. Figures 6 and 7 
illustrate the effect of heat treatment time on grain growth 
and magnetic properties in mechanically alloyed 
Smio, 5 Co 49 5 Fe 4 o during crystallization at 600 The 

dark field micrographs shown in Fig. 6 were obtained by 
positioning the objective aperture on the strongest diffraction 
ring for a-(Fe-Co). The diffracting grains are thus mainly 
a-(Fe-Co), although some bright Sm 2 (Fe,Co )7 grains are 
also present in the image due to the proximity of the (119) 
diffraction ring for the 2:7 phase with the (110) diffraction 
ring of a-(Fe-Co). In the sample heat treated for 60 min 
[Fig. 6(b)] the largest grains were identified by energy dis¬ 
persive spectra (EDS) to be a-(Fe-Co). Figure 7 shows the 
decrease in coercivity and M^IM^ with increasing crystalli- 




6260 J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


McCormick et al. 



FIG. 6. Dark field TEM micrographs of mechanically alloyed Sm|o ,5 
Co 4 i; < 5 Fe 4 o sample heat treated at 600 °C for: (a) 10 min, (b) 60 min (Ref. 
23)." 


zation time. As would be expected, the theoretical density 
values of decreased significantly with increasing 

time, from 129 kJ/m^ for samples crystallized for 5 min to 77 
kJ/m^ for 150 min?^ 

In Nd 2 Fei 4 B/a-Fe and SmFeCo nanocomposites crystal¬ 
lization occurs at temperatures of 550-600 °C and 430- 
530 °C, respectively, and grain growth of the soft phase oc¬ 
curs during crystallization. It is clear that to achieve smaller 
grain sizes it is necessary to reduce grain growth of the soft 
phase during crystallization. In alloys where a solid state 
reaction between the amorphous and nanocrystalline phases 
is required for crystallization of the hard phase, some grain 
growth of the soft phase is inevitable. Attempts to reduce 
grain growth of the soft phase through the addition of grain 
growth inhibitors such as Si, Ta, and Nb have met with 
mixed success. 

The effect of volume fraction of the soft phase in me¬ 
chanically alloyed nanocomposites has been studied 
in the Nd 2 Fei 4 B/a-Fe, Sm 2 Fe| 7 C 3 /a-Fe, and SmFeCo 



Time (min) 

FIG. 7. Effect of crystallization time on cocrcivity and reduced remanence 
in Smjo. 5 Co 4 Q sFe 4 () heat treated at 600 °C (Ref. 23). 

ft '70 09 00 00 

systems. ’’’* Increasing the fraction of the soft phase 
increases the remnence but decreases the coercivity, consis¬ 
tent with the results of modeling studies.^ 

The uniformity of the microstructure, in particular the 
distribution of hard and soft grains and the grain size distri¬ 
bution, is also important in determining magnetic properties. 
If clusters of soft grains are present, exchange coupling will 
be diminished even if the grain size is small. As a conse¬ 
quence, nonuniform microstructures cause a decrease in both 
remanence and coercivity. The higher values of M and 
observed in mechanically milled Nd 2 Fei 4 B/a'-Fe nanocom¬ 
posites, as compared to mechanically alloyed powders of the 
same nominal composition, have been attributed to the finer 
and more uniform microstructures obtained in the mechani¬ 
cally milled samples. The clustering of cr-Fe grains in hot 
pressed Nd 2 Fei 4 B/a-Fe nanocomposites has also been 
reported.*"^ ‘ 

A further factor limiting the performance of mechani¬ 
cally alloyed nanocomposite magnets is the difficulty of 
achieving high densities after consolidation. The magnetic 
properties reported in most studies to date are calculated 
from experimental measurements assuming samples are 
100% dense. Mechanically alloyed powders exhibit low as- 
pressed densities in comparison to melt spun materials. The 
as-pressed density of mechanically alloyed powders is gen¬ 
erally limited to about 50% of the theoretical density due to 
the irregular surface morphology of the particles. Density 
increases up to ^^70% may be achieved during heat treat¬ 
ment. However, higher densities can only be obtained by 
sintering at higher temperatures, resulting in significant grain 
growth and a loss of exchange coupled behavior. Alterna¬ 
tively, high densities may be achieved by hot pressing with 
minimal grain coarsening, provided closely controlled pro¬ 
cessing conditions are used.^‘ 

VI. CONCLUSIONS 

Mechanical alloying has been shown to be a promising 
method for the production of nanocomposite magnets. The 
nanocrystalline grain structure inherently developed by mill¬ 
ing and heat treatment is essential for effective exchange 
coupling and remanence enhancement, enabling high values 



J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


McCormick et al. 


6261 


of to be obtained. Heat treatment of the as-milled 

structure is required to form hard magnetic phases. The for¬ 
mation of novel metastable hard phases during heat treat¬ 
ment may provide the basis of new nanocomposite phase 
mixtures with improved magnetic properties. Recent studies 
have shown that grain growth accompanying crystallization 
of the hard magnetic phase and the formation of nonuniform 
grain structures are important factors which currently limit 
the magnetic properties of mechanically alloyed nanocom¬ 
posites. 

^E. F. Kneller and R. Hawig, IEEE Trans. Magn. 27, 3588 (1991). 

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chow, J. Phys. (Paris), Colloq. 8, 669 (1988). 

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80, 101 (1989). 

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(1993). 

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^^P. G. McCormick, Handbook on the Physics and Chemistry of Rare 


Earths, edited by K. A. Gscheidner and L. Eyring (North-Holland, Am¬ 
sterdam, 1997), Chap. 16, Vol. 24. 

S. C. Jang and C. C. Koch, J. Mater. Res. 5, 498 (1990). 

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833 (1992). 

^^W. F. Miao, J. Ding, P. G. McCormick, and R. Street, J. Appl. Phys. 79, 
2079 (1996). 

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Phys. 29, 2370 (1996). 

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240, 200 (1996). 

J. Ding, P. G. McCormick, and R. Street, J. Magn. Magn. Mater. 135, 200 
(1994). 

^^P. A. I. Smith, Ph. D. thesis. University of Western Australia, 1997. 

^^P. A. I. Smith, P. G. McCormick, and R. Street, Mater. Sci. Forum 179- 
181, 527 (1995). 

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(1996), 

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2320 (1996). 

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(1995). 

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(1993). 

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Magn. Magn. Mater. 157-158, 93 (1996). 

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36, 676 (1995). 

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(1994). 

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563 (1995). 

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formations in Metastable Materials, MRS, Warrendale, PA (unpublished, 
1998). 


JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Micromagnetic simulation of magnetizability of nanocomposite 
Nd-Fe-B magnets 

Thomas SchrefI®' and Josef Fidler 

Institute of Applied and Technical Physics, Vienna University of Technology, Wiedner Hauptstrasse 8-10, 

A-1040 Vienna, Austria 

Micromagnetic finite element calculations clearly show that the magnetizability of nanocomposite 
Nd 2 Fe 24 B magnets improves with increasing a-Fe content. The magnetization curves show a steep 
increase at the domain propagation field in dc demagnetized samples. Thermally demagnetized 
states store a higher amount of exchange energy, leading to an increase of the initial susceptibility. 
An applied field of 960 kA/m leads to a saturation of 85% for a two-phase a-Fe/Nd 2 Fej 4 B magnet, 
whereas the Fe 3 B/Nd 2 Fei 4 B magnet and the single-phase Nd 2 Fei 4 B magnets reach a saturation of 
only 70% and 50%, respectively. The improved saturation behavior of two-phase a-Fe/Nd 2 Fei 4 B 
magnets has to be attributed to the exchange field which is provided by a-Fe grains that are already 
oriented parallel to the field direction. Hard magnetic grains that remain oppositely magnetized after 
applying the maximum magnetizing field deteriorate the coercive squareness in single-phase 
Nd 2 Fei 4 B magnets and two-phase Fe 3 B/Nd 2 Fei 4 B magnets. © 1998 American Institute of Physics. 
[80021-8979(98)30711-2] 


I. INTRODUCTION 

Exchange-spring permanent magnets have become a 
topic of recent research in permanent magnets. A mixture 
of a magnetically hard and soft phases reduces the overall 
rare-earth content, while preserving good hard magnetic 
properties.^’^ In addition to the cost reduction, the improved 
magnetizability of nanocomposite Nd 2 Fei 4 B magnets is a 
major advantage as compared to conventional bonded 
magnets.^ Panchananthan^ compared the saturation behavior 
of single phase Nd 2 Fei 4 B, two phase Fe 3 B/Nd 2 Fei 4 B, and 
two-phase a-Fe/Nd 2 Fei 4 B magnets. The magnetization field 
of 800-960 kA/m leads to a saturation of 55%-60% for a 
standard, single phase Nd 2 Fei 4 B powder. The 
a-Fe/Nd 2 Fei 4 B composites show a saturation of about 80% 
with a field of only 960 kA/m, while the corresponding 
bonded magnet reaches a coercive field of 320 kA/m. Rave 
and co-workers^ investigated the effect of different initial 
states on the initial magnetization curve of nanocrystalline 
permanent magnets. They reported a higher susceptibility in 
thermally demagnetized samples than in dc demagnetized 
samples. This susceptibility difference was qualitatively re¬ 
produced by two-dimensional micromagnetic simulations as¬ 
suming a brick wall model to represent the grain structure. 

This work presents three-dimensional micromagnetic 
calculations of magnetizability and coercivity of 
a-Fe/Nd 2 Fei 4 B and Fe 3 B/Nd 2 Fei 4 B two-phase magnets. The 
magnetic properties of single phase Nd 2 Fei 4 B magnets are 
calculated as reference. The use of the finite element method 
allows modeling of realistic microstructures. 

II. MICROMAGNETIC SIMULATION OF 
DEMAGNETIZED STATES 

The theoretical description of magnetization processes in 
ferromagnetic materials starts from the total magnetic Gibb’s 


^taectronic mail: schrefl@email.tuwien.ac.at 


free energy. Its minimization provides a stable equilibrium 
state of a ferromagnetic structure. The actual path of the 
magnetization towards a local minimum can be computed by 
the time integration of the Gilbert equation of motion. The 
transient states show how reversed domains nucleate and 
propagate.In order to reduce the required computation 
time, a conjugate gradient method is used to minimize the 
energy in the present study. Details of the finite element 
algorithm are described Ref. 6. The cubic model magnet with 
an edge length of 80 nm consists of 125 polyhedral grains 
generated from grain growth simulation using Voronoi cells. 
The average grain diameter is 20 nm. The different phases 
and the anisotropy directions are randomly assigned to the 
grains. The composite magnet contains 40 vol % Nd 2 Fe| 4 B 
and either a-Fe or Fe 3 B as soft magnetic phase. Table I gives 
the intrinsic material parameters'^”*'^ used for the calcula¬ 
tions. 

The magnetization distribution with the lowest energy 
represents a thermally demagnetized state. The magnetocrys¬ 
talline anisotropy energy is the dominating energy term in 
Nd 2 Fei 4 B magnets. To minimize the energy, the magnetiza¬ 
tion within the hard magnetic grains must be parallel to the 
anisotropy directions. The requirement to minimize the mag¬ 
netostatic energy determines the orientation of the magneti¬ 
zation along the easy axes. Thus, an approximation of a ther¬ 
mally demagnetized state can be obtained from simulated 
annealing'^ to minimize the magnetostatic energy followed 
by the calculation of equilibrium states for increasing ex¬ 
change constant. Indeed the total energy of the thermally 
demagnetized state calculated by the above procedure is 
about 5% smaller than the total energy of an equilibrium 
state with grains initialized randomly along their easy axes. 
This procedure to calculate the thermally demagnetized state 
adopts the zero exchange formulation of micromagnetics as 
outlined by DeSimone.*'^ The minimization of the total en¬ 
ergy leads to a dc demagnetized state assuming an initial 


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© 1998 American Institute of Physics 



J. Appl. Phys., Vol. 83, No. 11,1 June 1998 


T, SchrefI and J. FIdler 6263 


TABLE L Intrinsic magnetic properties used for the calculations. The col¬ 
umns give the spontaneous magnetic polarization J^iT), the anisotropy con¬ 
stants and K 2 (MJ/m^), and the exchange constant A (pJ/m). 



Js 


K2 

A 

Reference 

Nd2Fei4B 

1.61 

4.5 

0.66 

12.5 

11 

FesB 

1.62 

-0.32 


12.5 

12 

a-Fe 

2.15 

0.046 

0.015 

25 

13 


magnetization antiparallel to each other in two halves of the 
cube. The net magnetization of the calculated demagnetized 
states is not exactly zero, owing to the limited number of 
grains. 

III. RESULTS AND DISCUSSION 

Figure 1 compares the magnetization curves starting 
from the thermally demagnetized and dc demagnetized 
states. The solid, dotted, and dashed lines refer to the 
a-Fe/Nd 2 Fei 4 B, the Fe 3 B/Nd 2 Fei 4 B, and the single-phase 
Nd 2 Fei 4 B magnets. The magnetization curve of the dc de¬ 
magnetized Nd 2 Fei 4 B magnet clearly shows three different 
regimes. At low external fields the magnetization rotates re¬ 
versibly towards the direction of the applied field within the 
grains originally magnetized oblique to the field direction. At 
an external field of about 1000 kA/m the region with upward 
magnetization starts to expand through the entire magnet 
leading to a steep increase of the dc magnetization curve at 
1340 kA/m. At external fields greater than 1400 kA/m the 
upward magnetization has completely swept through the 
magnet, and reversible rotations are the only process to in¬ 
crease the magnetization. The thermally demagnetized state 
stores a higher amount of exchange energy than the dc de¬ 
magnetized state, which can be released upon saturation. 
Only a small external field is required to initiate the irrevers¬ 
ible switching of entire grains in the thermally demagnetized 
Nd 2 Fei 4 B magnet, leading to a higher initial susceptibility. 

The soft magnetic grains of the two-phase 
a-Fe/Nd 2 Fei 4 B or Fe 3 B/Nd 2 Fei 4 B magnet become oriented 
parallel to the field direction at low applied fields. Their ex¬ 
change field helps to reverse neighboring hard magnetic 
grains. The comparison of the dc magnetization curves of 
Fig. 1 shows that the external field required to expand the 
upward domain through the hard magnetic grains decreases 
to 750 kA/m as 60% of the hard magnetic phase is replaced 
by Fe 3 B, and to 540 kA/m as Fe 3 B is substituted by a-Fe. 
Figure 2 shows the magnetization process of a two-phase 
a-Fe/Nd 2 Fei 4 B magnet starting from a dc demagnetized 
state. The plane where the magnetization component parallel 
to the field direction becomes zero indicates the position of 
the domain wall. The solid line denotes the trace of this 
plane on the surface of the cubic magnet. In nanocrystalline 
permanent magnets the competitive effects of magnetocrys¬ 
talline anisotropy and intergrain exchange interactions lead 
to a strongly inhomogeneous magnetization distribution.^ 
Whereas the magnetization remains parallel to the easy axes 
in the center of the grains, it deviates from the local easy axis 
in the vicinity of the grain boundaries. As a consequence, the 
two regions originally oppositely magnetized are not sepa¬ 




FIG. 1. Calculated magnetization curves starting from a dc-demagnetized 
state (top) and a thermally demagnetized state (bottom). The solid, dotted, 
and the dashed lines refer to the a-Fe/Nd 2 Fei 4 B, the Fe 3 B/Nd 2 Fei 4 B and the 
single-phase Nd 2 Fei 4 B magnet, respectively. The circles indicate the mag¬ 
netic states plotted in Fig. 3. 


rated by a well-defined domain wall. On both sides of the 
border between the oppositely magnetized regions, the direc¬ 
tion of the magnetization varies on a length scale comparable 
with the domain wall width. Thus the transition structure is 
far more complex than in a classical Bloch wall, where the 
magnetization changes only in the direction perpendicular to 
the wall. The plot on the left-hand side of Fig. 2 gives the 
position of the wall for zero applied field. As the external 
field is increased, the wall bends around Nd 2 Fei 4 B grains 
following their boundaries. However, the wall may go 
through a-Fe grains. The plot on the right-hand side of Fig. 


FIG. 2. Domain wall propagation in the dc demagnetized Q!-Fe/Nd 2 Fei 4 B 
magnet. The solid line gives the trace of the plane where the component of 
the magnetization parallel to the direction of the applied field becomes zero. 











6264 


J. Appl. Phys., Vol. 83, No. 11. 1 June 1998 


T. SchrefI and J. Fidler 



FIG. 3. Magnetization distribution during saturation of the thermally de¬ 
magnetized a-Fe/Nd 2 Fei 4 B and Fe 3 B/Nd 2 Fej 4 B magnet. The magnetization 
is projected onto a plane parallel to the field direction for a applied field of 
390 kA/m. The field is applied parallel to the vector from point b to point c. 


2 depicts the trace of the wall for an applied field of 340 
kA/m, showing the deflection of the wall around the hard 
magnetic grains. 

The comparison of the magnetization curves of Fig. 1 
clearly shows that the magnetizability increases with increas¬ 
ing of-Fe content. In the thermally demagnetized samples, an 
applied field of 960 kA/m leads to 85% saturation for a two- 
phase a-Fe/Nd 2 Fei 4 B magnet and to 70% saturation for the 
Fe 3 B/Nd 2 Fei 4 B magnet. For the same applied field, the 
single phase magnet reaches a saturation of only 50%. The 
very same mechanism which causes the decrease of the do¬ 
main propagation field in the dc demagnetized samples with 
increasing a-Fe content improves the saturation behavior of 
thermally demagnetized, two-phase magnets. The magnetiza¬ 
tion of the Fe 3 B and a-Fe grains becomes oriented along the 
saturation direction at an applied field of 400 kA/m. The 
exchange field provided by the saturated soft magnetic grains 
facilitates the alignment of neighboring hard magnetic 
grains. Figure 3 gives the magnetization distribution in a 
slice plane parallel to the field direction. Fe 3 B grains require 
a larger applied field to become aligned parallel to the field 
direction than a-Fe grains. Neighboring hard and soft mag¬ 
net grains already saturated at an applied field of 390 kA/m 
in the a-Fe/Nd 2 Fej 4 B magnet remain reversed in the 
Fe 3 B/Nd 2 Fei 4 B magnet. 

Figure 4 presents the calculated demagnetization curves 
as a function of the saturation field. Hard magnetic grains 



H,,,{kA/m) 


FIG. 4. Influence of the applied field on the loop shape and the coercive 
field for a-Fe/Nd 2 Fei 4 B and Fe 3 B/Nd 2 Fei 4 B magnets. The demagnetization 
curves were calculated after saturation with an applied field of 800, 960, and 
1120 kA/m. 

that remain oppositely magnetized deteriorate coercivity and 
remanence in Fe 3 B/Nd 2 Fe| 4 B magnets for a saturation field 
lower than 1000 kA/m. Two phase a'-Fe/Nd 2 Fei 4 B magnets 
show square hysteresis loops. The calculated values for the 
coercive field and the remanence are 340 kA/m and 1.2 T for 
a saturation field of 960 kA/m. 

ACKNOWLEDGMENTS 

This work has been supported by the Austrian Science 
Foundation FWF (Grant No. P10511-NAW) and the EC- 
BRITE/EURAM Project BRPR-CT95-0097. 

'R. Coehoom, D. B. DeMooij, and C. DeWaard, J. Magn. Magn. Mater. 
80, 101 (1989). 

^E. F. Kneller and R. Hawig, IEEE Trans. Magn. 27, 3588 (1991), 

^S. Hirosawa and H. Kanekiyo, Mater. Sci. Eng., A 217/218, 367 (1996). 

Crespo, V. Neu, and L. Schultz, J. Phys. D 30, 2298 (1997). 

^R. Skomski and J. M. D. Coey, Phys. Rev. B 48, 15812 (1993). 

^T, SchrefI, R. Fischer, J. Fidler, and H. Kronmiiller, J. Appl. Phys. 76, 
7053 (1994). 

^J. J, Croat, J. Appl. Phys. 81, 4804 (1997). 

^V. Panchanathan, IEEE Trans. Magn. 31, 3605 (1995). 

^W. Rave, D. Eckert, B. Gebel, A. Handstein, R. Schafer, and K.-H. 
Miiller, Proceedings of the XIV International Workshop on Rare Earth 
Magnets and their Application, Sao Paulo, Brasil, edited by F. P. Missel 
et al. (World Scientific, Singapore, 1996), p. 297. 

*°T. SchrefI, H. Roitner, and J. Fidler, J. Appl. Phys. 81, 5567 (1997). 
^’M. Sagawa, S. Fujimura, H. Yamamoto, Y. Mastuura, and S. Hirosawa, J. 
Appl. Phys. 57, 4094 (1985). 

Coene, F. Hakkens, R. Coehoorn, B. D. de Mooij, C. De Waard, J. 
Fidler, and R. Grdssinger, J. Magn. Magn. Mater. 96, 189 (1991). 

'^E. Kneller, Ferromagnetism (Springer, Berlin, 1962). 

*‘^A. Corana, M. Marches!, C. Martini, and S. Ridella, ACM Trans. Math. 
Softw. 13, 262 (1987). 

’^A. De Simone, Arch. Ration. Mech. Anal. 125, 99 (1993). 






JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Thick Fe3B/Nd2Fei4B nanocomposite permanent magnet flakes prepared 
by slow quenching 

H. Kanekiyo and S. Hirosawa®' 

Research and Development Division, Sumitomo Special Metals Co., Ltd., 2-15-17 Egawa, Shimamoto-cho, 

Mishima-gun, Osaka 618, Japan 

Thick permanent magnet flakes of Fe 3 B/Nd 2 Fei 4 B nanocomposites have been prepared directly 
from molten alloys by means of the low surface-velocity melt-spinning technique under a vacuum. 

Dependence of microstructure and magnetic properties of Nd 4 Fe 77 5 Bi 8 5 rapidly solidified alloys 
have been studied as functions of pressure of a melt-spinner chamber and the surface velocity of a 
Cu roll. An as-spun alloy of Nd 3 5 DyiFe 73 Co 3 GaiBj 8 5 obtained at a y^, = 3.3 m/s under a 1.3 kPa Ar 
atmosphere has a thickness of 240 /xm and the room temperature magnetic properties of 
kJ/m^, 1.15 T, and kA/m. © 1998 American Institute of Physics. 

[80021-8979(98)15611-6] 


I. INTRODUCTION 

Nanocomposite permanent magnet materials consisting 
of tetragonal Fe 3 B and Nd 2 Fei 4 B have been attracting much 
interest since they were reported by Coehoorn in 1988.^ The 
hard magnetic properties of these alloys have been signifi¬ 
cantly improved by the present authors by means of modifi¬ 
cations of composition,^’^ adding a practical importance on 
these materials as new candidates for hard magnetic ingredi¬ 
ents of resin-bonded permanent magnets. 

These materials are produced from amorphous alloys 
prepared by a single-roll melt-spinning technique and a sub¬ 
sequent heat treatment procedure, in which the amorphous 
alloys crystallize into a nanocomposite composed of the 
metastable Fe 3 B and the hard magnetic Nd 2 Fei 4 B phases 
with a minor amount of a-Fe.^ 

Although it has been known that Nd 2 Fei 4 B melt-spun 
materials show good hard magnetic properties in the as-spun 
state,"^ the effort to obtain the hard magnetic Fe 3 B/Nd 2 Fei 4 B 
as-spun alloys has been unsuccessful. However, to make a 
conclusive verdict, the effects of quenching conditions on the 
rapidly solidified alloys have not been thoroughly investi¬ 
gated in the vicinity of the Fe 3 B/Nd 2 Fej 4 B nanocomposite 
compositions. 

This article reports the effects of melt-spinning condi¬ 
tions, particularly the pressure of the chamber atmosphere of 
a melt spinner and the surface velocity of a Cu roll during 
melt spinning, on the microstructure and hard magnetic prop¬ 
erties of as-spun alloys. The Fe 3 B/Nd 2 Fej 4 B nanocomposites 
have been obtained in the as-quenched alloys for the first 
time by reducing the chamber pressure down to a practically 
vacuum regime and the roll surface velocity to a range be¬ 
tween 3 and 5 m/s. The hard magnetic materials thus ob¬ 
tained are thick flakes. They may be processed either into 
crushed powder for fabrication of resin-bonded magnets or 
directly into thin platelet permanent magnets simply by cut¬ 
ting or machining. 


^^Electronic mail: hirosawa.s@ssmc.co.jp 


II. EXPERIMENTAL PROCEDURES 

Alloys of compositions of Nd 4 Fe 77 5 Bi 8 5 and 
Nd 3 5 DyiFe 73 Co 3 GaiBi 8 5 were prepared by the single role 
melt-spinning technique under an Ar pressure (P) ranging 
from 1.3 to 95 kPa. About 30 g of alloys were taken from 
premelted large ingots and remelted in a quartz crucible. Im¬ 
mediately after the temperature of the molten alloys reached 
approximately 1300 °C, they were injected through an orifice 
of a diameter of 0.8 mm cut at the bottom of the crucible. 
The injection pressure was kept to be a constant value of 30 
kPa relative to the chamber pressure. The quenching roll was 
made of Cu and rotated at a surface velocity (in a range 
between 2 and 30 m/s. 

The rapidly solidified alloys were investigated using dif¬ 
ferential thermal analysis (DTA) and powder x-ray diffrac¬ 
tion (XRD) analysis using the Cu Xa radiation. The surfaces 
of rapidly solidified alloys were investigated by scanning 
electron microscopy (SEM). Magnetic properties of the ma¬ 
terials were measured at room temperature along the widest 
surface of flake-shaped specimens using a vibrating sample 
magnetometer (VSM). 

III. EXPERIMENTAL RESULTS 

When is 5 m/s, which is extremely slow compared to 
conventional conditions used for Nd-Fe-B melt-spun hard 
magnets is typically 20 m/s), rapidly solidified 
Nd 4 Fe 77 5 B 18.5 alloys are obtained as crystalline. For a cham¬ 
ber pressure (P) of 75 kPa, the condition used for our pre¬ 
vious studies, the existence of a-Fe in the alloy is readily 
confirmed by XRD as shown in Fig. 1. This alloy has an 
intrinsic coercivity of approximately 20 kA/m, which is neg¬ 
ligible as a hard magnet. When P is reduced to 1.3 kPa, the 
Fe 3 B/Nd 2 Fei 4 B composite structure is realized in the as-spun 
alloy for the same (Fig. 1). The diffraction peaks are 
relatively broad, indicating that the material consists of 
nanometer-sized crystallites. 

Observations of the surface morphology of the flakes by 
SEM reveal that the flakes obtained under a chamber pres¬ 
sure close to atmospheric pressure have shallow dimples of 


0021 -8979/98/83(11 )/6265/3/$15.00 


6265 


© 1998 American Institute of Physics 



6266 J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


H. Kanekiyo and S. Hirosawa 



FIG. 1. Comparison of x-ray diffraction patterns of Nd 4 Fe 77 5 B ,8 5 as-spun 
alloys under different chamber pressures of 75 and 1.3 kPa Ar on a Cu-roll 
surface moving at ^^.=5 m/s. 



FIG. 3. Dependence of thickness on roll surface velocity for Nd 4 Fe 77 5 Bj 8 5 
as-spun alloys obtained under an Ar pressure of 1.3 kPa. The width of the 
ribbons are in a range between 0.7 and 1.2 mm. 


an approximate diameter of 200 [xm on the surface which 
had contact with the quenching roll (“the roll-side surface” 
as opposed to the free surface). These are gas pockets created 
when a strand of the molten alloy had contact with the sur¬ 
face of the quenching roll. On the other hand, the roll-side 
surfaces are smooth and optically flat when the chamber 
pressure is lower than 30 kPa. It has been observed that, for 
these reduced chamber pressures, the quenched alloy is a 
continuous ribbon or a thin plate. 

Figure 2 shows powder XRD patterns of the as-spun 
Nd 4 Fe 77 5 Bi 8 5 alloys for a chamber pressure of 1.3 kPa, 
showing the effects of Vs on the microstructure. For Vs 
= 20 m/s, an amorphous material is obtained in an agreement 
with the previous studies. With decreasing V^, diffraction 
peaks from Fe 3 B and Nd 2 Fei 4 B gradually develop, indicating 
development of the nanocomposite structure. The depen¬ 
dence of the thickness on Vs of the rapidly solidified 



FIG. 2. X-ray diffraction patterns of Nd 4 Fe 77 5 Bi 8 5 as-spun alloys obtained 
under an Ar pressure of 1.3 kPa on a Cu-roll surface moving at different 
velocities. 


Nd 4 Fe 77 5 Bi 8 5 ribbons obtained with P= 1.3 kPa is shown in 
Fig. 3. Ribbon widths were in the range between 0.7 and 1.2 
mm with the inverse dependence on Vs . 

The dependence of magnetic properties of the rapidly 
solidified Nd 4 Fe 77 5 Bi 8 5 alloys on is shown in Fig. 4. 
Except for the magnetization measured under an external 
field of 1.2 T (J 12 ), the intrinsic coercivity, remanence 
and maximum energy product show strong de¬ 

pendencies on Vs . The optimum hard magnetic properties 
have been obtained with V^ = 5 m/s. 

Demagnetization curves of rapidly solidified 
Nd 4 Fe 77 5 Bi 8 5 and Nd 3 5 DyiFe 73 Co 3 GaiBi 8 5 alloys are 
shown in Fig. 5. The optimal Vs value depends on alloy 
concentration. The optimal for the latter alloy is 3.3 m/s 
and the thickness is 240 yum. The optimal magnetic proper¬ 
ties are kJ/m^, //cj=276 kA/m, and 

= 1.25T for Nd 4 Fe 77 , 5 B, 8.5 and 131.6 kJ/m^ 

//cj=400kA/m, and Rr=1.15T for 



FIG. 4. Dependence of magnetic properties of Nd 4 Fe 77 5 B 18 5 as-spun alloys 
obtained under an Ar pressure of 1.3 kPa on the roll surface velocity, V,.. 








J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


H. Kanekiyo and S. Hirosawa 6267 



FIG. 5. Demagnetization curves of as-spun Nd 4 Fe 77 5 Bi 8 5 and 
Nd 3 5 DyiFe 73 Co 3 GaiBi 8 5 obtained under an 1.3 kPa Ar atmosphere on Cu- 
roll surface moving at Vs = 5 and 3.3 m/s, respectively. 

Nd 3 5 DyiFe 73 Co 3 GaiBig 5 . These values are equivalent to 
those obtained previously on alloys crystallized from amor¬ 
phous precursors? These materials are magnetically isotro¬ 
pic. 

IV, DISCUSSION 

In this investigation, it has been clearly demonstrated 
that the chamber pressure during the melt-spinning proce¬ 
dure has a pronounced effect on microstructure and magnetic 
properties of as-spun alloys of the Fe 3 B/Nd 2 Fei 4 B nanocom¬ 
posite compositions. The presence of gas pockets observed 
on the roll-side surface of flakes obtained under a near atmo¬ 
spheric chamber pressure would significantly retard heat 
flow from the molten alloy to the surface of the quenching 
roll, causing large differences of cooling rates throughout the 
alloy flakes during solidification. Without the formation of 
gas pockets in the near vacuum atmosphere, uniform cooling 
must have been realized. As a result, an unequivocal depen¬ 
dence of microstructure and magnetic properties of these al¬ 
loys on Vs has been observed, showing the existence of a 
window in which as-spun hard magnet materials of the 
Fe 3 B/Nd 2 Fei 4 B nanocomposite structure can be obtained. 

In the Nd-Fe-B system, other types of nanocomposites 
consisting of a-Fe and Nd 2 Fei 4 B are possible in the Fe-rich 
composition regime. It has been reported that these nano¬ 
composites are obtainable either directly by a melt-spinning 
technique or via heat treatment of amorphous precursors, 
which is not surprising because both a-Fe and Nd 2 Fei 4 B are 
in equilibrium for compositions of the alloys. In contrast, the 
Fe 3 B/Nd 2 Fei 4 B nanocomposites are believed to be meta¬ 
stable because they decompose into a stable mixture of a-Fe 
and Ndj iFe 4 B 4 when annealed at a temperature above ap¬ 
proximately 800 °C.^ Therefore, the formation of a meta¬ 
stable composite structure in this type of alloy is not trivial. 
The possibility of Fe 3 B being a high temperature equilibrium 
phase above 1160 °C was pointed out by Kahn et al} There¬ 
fore, Fe 3 B may have been formed in the alloy at a high 


temperature to consume a substantial amount of boron to 
allow the formation of Nd 2 Fei 4 B at a lower temperature in 
the boron-depleted, neodymium-rich region of the alloy. In 
the present investigation, however, the as-quenched micro¬ 
structure changed gradually from an amorphous to a 
Fe 3 B/Nd 2 Fei 4 B nanocomposite with decreasing rotor surface 
velocity in a similar manner as the microstructure of a cor¬ 
responding amorphous alloy does during successive heat 
treatments.^ This observation may possibly indicate that an 
amorphous solid is formed first and subsequently decom¬ 
posed into Fe 3 B and Nd 2 Fei 4 B in the temperature range in 
which these phases are metastable when cooling rate is mod¬ 
erate. The elucidation of the rapid solidification behavior of 
this type of alloy is left for further investigations. 

The Fe 3 B/Nd 2 Fei 4 B hard magnets obtained in relatively 
slow surface velocities are continuous thick ribbons, the 
length of which may be as long as a few meters. The limi¬ 
tation of length occurs from a small span of a sample recov¬ 
ery chamber available in the experimental facility. The thick¬ 
ness of the materials is on the order of a few hundred 
micrometers, for which shaping of most conventional hard 
magnet materials by machining or polishing is not practical. 
Although it is known that MnAlC and FeCrCo permanent 
magnet materials can be fabricated by rolling in their manu¬ 
facturing process to produce plate-shaped permanent mag¬ 
nets, the former material has a lower saturation magnetiza¬ 
tion and the latter has only a small coercivity compared to 
the present materials obtained by direct quenching. There¬ 
fore, the thick flake magnets obtained in this investigation 
are unique and may open new application fields in which 
thin platelet permanent magnets with a high energy product 
are desired. 

V. CONCLUSION 

The Fe 3 B/Nd 2 Fei 4 B nanocomposite permanent magnets 
can be obtained directly from the melt via a melt-spinning 
technique by accomplishing the rapid solidification process 
under a reduced pressure of 1.3 kPa on a Cu roll moving at a 
surface velocity significantly slower than conventional melt 
spinning. Platelet permanent magnets with a thickness of 240 
jjm and magnetic properties of 

//cj“400 kA/m, and B^=1.15T have been obtained for 

Nd3 5Dy iFe73Co3GaiB 15 5. 

^R. Coehoorn, D. B. de Mooij, J. P. W. B. Duchateau, and K. H. J. Bus- 
chow, J. Phys. C 8, 669 (1988). 

^S. Hirosawa and H. Kanekiyo, J. Appl. Phys. 73, 6488 (1993). 

^S. Hirosawa and H. Kanekiyo, Proceedings of the Thirteenth International 
Workshop on Rare Earth Magnets and Their Applications (University of 
Birmingham, Birmingham, 1994), p. 87. 

J. J. Croat, J. F. Herbst, R. W. Lee, and F. E. Pinkerton, J. Appl. Phys. 55, 
2078 (1984). 

^A. Manaf, R. A. Buckley, and H. A. Davies, J. Magn. Magn. Mater. 128, 
302 (1993). 

^G. C. Hadjipanayis, L. Withanwasam, and R. F. Krause, IEEE Trans. 
Magn. 31, 3596 (1995). 

^E. F. Kneller and R. Hawig, IEEE Trans. Magn. 27, 3588 (1991). 

^Y. Kahn, E. Kneller, and M. Sostarich, Z. Metallkd. 73, 553 (1988). 




JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Analysis of magnetic behavior of exchange-enhanced SmFeCo magnets 

M. Dahlgren and R. Grossinger 

Institut fur Experimentalphysik, Technische Universitdt Wien, 

Wiedner Hauptstrasse 8-10A-1040 Wien, Austria 

D. R. Cornejo and F. P. Missell 

Instituto de Fisica, Universidade de Sdo Paulo, CP 66318, 05315-970 Sao Paulo, SP, Brazil 

A series of densified exchange-enhanced SmFeCo magnets was produced by mechanical alloying, 
followed by a heat treatment. The nanocrystalline phases and the grain size distribution of the 
samples were characterized from x-ray diffraction patterns. Magnetic measurements in terms of 
different models were analyzed for the temperature behavior of the magnetization and coercivity. 

One analytical formulation was derived from the random anisotropy model predicting that with 
increasing MyiM^ ratio a decreasing coercivity occurs. Another numerical approach, which is based 
on a micromagnetic calculation using finite element techniques was also applied. Attempts were 
made to improve the existing model derived from the finite element technique. The nucleation 
model was found to be unsatisfactory for describing the temperature-dependent coercivity. © 1998 
American Institute of Physics, [80021-8979(98)43011-1] 


Nanocrystalline hard magnetic materials increasingly 
form an important area for research on magnetic materials. 
This development started with the study of low rare earth 
containing materials like melt-spun Nd 4 Fe 7 gBi 8 by Coehoom 
et al in 1988.^ Independently, in 1987 Keem et al, reported 
a remanence enhancement in isotropic rapidly-quenched 
Nd-Fe-B ribbons containing additions of Al and Si.^’^ Since 
then many different compounds such as Sm-Co"^ with a 
maximum coercivity up to 75 kOe or a two-phase 
a-Fe/Sm-Fe-N^ were produced in the nanocrystalline or 
nanocomposite state. 

Stoner and Wohlfarth^ predicted that the remanence 
should be half of the saturation magnetization (MJ for 
single phase uniaxial materials assuming an isotropic set of 
noninteracting grains. From this prediction single-phase 
uniaxial materials are defined as remanence enhanced when 
the remanence is above half of . In all these materials 
nanocrystals of the hard magnetic phase with grain sizes be¬ 
tween 10 and 35 nm were found. For hard magnetic materi¬ 
als, the anisotropy energy overrides in general the stray field 
energy. In this case, the length where the extension of spin 
inhomogeneities is r educe d by 1/e is referred to as the ex¬ 
change length /e^= ^lA/K (where A is the exchange stiffness 
constant and K is the anisotropy constant). Due to the fact 
that the grain size is of the same order as the magnetic ex¬ 
change length, the coupling between the grains becomes ex¬ 
tensive enough to considerably enhance the remanence. 

All these materials are isotropic due to the production 
processes generally used (rapidly quenching, mechanical al¬ 
loying). It was found that the exchange coupling influences 
intrinsic properties such as the spin reorientation 
temperature^ as well as the Curie temperature.^ A simple 
measure of the exchange coupling is, in addition to the shape 
of recoil curves^ and the hysteresis loop, the ratio remanence 

to saturation magnetization . 

Starting from elementary powders, three com¬ 
positions, Smi8.iFen.oCo7o.9, Smi8 4Fe23.4Co58 2 » and 


Smi 8 . 2 Fe 33 2 Co 48 6, Were produced by mechanical alloying 
resulting in a quasi-amorphous matrix. The quasi-amorphous 
materials were cold pressed into 3 mm diameter cylinder, 
wrapped in Ta foil, and heated under 10"^ mbar vacuum for 
15 min at 600-700 °C. So, the quasi-amorphous Sm-Fe-Co 
can transform into many different nanophases, such as 
Sm 2 (Co, Fe)i 7 , Sm(Co, Fe) 5 , Sm 2 (Co, Fe) 7 , Sm(Co, Fe) 3 , 
and a-(Fe, Co). Because the phases have similar crystallo¬ 
graphic structure it is very difficult to distinguish the differ¬ 
ent phases from x-ray diffraction. For the compositions used 
in the present work, the expected hard magnetic phase would 
be the Sm(Co, Fe )5 phase. However, according to a previous 
study^^ the presence of Fe in the quasi-amorphous phase 
seems to prevent the formation of Sm(Co, Fe) 5 . Instead a 
mixture Sm 2 (Co, Fe)i 7 , Sm 2 (Co, Fe) 7 , Sm(Co, Fe) 3 , and a- 
(Fe, Co) was found.From our x-ray measurement it seems 
that Sm 2 (Co, Fe )7 and Sm(Co, Fe )3 do not exist in the 
samples. The average grain size and the grain size distribu¬ 
tion of the samples were evaluated by analyzing the x-ray 
diffraction line broadening (Table I).*^’*^ 

The determination of the saturation magnetization, , 
is very important to obtain the characteristic ratio M,.IM^ for 
exchange enhanced magnets. To determine of isotropic 
hard magnetic materials accurately, high fields magnetic 
measurements are necessary in order to exceed the high mag¬ 
netocrystalline anisotropy of the hard magnetic phases as 
well as a reliable extrapolation method (e.g., the law of ap¬ 
proach to saturation). Therefore magnetization measure¬ 
ments were performed on the SmFeCo magnets in a pulsed 
field magnetometer with a maximum applied field of 35 T. 
With this method the temperature dependence of the ratio 
M^/Ms as well as the coercivity were measured from 4.2 K 
up to room temperature. The anisotropy field was estimated 
from the law of approach to saturation. The estimated anisot¬ 
ropy field for the samples were determined to be between 20 
and 30 T at room temperature. This indicates that 
Sm 2 (Co, Fe )7 at room temperature) or 


0021 -8979/98/83(11 )/6268/3/$15.00 


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© 1998 American Institute of Physics 


J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Dahlgren et ai 6269 


TABLE 1. The average grain size, (see Refs. 11, 12) for different com¬ 
positions evaluated by analyzing the x-ray diffraction line broadening. (Sm, 
Fe, Co) grain corresponds to the grains composed from the hard magnetic 
(Sm, Fe, Co) phases. 



Sm](Co, Fe )5 T at room temperature) is more prob¬ 
able instead of Sm 2 (Co, Fe)i 7 at room tempera¬ 

ture). 

In Fig. 1 it is evident that the ratio M^fM^ is increasing 
with decreasing temperature. This indicates that the coupling 
is increasing at lower temperature. If the coupling is increas¬ 
ing we would expect that the exchange length should in¬ 
crease with decreasing temperature. This is possible if the 
anisotropy constant K is decreasing. Blaettner et alP found 
this behavior for Sm 2 Co 7 . Therefore those data were used to 
describe the anisotropy field. 

Using the available data, analytical relations between the 
coercivity and the enhanced remanence can be tested. There 
exists one analytical prediction relating coercivity and re¬ 
manence: 


1 

W~2 






( 1 ) 


This formula was derived from the random anisotropy 
model^^ and predicts a decreasing coercivity with increasing 
MylM^ ratio. This analytical relation was tested for our mea¬ 
surements and could not reproduce the temperature behavior. 
In fact, the results showed a behavior opposite to the predic¬ 
tion of the model. In our measurements both M^IM^ and the 
coercivity are increasing (compare Fig. 1 and Fig. 3). 

Another numerical approach, which is based on a micro- 
magnetic calculation using finite element techniques'^ deliv¬ 
ers a relation of the type: 



Temperature (1^ 


FIG. 1. The temperature behavior of the remanence to saturation magneti¬ 
zation ratio measured using a pulsed field magnetometer. A fit according to 
the model of Fischer et al. (see Ref, 16) is included for comparison. 



Temperatire (1^ 


FIG. 2. The modified model of Fischer et al (see Ref. 16) which assumes 
the exchange coupling to be three dimensional, is compared to the measured 
data. 


■^ = a^bHD/8t^) (2) 

with = where D is a grain size, 

Ss=7t4aIk represent the domain wall width of the hard 
magnetic phase, are the saturation polarization 

of the hard and soft magnetic phases, and are the 

volume fractions of the hard and soft magnetic phases. In the 
case of only uncoupled hard magnetic grains a = 0.5 and b 
= 0, whereas in the other cases a increases with the amount 
of the soft magnetic phase: 0.5<a< 1. ^ is -0.045 without 
the soft magnetic phase and may increase to —0.15 depend¬ 
ing on the amount of the soft magnetic phase. 

Since, in all of the samples measured, there existed only 
a small amount of soft magnetic phase, a was fixed to be 0.5. 
If the parameter a was left free in the fitting procedure it 
tended to reach values in the range of 0.1-0.3, which have 
no physical meaning. 

This model shows the right tendency when applying it to 
the measured data, but the fit was not able to reproduce the 
actual temperature behavior. One disadvantage of Eq. (2) is 



Temperature (K) 


FIG. 3. Temperature dependence of the coercivity measured by using a 
pulsed field magnetometer. 


















6270 


J. Appl. Phys., VoL 83, No. 11, 1 June 1998 


Dahlgren et ai 



that DISb describes the coupling of the phases for a one¬ 
dimensional model. A 2D model would be able to describe 
the ratio of the total grain area to the exchange coupled grain 
area. If, instead of DI8g, the ratio of total volume Vtot to 
coupled volume Vcoupi is used, a 3D model would result. The 
ratio of coupled volume to total volume can be defined as the 
reduced volume . 

Vcoupi (£>/2)^-(D/2-/,J^ 

{D/2f • ^ 

By introducing the reduced volume, the following ex¬ 
pression can be defined: 

M, 

— = a + Ml/Vred)- (4) 

If the sample is fully exchange coupled, M^JM^ in Eq. 
(4) should be equal to 1 when Ered is equal to 1. For the 
coupled boundary condition M^IM^ [ln(l)=0] would be 
equal to a and with a=\ the boundary condition is fulfilled. 
If the grains in the magnet are uncoupled, M^.IM^ in Eq. (4) 
should be between 0.5 and 1 (depending on the amount of 
soft magnetic phase), when b and Vred ^*'e equal to zero. By 
applying THospital rule on Eq. (4) and letting b and E^d 
approach zero M^iM^ will be equal to a. Since a can be 
chosen between 0.5 and 1 also this boundary condition is 
fulfilled. 

In Fig. 2 the modified model of Eq. (4) is tested and 
indeed the experimental data fit the model. Increasing the 
amount of Fe in the samples results in a maximum for the 
parameter a and a minimum for parameter b for the sample 
with Fe=^23 at%. By comparing the values in Fig. 1 with the 
values in Fig. 2, b seems to be of a factor 10 larger in the 
modified model. Also the expected values for b{ — 0.0A5<b 
< “0.15) from Fischer et are exceeded by a factor of 2 
in the modified model. 

We also attempted to fit the coercivity using an equation 
similar to that for the ratio from Fischer et al‘}^ 

Hc=HJic + d\Q{DI^B'^)\ (5) 


However, this formula shows a different behavior than 
the measured data. Here HcIH^ has a convex shape and 
ln(D/<%) has a concave shape with the temperature. 

The nucleation model‘s can be used to describe 


Hc(T)/J,(T): 


Hr 




Js "" J. 


eff- 


( 6 ) 


The values obtained from the nucleation model are 
shown in Fig. 4. 

Here the microstructural a parameter has negative val¬ 
ues. A negative value of the a parameter has no physical 
meaning, which indicates that the nucleation model cannot 
be applied for our samples. However, it is worth noting that 
an increase of Fe in the samples results in a decrease of the 
microstructural parameters. One more disadvantage of the 
nucleation model is that it only indicates if the magnetization 
processes is nucleation controlled and do not delivers any 
deeper understanding of the exchange coupling. The same 
problems arise when applying a similar model such as the 
nucleus-expansion model. 

This work was partly supported by Austrian Science 
Foundation under the project PI0945-PHY, by the EC within 
the framework Alfa (Project No. ALR/B7-3011/94.04- 
5.0263.8) and also by a traveling grant from Ostereichische 
Forschungsgemeinschaft. 


' R. Coehoorn, D. B. de Mooij, J. P. W. B. Duchateau, and K. H. J. Bus- 
chow, J. Phys. (France) C8, 669 (1988). 

^J. E. Keem, G. B. Clemente, A. M. Kadin, and R. W. McCallum, “Hard 
and Soft Magnetic Materials with Applications including Superconductiv¬ 
ity,” in Proceeding Conference on ASM Materials Week 87, edited by J. 
A. Salsgiver (American Society for Metals, Metals Park, OH, 1987). 

^G. B. Clemente, J. E. Keem, and J. P. Bradsley, J. Appl. Phys. 64, 5299 
(1988). 

Liu, M. P. Dallimore, P. G. McCormick, and T. Alonso, J. Magn. 
Magn, Mater. 116, L320 (1992). 

^J. Ding, Y. Liu, P. G. McCormick, and R. Street, J. Magn. Magn. Mater. 
123, L239 (1993). 

^E. C. Stoner and E. P. Wohlfarth, Philos. Trans. R. Soc. London, Ser. A 
240, 599 (1948). 

^X. C. Kou, M. Dahlgren, R. Grossingcr, and G. Wiesinger, J. Appl. Phys. 
81, 4428 (1997). 

*M. Dahlgren, R. Grossinger, E. de Morais, S. Gama, G. Mendoza, J. F. 
Liu, and H. A. Davies, Proceedings of Intermag, New Orleans, 1997 (in 
print). 

^E. F. Kneller and R. Hawig, IEEE Trans. Magn. 27, 3588 (1991). 

*°P. A. I. Smith Ph.D. thesis, the University of Western Australia, Australia, 
1997. 

^'S. Enzo, G. Fagherazzi, and A. Benedetti, J. Appl. Crystallogr. 21, 536 
(1988). 

*^A. Benedetti, G. Fagherazzi, S. Enzo, and M. Battagliarin, J. Appl. Crys¬ 
tallogr. 21, 543 (1988). 

’^H. E. Blaettner, K. J. Strnat, and A. E. Ray, in The Rare Earths in Modern 
Science and Technology, edited by G. J. McCarthy and J. J. Ryhne (Ple¬ 
num, New York, 1978), p. 421. 

^'^S. Huo and H. A. Davies, 8th International Symposium on Magnetic An¬ 
isotropy and Coercivity, Birmingham, UK, 1994, p. 155. 

*^R. Alben, J. J. Becker, and M. C. Chi, J. Appl. Phys. 49, 1653 (1978). 

*^R. Fischer, T. Schrefl, H. Kronmiiller, and J. Fidler, J. Magn. Magn, 
Mater. 153, 35 (1996). 

*^G. Herzer, W. Fernengel, and E. Adler, J. Magn. Magn. Mater. 58, 48 
(1986). 

‘^D. Givord, A. Lienard, P. Tenaud, and T. Viadieu, J. Magn. Magn. Mater. 
67, L281 (1987). 



JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


The effect of boron and rare earth contents on the magnetic properties 
of La and Cr substituted a^Fe/R2Fei4B-type nanocomposites 

W. C. Chang,D. Y. Chiou, and S. H. Wu 

Department of Physics, National Chung Cheng University, Ming-Hsiung, Chia-Yi 621, Taiwan, 

Republic of China 

B. M. Ma, Q. Chen, and C. O. Bounds 

Rhodia, Rare Earths and Gallium, CN 7500, Cranbury, New Jersey 08512 

The effect of phase transformations on the magnetic properties of rare earth lean 
(Ndo.gsLao 05 ) 9 . 5 ^^ 82 . 5 (-^ = 0 to 4.5) and (Ndo,95Lao.o5)7.5+jF^80.5-)?Cr2Bio Cy = 0 to 4) 
melt spun ribbons has been investigated. The phase mixture, after optimum thermal processing, was 
found to be strongly dependent upon the rare earth and boron contents. Two magnetic phases, 
namely a-Fe and R 2 Fei 4 B, were found in (Ndo. 95 Lao.o 5 ) 9 . 5 Fe 82 . 5 -;cCr 2 B 6 +j, alloy ribbons with x 
ranging from 0 to 4.5. For a fixed rare earth content, increases in the boron concentration resulted 
in a higher volume fraction of the R 2 Fei 4 B phase, which led to an increase in the intrinsic coercive 
force from 7.1 kOe for x = 0 to 12.6 kOe for x = 4.2. A R,=9.6kG, iH, = 9,5 kOe, and 
= 15.5 MGOe have been obtained in the alloy ribbons with x = 4.5. On the other hand, the increase 
in the total rare earth content, or y, was found to suppress the formation of the metastable Fe 3 B 
and/or R 2 Fe 23 B 3 phases and to yield an a-Fe/R 2 Fei 4 B mixture for y > 1. This increase in total rare 
earth content not only increases the volume fraction of both the R 2 Fei 4 B and a-Fe phases but also 
decreases the average grain size of these phases as evidenced by transmission electron microscopy 
analysis. This decrease in the average grain size may subsequently enhance the intrinsic coercivity 
and the remanence of the ribbons. A of 9.5 kG, a of 13.2 kOe, and a of 18 MGOe 

were achieved in (Ndo. 95 LaQ 05 )iiFe 77 Cr 2 Bio. © 1998 American Institute of Physics, 
[80021-8979(98)20711-0] 


Because of their high remanence {Bf) and high maxi¬ 
mum energy product two types of nanocomposite 

magnets, namely, a-Fe/Nd 2 Fei 4 B^ and Fe 3 B/Nd 2 Fei 4 B^’^ 
have been widely studied for the bonded magnet application. 
The B^ of these nanocomposites can be strongly influenced 
by incorporating group II or IV elements'^’^ and/or by the 
controlling of the grain size and volume fraction of a-Fe and 
Nd 2 Fei 4 B^ or Fe 3 B and Nd 2 Fe] 4 B.^’^ Similarly, flc and 
squareness of the demagnetization curve are also strongly 
affected by elemental substitution and microstructure.^’^ 
Production of precursor materials with an amorphous or 
nanoscaled structure and precise thermal treatment are the 
two key processes which determine the magnetic perfor¬ 
mance of nanocomposite materials. For a-Fe/Nd 2 Fei 4 B type 
nanocomposites, it was found that the alloy composition can 
ease the production of amorphous ribbons by melt spinning.^ 
Furthermore, the size and volume fraction of a-Fe and 
Nd 2 Fei 4 B can be manipulated by thermal processing.^ Al¬ 
though (57/)jnax values of 19-21 MGOe have been obtained 
on a-Fe/Nd 2 Fei 4 B-type nanocomposites,the correspond¬ 
ing flc obtained was normally less than 9 kOe, regardless of 
the method of fabrication or elemental substitution. Previ¬ 
ously, we have shown that La and Cr substitution for Nd and 
Fe, respectively, in Nd 9 5 Fegi 5 B 9 improved the flc of the 
optimized crystallized ribbons.^ This increase in was as¬ 
cribed to the formation of Cr-rich borides in the grain bound¬ 
ary region which enhance the grain separations, suppress the 


^^Electronic-mail: phywcc@ccunix.ccu.edu.tw 


grain growth, and/or smooth the grain surface defects. An 
flc of 9.1 kOe and a {BH)^^^ of merely 12.5 MGOe have 
been obtained. It is of interest to extend this study to alloys 
of various boron contents to see if this trend still holds. An 
alloy series with compositions of (Nd,La )9 5 Fe 82 . 5 -xCr 2 B 6 +^ 
{x~0 to 4.5) was selected for investigation. 

To obtain strong exchange-coupling interaction, the vol¬ 
ume fraction of Nd 2 Fei 4 B (the hard magnetic phase) and 
a-Fe (the soft magnetic phase) phases must be maintained 
above a critical ratio.^“^^ Although forming grain boundary 
phase(s) may increase the , one usually needs to balance 
the amount of grain boundary phase to increase with the 
requirement to achieve a high saturation magnetization and 
an effective exchange coupling. For a given boron content, 
varying the total rare earth content could be one of the ways 
to adjust the amount of Nd 2 Fei 4 B and a-Fe phase to achieve 
this goal. For this reason, (Ndo.95Lao,o5)7.5+yFe8o.5-yCr2Bio, 
where y = 0, 1, 2, 3.5 and 4, was selected for further study. 

Alloy ingots with compositions 

(Ndo. 95 Lao 05 ) 9 . 5 ^ 682 . 5 -A:Cr 2 B 5 +^ (x = 0 —4.5) and 
(Ndo. 95 Lao.o 5 ) 7 . 5 +>.Fe 8 o. 5 ~);Cr 2 Bio (y = 0“4) were prepared 
by vacuum induction melting. Ingot pieces of approximately 
3 grams were crushed into small pieces to accommodate the 
size of crucible for melt spinning. Ribbons were produced 
with wheel speeds (V^) ranging from 15 to 30 m/s. X-ray 
powder diffraction with Cu Xa radiation was utilized to de¬ 
termine the degree of crystallinity in the ribbons. Selected 
ribbons were thermally treated at 650-700 °C for 10 min for 
crystallization and to improve the permanent magnetic prop- 


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J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Chang et al. 



FIG. 1. TMA curves for crystallized (Ndo. 95 Lao.o 5 ) 9 . 5 Fe 82 . 5 -xCr 2 Bg+^ rib¬ 
bons (a) ;r = 0, (b) x=3, (c) x = 4, (d) x = 42, and (e) x = 4.5. 


erties. The magnetic phases and the corresponding Curie 
temperatures (1^) were identified by a thermal gravimetric 
analyzer (TGA) with an externally applied magnetic field, 
i.e., conventionally referred to as the thermo magnetic analy¬ 
sis (TMA). The magnetic properties of the as-quenched rib¬ 
bons and the thermally treated ribbons were measured by a 
vibrating sample magnetometer (VSM). Transmission elec¬ 
tron microscopy (TEM) with energy dispersion analytical x 
ray (EDAX) was employed to examine the microstructure 
and identify the phases of the ribbons obtained. 

Shown in Fig. 1 are the TMA scans of 
(Ndo.95Lao,o5)9.5l^^82.5-xC*'2B6+;j. (x = 0, 3, 4, 4.2, and 4.5) 
ribbons after optimum annealing treatments. Despite the bo¬ 
ron content being varied from 6 to 10.5 at. %, only two mag¬ 
netic phases, namely, a-Fe and R 2 Fei 4 B, were detected. The 
metastable Fe 3 B and R 2 Fe 23 B 3 phases that usually appear in 
the ternary boron rich Nd-Fe-B system were not detected. 
This suggests that La and Cr substitution may be effective in 
suppressing the formation of Fe 3 B and R 2 Fe 23 B 3 phases in 
ribbons at least in the range of boron contents studied. As¬ 
suming that a-Fe and R 2 Fei 4 B exhibit the same magnetiza¬ 
tion during TMA measurement, one may estimate the vol¬ 
ume fractions of the a-Fe and R 2 Fei 4 B phases in each ribbon 
by comparing the relative peak heights. In general, the vol¬ 
ume fraction of R 2 Fei 4 B in the ribbons with a higher boron 
content, jc = 4, 4.2, and 4.5, is more than those with a lower 
boron content, a: = 0 and 3. 

Shown in Fig. 2 are the variation of flc, and 
(^^)max of (Ndo.95Lao.05)9.5F082.5-xCr2B6+;j. {x = 0, 3, 4, 4.2, 
and 4.5) ribbons after an optimum annealing treatment. At 
jc = 0, a Br of 9.5 kG, a (BH)^^^ of 15.5 MGOe and an 
of merely 7.1 kOe were obtained. Both B^. and de¬ 

crease initially with increasing boron content, then increase 
slightly when x was increased above 3. On the contrary, the 



FIG. 2. Comparison of the magnetic properties of 
(Ndo. 95 Lao.o 5 ) 9 . 5 Fe 82 . 5 -xCr 2 B 6 +j, (;c = 0-4.5) ribbons annealed at optimum 
condition. 


increased initially with increasing boron content, reached 
a maximum of 12.6 kOe at .x = 4.2 then decreased drastically 
at x = 4.5 indicating a possible phase transformation or a 
change of phase mixture. A B^ of 9.6 kG, an of 9.5 kOe, 
and a of 15.5 MGOe were obtained at jr = 4.5. This 

suggests that a B^ of more than 9 kG, (BH)^^^ of more than 
15 MGOe, and of more than 9 kOe can simultaneously 
be obtained in (Ndo. 95 Lao.o 5 ) 9 . 5 Fe 82 . 5 -jcCr 2 B 6 +^ ribbons if x 
is maintained at slightly above 4. Around this boron level, 
the boron was surmised to react with Cr forming Cr boride(s) 
in the grain boundary region and freeing some Nd (and La) 
and Fe to form the desired R 2 Fei 4 B phase. The increase of 
iHc with increasing x, presumably, arises from two factors: 



0 100 200 300 400 500 600 700 800 900 

Temperature (®C) 


FIG. 3. TMA curves for crystallized (Ndo. 95 Lao.o 5 ) 7 . 5 +jFe 8 o. 5 -j-Cr 2 Bio rib¬ 
bons (a) y = 0, (b) y-\, (c) y = 2, (d) y = 3.5, and (e) y = 4. 






J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Chang et a!. 6273 


TABLE I. Estimated volume fraction ratio of magnetic hard and soft phases 
(R 2 Fei 4 B-type/a-Fe ratio) of (Ndo,95Lao.o5)7 5 +>-Fe 80 5 -yCr 2 Bio ribbons (y 
= 0 to 4). 


Peak height (arb. units) 

Composition 

Hard phase 

Soft phase 

R2Fei4B/Q:-Fe 

y = 

(R 2 Fei 4 B type) 

(of-Fe) 

Ratio 

0 

4.498 

1.260 

3.57 

1 

2.014 

0.968 

2.08 

2 

1.387 

0.701 

1.98 

3.5 

0.945 

0.736 

1.28 

4 

0.809 

0.504 

1.61 


the increase in the volume fraction of 2:14:1 phase^’^^ and 
the increase in the amount of grain boundary phases which 
serves as grain separator. How to balance these two contri¬ 
butions is the key for successful production of nanocompos¬ 
ites with high iHc and 

Shown in Fig, 3 are the TMA scans of 
(Ndo.95Lao.o5)7.5+);I'^80.5“>’C!r2Bio (y = 0, 1, 2, 3.5, and 4) rib¬ 
bons after the crystallization treatment. Three magnetic 
phases, namely, (Nd, La) 2 (Fe, Cr)i 4 B, R 2 Fe 23 B 3 , and a-Fe 
were found in y = 0 and 1. However, only two magnetic 
phases, (Nd, La) 2 (Fe, Cr)i 4 B and a-Fe, were observed on 
y = 2, 3.5, and 4, The peak heights of the hard magnetic 
phase (R 2 Fei 4 B) and soft magnetic phase (a-Fe) measured 
by TMA scans and the estimated R 2 Fei 4 B/a-Fe ratio of these 
materials are listed in Table I. The R 2 Fei 4 B/a-Fe ratio de¬ 
creases from 3,57 fory = 0 to 1.28 for y = 3.5 then increases 
again to 1.61 for 3; = 4. It is worth noting that the estimated 
R 2 Fei 4 B/a-Fe ratio only takes into account the two magnetic 
phases detected. Phases which were not detected by TMA 
scans are not included in this consideration. A detailed ana¬ 
lytical work by TEM or microprobe is certainly needed along 
this aspect to confirm our hypothesis. 

Shown in Table II are the comparison of flc , and 
(^-^)max obtained for (Ndo. 95 Lao.o 5 ) 7 . 5 + 3 ;Fe 8 o. 5 ->>Cr 2 Bio (y 
= 0, 1, 2, 3.5, and 4) ribbons after optimum crystallization 
treatments. The B^ and of the ribbons with y = 0 and 1 
are extremely low. However, these values are improved sig¬ 
nificantly when the rare earth content was increased to y 
= 2 or 3,5, A of 9.5 kG, an of 13.2 kOe, and a 
(5//)jnax of 18.0 MGOe have been achieved on y = 3.5. Most 
importantly, an as high as 13 kOe, a B^ of more than 9.5 
kG, and a {BH)^^^ of 18 MGOe have been achieved. These 


TABLE IL Magnetic properties of (Ndo, 95 Lao,o 5 ) 7 . 5 +yFe 8 o. 5 -;yCr 2 Bio 
~ 4) ribbons after optimum annealing. 


Composition 

Br 

(kG) 

,ffc 

(kOe) 

(MGOe) 

0 

8.1 

3.1 

4.0 

1 

10.3 

4.0 

10.0 

2 

8.6 

9.5 

12.6 

3.5 

9.5 

13.2 

18.0 

4 

9.9 

5.0 

14.0 



FIG. 4. Transmission electron micrographs of crystallized 
(Ndo.95Lao,o5)7.5+>>Fe8o.5->-Cr2Bio ribbons (a) y = Q, (b) y = 2, and (c) y 
= 3.5. 

high values have never been reported in either the a- 
Fe/Nd 2 Fei 4 B or the Fe 3 B/Nd 2 Fei 4 B nanocomposites. 

Shown in Figs. 4(a), 4(b), and 4(c) are the TEM micro¬ 
graphs of ribbons with y = 0, 2 and 3.5, respectively, after 
optimum thermal treatments. Three distinct phases, namely, 
(Nd, La) 2 (Fe, Cr)i 4 B, R 2 Fe 23 B 3 (as the arrows indicate), 
and a-Fe were found in y = 0. Only two magnetic phases, 
(Nd, La) 2 (Fe, Cr)i 4 B and a-Fe, were detected in y = 2 and 
3.5. These results are consistent with TMA scans. In addi¬ 
tion, a thin layer grain boundary phase (nonmagnetic) was 
found only in y = 2 but not in y = 0 and 3.5. Moreover, the 
grain sizes, both the (Nd, La) 2 (Fe, Cr)i 4 B or the a-Fe 
phases, in y = 3.5 and 0 are finer than those in y = 2. The 
sizes of a-Fe and (Nd, La) 2 Fei 4 B are estimated around 20 
and 20-30 nm for y = 3.5 and 0, and 25 and 70-80 nm for 
y = 2, respectively. This suggests that the presence of the 
R 2 Fe 23 B 3 phase may restrict the grain growth in 
(Ndo. 95 Lao.o 5 ) 7 . 5 Fe 8 o. 5 Cr 2 Bio and the higher La concentration 
in y>2 may also limit the grain growth. A fine grain size is 
essential to induce a higher exchange coupling interaction 
between the 2:14:1 and a-Fe phases, resulting in a high B^. 

This work was supported by National Science Council, 
Taiwan, R.O.C. under Grant No. NSC-86-2112-M-194-012. 

'a. Manaf, R. A. Buckley, and H. A. Davies, J. Magn. Magn. Mater. 128, 
302 (1993). 

Schneider, D. Eckert, K. H. Muller, A. Handstein, H. Muhlbach, H. 
Sassik, and H. R. Kirchmayer, Mater. Lett. 9, 201 (1990). 

^H. Kanekiyo, M. Uehara, and S. Hirosawa, IEEE Trans. Magn. 29, 2863 
(1993). 

“^A. Manaf, P. Z. Zhang, I. Ahmed, H. A. Davies, and R. A. Buckley, IEEE 
Trans. Magn. 29, 2866 (1993). 

^A. Manaf, M. Al-Khafaji, P. Z. Zhang, H. A. Davies, R. A. Buckley, and 
W. Rainforth, J. Magn. Magn. Mater. 128, 307 (1993). 

^W. C. Chang and D. M. Hsing, J. Appl. Phys. 79, 4843 (1996). 

^ J. Bauer, M. Seeger, A. Zern, and H. Kronmuller, J. Appl. Phys. 80, 1667 
(1996). 

^W. C. Chang, S. H. Wu, B. M. Ma, and C. 0. Bounds, J. Appl. Phys. 81, 
4453 (1997). ’ 

^T. SchrefI, J. Fidler, and H. Kronmuller, Phys. Rev. B 49, 6100 (1994). 
^®R. Skomski and J. M. D. Coey, Phys. Rev. B 48, 1581 (1992). 

^^E. F. Kneller and R. Hawig, IEEE Trans. Magn. 27, 3588 (1991). 

O’Donnell, X.-L. Rao, J. R. Cullen, and J. M. D. Coey, IEEE Trans. 
Magn. (to be published). 





JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Anomalous high-temperature coercivities in hard nanocomposite alloys 

L. H. Lewis,®* J.-Y. Wang,'^* and D. O. Welch 

Department of Applied Science, Brookhaven National Laboratory, Upton, New York 11973-5000 

V. Panchanathan 

Magnequench International, Inc., 6435 Scatterfield Road, Anderson, Indiana 46013 

To elucidate the interphase interactions inherent to nanocomposite magnetic alloys, measurements 
of remanence , and coercivity were made on a series of four meltspun, remanence-enhanced 
nanocomposite alloys consisting solely of various amounts of Nd 2 Fe] 4 B and a-Fe. The phase 
constitution and microstructural scale of the alloys were characterized with synchrotron x-ray 
diffraction. Magnetic measurements were made using superconducting quantum interference device 
(SQUID) magnetometry on evacuated and encapsulated samples in the temperature range of 
300K^r^750K, in order to characterize the a-Fe component independently of the Nd 2 Fei 4 B 
component. The high-temperature coercivities of the samples increase with the amount of a-Fe 
present in the samples, ranging from an average value of approximately 75 Oe for the sample with 
14 wt % excess Fe to over 400 Oe at 700 K for the sample with 27 wt % excess Fe. The relatively 
high coercivities of the samples found at elevated temperatures imply that a tabular morphology of 
the a-Fe grains is conferring anisotropy to the phase; this conclusion is supported by transmission 
electron microscopy. It is concluded that while the significant coercivity of the a-Fe phase likely 
reduces the room-temperature remanence enhancement of the alloy below its theoretical ideal, the 
favorable interphase interface orientation promotes exchange coupling. © 1998 American Institute 
of Physics. [80021-8979(98)20811-5] 


I. INTRODUCTION 

A detailed understanding of the nature of the interphase 
magnetic coupling in exchange-spring nanocomposite alloys 
is of paramount importance to the modeling and optimization 
of their performance as permanent magnets. To this end, 
measurements of magnetization and coercivity 7/^ were 
made on a series of four meltspun nanocomposite alloys con¬ 
sisting solely of various amounts of Nd 2 Fei 4 B and a-Fe us¬ 
ing superconducting quantum interference device (SQUID) 
magnetometry on evacuated and encapsulated samples in the 
temperature range of 300 7^750 K, in order to follow 

the evolution of the magnetic properties as the Nd 2 Fei 4 B 
passes from the ferromagnetic to the paramagnetic regime. 
The result thus obtained and expounded upon below eluci¬ 
date the microstructural evolution of the alloys as increasing 
amounts of a-Fe are added to the Nd 2 Fei 4 B system. 

II. EXPERIMENTAL DETAILS 

The alloys were made from commercial-grade materials 
by standard melt-quenching techniques and annealed for 4 
min at 690 °C to optimize their magnetic properties. To 
verify the phase composition and average grain size of the 
alloys, synchrotron x-ray diffraction was performed on pow¬ 
dered samples using radiation of wavelength 0.90 A^X 
^1.18 A, well away from the absorption edge of iron and 
thus preventing fluorescence. Lattice parameters were deter¬ 
mined by a least-squares fitting program. Only two phases 


^^Electronic mail; lhlewis@bnl.gov 

’^^Present address: Applied Materials, Burton Drive, Bldg. 24, Santa Clara, 
CA 95054. 


were found, Nd 2 Fei 4 B and a-Fe; it is estimated that synchro¬ 
tron x-ray diffraction would detect minor phases of 0.1-1.0 
wt %} The crystallite sizes are determined from the half¬ 
width of the Bragg peak at the half-maximum intensity po¬ 
sition, corrected for the intrinsic broadening of the synchro¬ 
tron beam, using the Scherrer formula.^ The nominal 
compositions, lattice parameters, and the average grain size 
found for each constituent phase are given in Table I. The 
alloys are identified by their excess iron enrichment 8, de¬ 
fined as Nd 2 Fei 4 +^. The specimens studied contained the 
following amounts of excess Fe: 1 (^=0), 14 (^=4.6), 18 
(<5=7.2), and 27 wt %(^=9.3). The amount of excess iron 
was determined from the ferromagnetic hysteretic response 
measured at 750 K.^ The magnetic data were obtained on 
packed samples evacuated to 1X 10“^ Torr"^ using a 
maximum applied field of 5 T in the temperature range of 
300 7^ 780 K with a Quantum Design SQUID magne¬ 

tometer. The magnetic data were corrected for demagnetiza¬ 
tion effects, and the paramagnetic response from the 2-14-1 
phase was subtracted at each measurement temperature from 
the corrected data to yield the saturation magnetization of the 
a-Fe phase. Room-temperature remanence ratios were calcu¬ 
lated from corrected demagnetization extrapolated out to in¬ 
finite field, Table I. Electron microscopy (TEM) was per¬ 
formed on the sample containing the largest amount of 
excess a-Fe (^=9.3) using a JEOL 2000 FX transmission 
electron microscope on dimpled and subsequently ion-milled 
samples. 

III. RESULTS 

The data in Table I indicate that the scale of the micro- 
structure of all samples is similar, although not identical. The 


0021 -8979/98/83(11 )/6274/3/$15.00 


6274 


© 1998 American Institute of Physics 



J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Lewis et al. 6275 


TABLE L Alloy characterization S characterizes the iron enrichment, defined as Nd 2 Fei 44 .^. 


Stoichiometry 
(excess Fe wt %, S) 

Lattice parameters 

(A) 

Grain sizes 

Remanence (kG) 
at 300 K 

Remanence ratios 
B,/M,(/ 7 =oo), 300 K 

Nd 2 . 39 Fe 14 B 0.95 
(1 wt %, ^= 0 ) 

2-14-1: 

a = 8.804±0.002 
c= 12.261 ±0.005 

2-14-1: ^340 A 

6.3 

0.53 

Nd 2 Feig jB23g 

(14 wt%, S=4.6) 

2-14-1: 

fit = 8.791 ±0.001 
c= 12.170± 0.002 
a-Fe: a = 2.86 

2-14-1: -525 A 
a-Fe: ^ 175 A 

8,06 

0,52 

Nd2Fe2i 2 B 1.65 

(18 wt%. ^=7.2) 

2-14-1: 

a = 8.787 ±0.002 
c=12.178±0.003 
a-Fe: a = 2.87 

2-14-1: >«340A 
a-Fe: *“290 A 

9.21 

0.56 

Nd2Fe23.3Bi 45 

(27 wt% S=9.3) 

2-14-1: 

a = 8.805 ±0.002 
c=12.214± 0.005 
a-Fe: a = 2.88 

2-14-1: ^235 A 
a-Fe: *®180A 

10.09 

0.60 


grain sizes of the Nd 2 Fei 4 B phase are in the range of 25-50 
nm, and are always larger than that of the a-Fe phase, which 
is smaller than 30 nm in all instances. There is no obvious 
correlation between the amount of excess iron and the pre¬ 
cise scale of the resultant microstructure. Similarly, there is 
no obvious trend in the lattice parameters of the Nd 2 Fei 4 B 
phase with excess iron content, and the lattice parameter of 
the of-Fe phase agrees well with the JCPDS reference lattice 
parameter value for of-Fe of a = 2.8664 A.^ All samples ex¬ 
hibit moderate remanence enhancement and a smooth 
second-quadrant demagnetization curve. Figures 1 and 2 il¬ 
lustrate the trends of coercivity and saturation magnetization 
of the a-Fe phase, respectively, with temperature. The nomi¬ 
nally single-phase Nd 2 Fei 4 B sample exhibits a room- 
temperature coercivity value of 15 kOe, much higher than 
the coercivities of the two-phase nanocomposite samples; 
however, the temperature coefficient of coercivity (i.e., the 
slope of the coercivity versus temperature curve) is much 
smaller for the nanocomposite samples than it is for the 
single-phase sample. The inset of Fig. 1 shows an enlarge¬ 
ment of the coercivity trend at high temperatures of the 
samples studied. The high-temperature coercivity measure¬ 



FIG. 1. The variation of coercivity with temperature for the four alloys 
studied. Inset: Enlargement of the high-temperature portion of the graph. 


ments are quite reproducible and are essentially independent 
of temperature. Both Fig. 1, inset, and Fig. 2 indicate that 
there is a direct correlation between the amount of excess 
Q:-Fe present in the composite and the resultant remanences 
and coercivities. 

IV. DISCUSSION 

The measured saturation magnetizations for the samples 
at elevated temperatures confirm that the additional Fe added 
to the starting composition results in the formation of in¬ 
creasing amounts of a-Fe. The coercivities measured at el¬ 
evated temperatures are much greater than that expected for 
isotropic grains of a-Fe with diameters under 300 A. If one 
assumes that the a-Fe particles are randomly oriented and 
reverse coherently by rotation under the influence of a de¬ 
magnetizing field, the maximum coercivity expected at 
r=750 K is equal to^ 0.64- (Ky /Ms) ^^3 Oe, which is ap¬ 
proximately an order of magnitude less than the greatest co¬ 
ercivity measured. However, if the assumption that the par¬ 
ticles are isotropic is relaxed, the concept of shape anisotropy 
may be invoked to account for the relatively large measured 
coercivities. The maximum coercive force that may be ob¬ 
tained in iron from shape anisotropy may be as high as 4300 



FIG. 2. Saturation magnetizations at elevated temperatures of the ferromag¬ 
netic components present in the nanocomposite alloys studied. 



6276 J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Lewis et al. 



FIG. 3. TEM micrograph of a high-Fe region of microstructure of the 
sample ^=9.3, containing nominally 27 wt % excess iron. The arrow indi¬ 
cates the blocky a-Fe phase. 

Oe at 750 K.^ The relative temperature independence of the 
a-Fe coercivities also supports the hypothesis that the origin 
of the coercivity is likely to be shape anisotropy.^ 

Electron microscopy investigations also support the con¬ 
clusion that the a-Fe particles do not have the shape of ran¬ 
domly distributed spheres. Figure 3 is a TEM micrograph of 
a portion of the <5=9.3 sample that shows a higher relative 
concentration of iron than the bulk of the sample. The blocky 
phase, indicated by the arrow in Fig. 3, has been identified 
by energy-dispersive spectroscopy to largely consist of iron 
and is thus identified as the a-Fe component. Although the 
grain size of this region is not typical of the entire sample, it 
does illustrate the morphology of regions with large concen¬ 
trations of a-Fe. It is hypothesized that the a-Fe phase de¬ 
velops an increasingly tabular morphology with increasing 
excess Fe content in the alloys. 

The data presented above have two results that are sig¬ 
nificant for the hard magnetic performance of the nanocom¬ 
posites. The first result is that the coercivity of the a-Fe 


component is not extremely low when both phases are in the 
ferromagnetic regime, as is desired for optimum exchange 
coupling and remanence enhancement.^’^ If the coercivity 
measured at 750 K is normalized to the maximum coercivity 
expected at that temperature from shape anisotropy alone, 
extrapolation from the high-temperature data implies that the 
room-temperature coercivity of the a-Fe phase in the most 
Fe-enriched nanocomposite (^=9.3) is around 535 Oe. This 
conclusion implies that the entire volume of the constituent 
a-Fe grains is not exchange-coupled to the 2-14-1 phase, 
resulting in both a lower remanence enhancement and com¬ 
plex internal demagnetizing fields. However, the deduced 
elongated shape of the a-Fe precipitates in the alloy may 
serve to increase the remanence enhancement by realizing 
maximum interphase contact. 

ACKNOWLEDGMENTS 

Research performed under the auspices of the U.S. 
D.O.E., Division of Materials Sciences, Office of Basic En¬ 
ergy Sciences under Contract No. DE-AC02-76CH00016, 
and carried out in part at the National Synchrotron Light 
Source, Brookhaven National Laboratory, which is sup¬ 
ported by the U.S. D.O.E., Divisions of Materials and 
Chemical Sciences. 

‘ D. Cox (personal communication). 

^B. D. Cullity, in Elements of X-Ray Diffraction (Addison-Wesley, Read¬ 
ing, MA, 1978), p. 102. 

^L. H. Lewis, D. O. Welch, and F. Pourarian, J. Appl. Phys. 79, 5513 
(1996). 

H. Lewis and Konrad M. Bussmann, Rev. Sci. Instrum. 67, 3537 
(1996). 

^JCPDS Powder file #6-696; JCPDS-ICDD Copyright © 1995. 

^C. Kittel, Rev. Mod. Phys. 21, 541 (1949). 

^R. M. Bozorth, Ferromagnetism, American Telephone and Telegraph 
Company, 1978, reissued by IEEE Press, Piscataway, NJ, 1993, p. 833. 

^Eckart F. Kneller and Reinhard Hawig, IEEE Trans. Magn. 27, 3588 
(1991). 

^R. Fischer, T. Schrefl, H. Kronmiiller, and J. Fidler, J. Magn. Magn. 
Mater. 150, 329 (1995). 





JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Magnetic interactions in Fe-Ba hexaferrite nanocomposite materials 

M. I. Montero, F. Cebollada, M. P. Morales, J. M. Gonzalez,®^ and A. Hernando'^' 

Instituto de Ciencia de Materiales de Madrid —C.5./.C., Cantoblanco, 28049 Madrid, Spain 

Results are presented on the hysteretic behavior of Fe-rich, composite Ba hexaferrite-Fe samples 
prepared by ball milling. The most remarkable feature of these samples was the observation of loops 
which were displaced in the negative sense of the field axis. Similar to this, the field evolution of the 
isothermal and the demagnetization remanences evidenced the achievement upon the application of 
8 kOe fields of nonequivalent values of both quantities. Our results are discussed considering the 
different magnetic hardness of the two phases forming the sample and the occurrence of interphase 
(dipolar) interactions. © 1998 American Institute of Physics. [80021-8979(98)43111-6] 


I. INTRODUCTION 

Short range exchange and long range dipolar interactions 
are crucial in determining the hysteretic properties of many 
real magnetic materials, for example, the achievement of ex¬ 
treme softness in melt spun, partly crystallized FeSiBCuNb 
alloys or the induction of remanence enhancement in nano¬ 
crystalline, NdFeB-based alloys. In the first case the basic 
softening mechanism is the average, down to a reduced ef¬ 
fective value, of the grain magnetocrystalline anisotropy of 
large sets of exchange and dipolarly coupled grains.^ The 
remanence enhancement, observed in hard isotropic materi¬ 
als, is also related to the occurrence of strong intergranular 
exchange which helps to keep the magnetization direction of 
the nanograins away from their local easy axis and close to 
the internal field direction.^ The influence of interactions on 
the extrinsic properties is specially relevant in the case of 
composite materials where it has been predicted^ (and ex¬ 
perimentally tested in some particular cases) that the cou¬ 
pling of several magnetic phases could result in extremely 
soft"^ or hard properties.^ There are, however, two relevant 
obstacles to overcome in order to achieve some degree of 
control of the interactions and, through this, to improve the 
behavior of known materials for particular applications. On 
one hand, the absence of experimental techniques allowing 
one to measure interactions at a local level^ and on the other, 
the lack of a simple but realistic description of the influence 
of the dipolar coupling on the magnetization reversal 
mechanisms^ (dipolar interactions have a many-body nature, 
making them unsuitable to be analyzed in mean field terms). 
The aim of the present work is to contribute to the descrip¬ 
tion of the phenomenology associated with the presence of 
interactions. For this purpose we will present data on a com¬ 
posite material formed by nanosized Ba hexaferrite particles 
and micronsized Fe ones where the interphase interactions 
are, exclusively, of the dipolar type. 

II. PREPARATION OF SAMPLES AND EXPERIMENTAL 
TECHNIQUES USED 

We have prepared nanocomposite samples with nominal 
compositions given by Fej^/(BaFei 20 i 9 )i_;c, where x (x 


®^Electronic mail: jgonzalez@pinarl.csic.es 

*’^Also with: Instituto de Magnetismo Aplicado “Salvador Velayos”, REN- 
FEUCM, 28230 Las Rozas, Madrid, Spain. 

0021 -8979/98/83(11 )/6277/3/$15.00 


=0.7 and x = 0,9) denoted a volume fraction. The samples 
were prepared by milling for 2 h in ball mill appropriate 
mixtures of Fe (45 jum average particle size) and Ba hexa¬ 
ferrite [30 nm average particle size, according to the mea¬ 
surement of the (0001) reflection half maximum width] pow¬ 
ders. The precursor Ba hexaferrite particles were obtained by 
synthesis using a water-in-oil microemulsion.^ The phase 
distribution of the as-milled samples was checked through 
x-ray diffraction (XRD). The study of the hysteretic proper¬ 
ties of both the precurson Ba hexaferrite and the composite 
samples was performed in press-powder cylinders (3 mm 
height X 3 mm diameter) by using a vibrating sample magne¬ 
tometer. 

III. EXPERIMENTAL RESULTS 

Figure 1 shows the x-ray diffractogram taken in different 
as-milled Fe-Ba hexaferrite composite samples. As observed 
in the figure the only detected reflections were those corre¬ 
sponding to <x-Fe. (The diffractograms did not show any in¬ 
dication of the presence in the milled materials of phases 
different from the precursor ones.) 

In Fig. 2 we present the room temperature demagnetiza¬ 
tion branch of the hysteresis loop measured in the starting Ba 
hexaferrite particles. The inset in that figure shows the field 
dependence of the associated differential susceptibility. The 
critical field of the precursor Ba hexaferrite (demagnetizing 
field for which a differential susceptibility maximum is mea- 



6277 


© 1998 American Institute of Physics 


6278 


J. Appl. Phys., Vol. 83, No, 11, 1 June 1998 


Montero et al. 



FIG. 2. Demagnetization curve measured, at room temperature, in the start¬ 
ing Ba hexaferrite particles. Inset: field dependence of the associated differ¬ 
ential susceptibility. 


sured) was of 6225 Oe. Upon milling, the different samples 
exhibited, at all the considered temperatures, smooth demag¬ 
netization curves indicating the occurrence of coupling be¬ 
tween the two present magnetic phases. In Fig. 3 we present 
a loop measured at room temperature and with a maximum 
applied field of 8 kOe in the jc = 0.9 sample. Very interest¬ 
ingly, the loop was measurably displaced (36 Oe) in the 
sense of the negative fields (see the inset in Fig. 3). The 
magnitude of this displacement decreased with the decrease 
of the Fe volume percentage. In the upper inset in Fig. 3, we 
present the evolution with the applied demagnetizing field of 
the room temperature differential susceptibility measured in 
the jc = 0.9 sample. The demagnetization of the softest (a-Fe) 
regions of the sample originated from the low field peak after 
which the susceptibility monotonously decreased. A com¬ 
parison of the behavior observed in the precursor Ba hexa¬ 
ferrite particles with that measured in the composite samples 
showed that the field range in which the demagnetization of 
the hard phase proceeded was, in both cases, clearly differ¬ 
ent, whereas in the case of the precursor powders (Fig. 2) 
that range spanned —4000 Oe around the critical field, in the 
case of the composite samples (Fig. 3) the demagnetization 
took place due to the Fe-Ba hexaferrite interactions in a 
much wider field region starting at fields of the order of those 
involved in the a-Fe reversal and spanning up to 12 kOe. 



H,pp(KOe) 


FIG. 3. Hysteresis loop measured, at room temperature, in the .r-0.9 
sample. Upper inset: field dependence of the associated differential suscep¬ 
tibility. 



0 2 4 6 8 


H.„(KOe) 


D 

E 

<D 


C 

0 ) 

c 

(0 

E 

0) 

q: 



HapptKOe) 


FIG. 4. Isothermal and demagnetization remanences curves measured, at 
room temperature, in the samples .x = 0.9 and jc = 0.7. Insets: associated 
plots. 


Our results for the field evolution of the isothermal, M/, 
and demagnetization, Mj , remanences are presented in Fig. 
4. [Mi was measured by increasing (starting from the demag¬ 
netized state) the maximum applied field up to 8 kOe and 
was obtained by first saturating the sample under a magne¬ 
tizing 8 kOe field and then applying increasing demagnetiz¬ 
ing fields down to -8 kOe.] In Fig. 4 it is observed in both 
samples that the 8 kOe isothermal and demagnetization re¬ 
manences are different. As a consequence of this asymmetry, 
the delta plots (see the insets in Fig. 4 where we have repre¬ 
sented the field evolution of the quantity ^^~[M^/(//)/M,(8 
kOe)]-{l“2[M^(//)/M/(8 kOe)]}^) evidenced the occur¬ 
rence of positive (magnetizing) interactions in the high field 
range. The magnitude of the high field SM value decreased 
with the increase of the Ba hexaferrite volume percentage. 


IV. DISCUSSION 

The preparation procedure and the absence (in the dif- 
fractograms taken in the Fe-rich samples) of any Ba hexafer¬ 
rite reflection led us to suppose that in these samples the Ba 
hexaferrite particles were fully embedded in the much larger 
a-Fe ones. We also will assume that the only interaction 
between both phases was the dipolar one. This assumption 
was supported by the characteristics of the preparation pro¬ 
cedure of the composite samples (which does not result in 








J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Montero et ai 


6279 


intimate phase contact) and by the absence of any milling 
process-induced secondary phase. In particular we have not 
detected any Fe oxide which, considering the resolution of 
the x-ray diffraction, could be nevertheless present in small 
amounts. We would like to note that our Fe particles are 
large (they have typical dimensions of the order of tens of 
/iim) and therefore their reversal process should not be sig¬ 
nificantly influenced by a possible exchange induced anisot¬ 
ropy related to the occurrence of surface oxides. Thus, we 
propose that the observed loop displacement and remanence 
asymmetry should result from the local fields, created in the 
soft regions of the samples by the Ba hexaferrite particles. 
Let us remark in this sense that the loop in Fig. 3 is not a 
saturation one: the maximum applied field is smaller than the 
field for which the demagnetization differential susceptibility 
of the samples goes to zero (that maximum field and those 
applied in the remanence measurements are, nevertheless, 
much larger than the field for which the a-Fe reverses its 
magnetization). Therefore, for the fields considered in the 
remanence measurements a substantial fraction of the Ba 
hexaferrite particles are unreversed, that is, have magnetic 
moments still pointing along the hemisphere centered along 
the direction of the initial magnetizing field. Our point is 
that, when both phases are close to saturation, the stray fields 
created by the Ba hexaferrite nanoparticles originate signifi¬ 
cant fluctuations of the local internal field inside the a-Fe 
particles. The magnitude of those fluctuations depends of the 
relative orientations of the magnetizations of the a-Fe and 
Ba hexaferrite particles. If we assume, for instance, that the 
presence of a single platelet-shaped Ba hexaferrite particle is 
embedded in the central region of a spherical a-Fe one with 
the magnetization vectors of both particles perpendicular to 
the bases of the platelet and pointing in the same sense (see 
Fig. 5), the (demagnetizing) dipolar field in the a-Fe region 
close to the bases of the platelet is lower than that existing in 
the same region if the Ba hexaferrite particle was absent. 
(There are also regions close to the platelet lateral surface 
where the local demagnetizing field is increased but, due to 
the platelet geometry, the volume of these regions is smaller 
than that corresponding to the regions where the demagne¬ 
tizing field decreases.) The (predominating) decrease of the 
local dipolar field results in a coercivity increase (a shift in 
the negative field sense of the hysteresis loop). Conversely, if 
the magnetization of the a-Fe particle were already reversed 
and, as in our remanence experiments, that of the Ba hexa¬ 
ferrite platelet were still pointing along the original satura¬ 
tion direction, the dipolar field created by the hard particle 
reinforces that associated to the poles in the surface of the 


Hint local Happ (l/3)M3Fe “MgFerrite 



FIG. 5. Simplified scheme of the internal field in a spherical a-Fe particle 
with a single platelet-shaped Ba hexaferrite particle embedded in its central 
region. 

soft particle, resulting in an easier a-Fe reversal. In terms of 
energy, our simplified description of the influence of the di¬ 
polar interactions in the reversal process can be summarized 
by stating that when the moments of the a-Fe particle and 
the Ba hexaferrite platelet point parallel, the dipolar energy 
of the composite particle is clearly lower than that stored by 
if both moments point antiparallel. We also would like to 
propose that, since the Ba hexaferrite particles have typical 
dimensions corresponding to, approximately, one third of the 
a-Fe domain wall width, the local dipolar field fluctuations 
should predominantly influence the nucleation process. The 
nucleation field is minimized if the wall is originated around 
defects having transverse dimensions of the order of the 25% 
of the total domain wall width,whereas the pinning effects 
should predominantly be linked, for the dimensions of our 
Ba hexaferrite particles, to the spatial fluctuations of the par¬ 
ticle density. 

^G. Herzer, IEEE Trans. Magn. MAG-26, 1397 (1990). 

^T. Schrefl, H. Roitner, and J. Fidler, J. Appl. Phys. 81, 5567 (1997). 

M. D. Coey, J. Magn. Magn. Mater. 140-144, 1041 (1995). 

M. Alameda, L. T. Baczewski, B. Dieny, D. Givord, J. M. Ndjaka, J. P. 
Nozieres, J. J. Prejean, J. P. Rebouillat, and F. H. Salas, J. Magn. Magn. 
Mater. 104-107, 1813 (1992). 

^M. V. P. Altoe, M. S. Lancarotte, H. R. Rechemberg, F. P. Missell, and J. 
M. Gonzalez, IEEE Trans. Magn. 31, 3614 (1995). 

^C. de Julian, M. Emura, F. Cebollada, and J. M. Gonzalez, Appl. Phys. 
Lett. 69, 4251 (1996). 

^J. M. Gonzalez, R. Ramirez, R. Smimov-Rueda, and J. Gonzalez, Phys. 
Rev. B 52, 16034 (1995). 

^D. A. Rawlinson and P. A. Sermon, J. Phys. IV 7, 755 (1997). 

^D. Richards, J. W. Harrel, and M. R. Parker, J. Magn. Magn. Mater. 120, 
164 (1993). 

^°A. Aharoni, Phys. Rev. 119, 127 (1960); 131, 1478 (1963). 


Published without author corrections 





JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Surface and Interface Effects 


Chuck Rogers, Chairman 


Infrared studies of magnetic surface modes on antiferromagnets (invited) 

R. E. Camley®) 

Department of Physics, University of Colorado at Colorado Springs, Colorado Springs, 

Colorado 80933-7150 

M. R. F. Jensen, S. A. Feiven, and T. J. Parker 

Department of Physics, University of Essex, Colchester C04 3SQ, England 

In contrast to ferromagnets, where low frequency surface excitations typically have frequencies in 
the 10 GHz range, surface excitations in antiferromagnets are often in the several hundred GHz to 
few THz range. Theoretical predictions for surface spin waves on antiferromagnets indicate that 
they should be highly nonreciprocal, i.e., the properties of a wave with wave vector + k would be 
very different from those with a reversed wave vector of —k. Surface spin waves on 
antiferromagnets have recently been measured using a high resolution Fourier transform infrared 
spectrometer. The results show evidence of both true surface modes and surface resonances. The 
nonreciprocal features of the surface modes are seen in a dramatic nonreciprocal reflection. For 
example, the reflectivity can be 80% for one orientation, but when the incident and reflected waves 
are reversed the reflectivity drops to near zero. While the initial measurements were done on a bulk 
antiferromagnet, we also present calculations showing the results for thin films. © 1998 American 
Institute of Physics. [80021-8979(98)36811-5] 


The properties of antiferromagnets have recently re¬ 
ceived renewed attention for a variety of reasons. Many an¬ 
tiferromagnets are insulators and therefore have very differ¬ 
ent properties from the thoroughly studied ferromagnetic 
metals of Fe, Ni, and Co. For example, anisotropy fields in 
antiferromagnets are often in the 100 kG range compared to 
the 1 kG or less found in the transition metals. Also, antifer¬ 
romagnets play an important role in the exchange biasing^ of 
ferromagnetic films, a feature of current importance in mag¬ 
netoresistive reading heads.^ Again in contrast to ferromag¬ 
nets, antiferromagnets can have long-wavelength spin exci¬ 
tations in the infrared (IR) frequency regime. This makes 
antiferromagnets of interest for signal processing in the in¬ 
frared. 

In this paper we report on theoretical and experimental 
studies of the infrared reflectivity from a bulk antiferromag¬ 
net sample of FeF 2 . We concentrate in particular on the sur¬ 
face spin waves that propagate in this structure. In contrast to 
the bulk waves, the surface waves show significant 
nonreciprocity^ in that reversing the wave vector can signifi¬ 
cantly change the frequency of the excitation when the sys¬ 
tem is in the presence of an external magnetic field. In a 
reflectivity experiment this corresponds to interchanging the 
incident and reflected waves, and a nonreciprocal reflectivity 
is also observed. 

We also indicate the possibility of IR studies of thin 
antiferromagnetic films by theoretical calculations. In very 
thin ferromagnetic films, it is the surface waves which will 
have the lowest frequencies and which are most easily mea¬ 
sured. This is likely to be true in antiferromagnets as well, 


^^Electronic mail: rcamley@brain.uccs.edu 


and our initial calculations show that it should be possible to 
see signals from antiferromagnetic films with thicknesses in 
the 100-1000 A range. 

In the long-wavelength limit the reflectivity of a mag¬ 
netic insulator is governed primarily by the frequency depen¬ 
dent permeability tensor. For the antiferromagnet, a calcula¬ 
tion of this tensor begins with the equations of motion for the 
spins on the two sublattices: 

JMi .. 

-^ = r(M,xHf), (1) 

and 

dM2 

^ = r(M2XHf). (2) 

In the above equations Mj and M 2 are the magnetizations on 
the two sublattices, y is the gyromagnetic ration, and is 
an effective field acting either on sublattice 1 or 2. 

The effective field is composed of a number of contribu¬ 
tions. For example the effective field acting on sublattice 1 is 
given by 

jjexchange^ Hf+ Hq + h^ipoiar, (3) 

with a similar expression for the effective field on sublattice 
2. Here Hq is the applied field. The exchange field is typi¬ 
cally the largest of all the fields above with a magnitude on 
the order of 100-1000 kG. A key point to notice is that the 
exchange field acting on sublattice 1 comes primarily from 
the magnetization on sublattice 2, i.e., 

jjexchange^^jy^^^ (4) 

where X is the exchange coupling constant. Even in the long- 
wavelength limit, the two sublattices do not have to be par- 


0021 -8979/98/83(11 )/6280/4/$15.00 


6280 


© 1998 American Institute of Physics 




J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Camley et ai 6281 


allel and as a result the large exchange field produced by 
sublattice 2 influences the motion of sublattice 1 through Eq. 
(1). 

The large exchange field is a significant difference be¬ 
tween the ferromagnet and the antiferromagnet and explains 
why antiferromagnet excitations lie in the infrared while 
long-wavelength ferromagnetic spin wave frequencies are in 
the few GHz region. In the ferromagnet—in the long wave¬ 
length limit—the exchange field is simply proportional to the 
magnetization: 

Rexchange^^jyi^ (5) 

As a result the contribution of the exchange field in the equa¬ 
tions of motion is zero since MX XM=0. So even though the 
exchange field is very large, it does not influence the motion 
of the spins. In the antiferromagnet, however, the exchange 
field does play a role, and the resulting frequencies are much 
higher. 

Using the expressions for the exchange field and any 
external and anisotropy fields, the coupled equations of mo¬ 
tion for the two sublattices can be solved to relate the dipolar 
driving fields to the fluctuating magnetization. We assume a 
time dependence of exp(—io)t) for all the dynamic fields and 
obtain the frequency dependent susceptibility tensor defined 
through the equation 

M —j^((u)hdipoiar • (6) 

The frequency dependent permeability is then found through 
the usual definition 

fA.(w)=l+4Trxi(o). (7) 

The explicit form for the permeability can be found in Ref. 4. 
Having found the permeability, the electromagnetic modes 
for the antiferromagnet may be found in the usual way.^ One 
looks for wavelike solutions which satisfy Maxwell’s equa¬ 
tions inside and outside the antiferromagnet. These solutions 
are then matched at the surface of the antiferromagnet and 
this results in the dispersion relation. The reflectivity may 
also be calculated similarly.^ 

We note that a number of different structures and geom¬ 
etries have been considered theoretically in the literature. 
Both easy plane and uniaxial antiferromagnets have been 
studied, and general geometries with arbitrary directions for 
the applied magnetic field and for the direction of propaga¬ 
tion have been examined. Much of this work is summarized 
in the review article found in Ref. 7. 

We consider a geometry where the surface of the anti¬ 
ferromagnet lies in the xz plane. The results take a particu¬ 
larly simple form for a uniaxial antiferromagnet where the 
easy axis and the external field are both along the surface and 
parallel to each other (along the z axis), and the direction of 
propagation is perpendicular to the external field, i.e., in the 
xy plane. We look for electromagnetic waves with the elec¬ 
tric field parallel to z and the magnetic field in the xy plane 
(s polarized). With no external field, one may find that the 
permeability tensor is given by 

/ ^1 0 0\ 

/M(a))=| 0 /A, 0 j , (8) 

\ 0 0 1 / 



Wave Vector (ck,,/©^ 


FIG. 1. Dispersion relations for bulk and surface polaritons in FeF 2 . The 
frequency, co/Ittc, is given in wave numbers. The applied field is zero and 
so both bulk and surface modes are reciprocal, i.e., o)( + y = &)(—/: 
Propagation is perpendicular to the easy axis. 


where 


SttHaM 

/A,(w)=l + —2- 2 - 

(Oq—O) 

Here coq is the resonance frequency given by 


(9) 

( 10 ) 


and M is the saturation magnetization of one of the sublat¬ 
tices. In FeF 2 the anisotropy field 197 kG and the ex¬ 
change field //£=533kG, and M—0.56kG. With a gyro- 
magnetic ratio of 7=0.105 cm~^/kG this gives a resonance 
frequency of 52.4 cm“^ or about 1500 GHz. 

When the applied field is zero the dispersion relations 
have relatively simple forms. The dispersion relation for the 
bulk polaritons in zero field is given by the usual relation. 

+ ky~ e/iiico^/c^, ( 11 ) 

where is the component of the wave vector parallel to the 
surface and ky is the wave vector component perpendicular 
to the surface. The dispersion relation for surface polaritons 
is given by an implicit dispersion relation 

(12) 

The results for the bulk and surface polaritons in FeF 2 with 
zero applied field are shown in Fig. 1. We see two frequency 
regions which represent the bulk excitations. Between the 
bulk bands we see a surface mode which is reciprocal, i.e., 
the frequency does not depend on the sign of the wave vec¬ 
tor. 

A very different dispersion curve is found when there is 
an external magnetic field as can be seen in Fig. 2. Now there 
are three bulk bands. While the bulk modes are reciprocal, 
the surface modes are clearly nonreciprocal. For example, 
one mode which exists at higher frequencies for — k^^ has no 
counterpart for +kj^ in the same frequency range. We note 
that for the geometry considered here reversing the applied 
field is equivalent to a reversal of the propagation direction. 
Thus one may determine nonreciprocal propagation and re¬ 
flectivity characteristics by leaving the optical setup un- 




6282 J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Camley et a!. 


j ATR scan lines | 



FIG. 2. Dispersion relations for bulk and surface polaritons in FeF 2 with an 
applied field of 3 kG. In contrast to the //=0 case there are now three bulk 
bands and the surface modes are strongly nonreciprocal. 



FIG. 4. Experimental and theoretical ATR reflectivity as a function of fre¬ 
quency for FeF 2 in zero field. The broad regions of depressed reflectivity 
represent losses to bulk modes. The sharp dip in reflectivity represents the 
loss to the surface mode. The angle of incidence in the prism is 30° and the 
gap between the prism and the antiferromagnet is 17 fim. 


changed and simply reversing the applied field. This is a 
much simpler procedure experimentally and we use this 
method. 

Since these excitations are in the infrared, it is natural to 
use infrared radiation as a probe. We note that this has been 
done in the past using a laser at a single frequencyand 
also with a Fourier transform infrared (FTIR) system.^ How¬ 
ever, none of these experiments truly identified the surface 
modes. There are several reasons for this. First, the fre¬ 
quency gap between the bulk and the surface modes is quite 
small, requiring a system with high frequency resolution. 
Second, an ordinary reflectivity measurement is normally 
sensitive to bulk modes and not to surface modes. 

To overcome the difficulties outlined above, we have 
used a specially designed FTIR system with a resolution on 
the order of 0.01 cm“^ This requires the scanning arm of the 
interferometer to be about 1 m long. Additional information 
on the interferometer may be found in Ref. 10. In addition 
we use the attenuated total reflection (ATR) technique which 
allows the external radiation to couple to the surface modes 
effectively.^^ This technique is illustrated in Fig. 3. External 
light is incident on a Si prism with dielectric constant e 
= 11.57. Because of the high index of the prism, the light is 
totally internally reflected at the base of the prism and the 
reflectivity, in the absence of a sample, would be unity. 
However, there is an evanescent wave below the prism base 
which can couple to electromagnetic modes in the sample. 
When this occurs, the reflectivity is reduced from unity since 
some of the energy is transferred to the sample. 



applied 

field 


FIG. 3, ATR reflectivity geometry. Reversing the incident and reflected 
waves reverses the direction of . 


To understand the ATR curves, it is helpful to plot the 
dispersion curve representing the incident light in the prism 
on top of the magnetic polariton dispersion curves. When we 
write the dispersion relation in terms of the component of the 
wave vector parallel to the surface we obtain 

kx~i(o/c)\[€ sin $. (13) 

This gives the straight lines shown in Figs. 1 and 2 for posi¬ 
tive and negative Where the dispersion curve (or scan 
line) of the incident light crosses the bulk or surface modes 
of the antiferromagnet, there can be a loss of energy from the 
incident wave to the modes of the antiferromagnet and a 
corresponding reduction in reflected intensity. Thus a broad 
region of depressed reflectivity corresponds to the existence 
of bulk bands, while a sharp dip at one particular frequency 
corresponds to a surface mode. 

In Fig. 4 we plot the ATR reflectivity for the case of zero 
field. The temperature here and in Fig. 5 is 1.7 K. In this plot 
we see two broad regions of depressed reflectivity corre¬ 
sponding to the two bulk bands of Fig. 1. In between there is 
a sharp dip in reflectivity, corresponding to the surface mode, 
and then an increase in reflectivity corresponding to the gap 
between the bulk modes. It is clear that the experimental 
results are in very good agreement with both the theoretical 
calculations for ATR reflectivity and for the dispersion rela¬ 
tions calculated in Fig. 1. 

In Fig. 5 we again plot ATR reflectivity presently for a 
field of ± 3 kG. From the dispersion curve in Fig. 2, we 
expect a total of three regions of reduced reflectivity corre¬ 
sponding to the three bulk bands. In addition we expect 
sharper dips representing the surface modes. These features 
are all present in Fig. 5. A key feature to note is that the 
surface modes appear at different frequencies depending on 
the sign of applied magnetic field. This clearly demonstrates 
the expected nonreciprocity of the surface modes. It may be 
possible to exploit this nonreciprocity for signal processing 
in the infrared. For example the ATR reflectivity near 
52.5 cm“^ is close to zero for positive field. In contrast, the 
wave traveling in the reversed direction (equivalent to re¬ 
versing the applied field) has a reflectivity of close to 80%. 
Thus this system might be used as the basis for a nonrecip¬ 
rocal isolator in the infrared. 







J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Camley et af. 6283 




FIG. 5. ATR reflectivity as a function of frequency for FeF 2 with an applied 
field of 3 kG. The angle of incidence in the prism is 30° and the gap between 
the prism and the antiferromagnet is 17 juum. Note the large nonreciprocity in 
frequency at 52.5 cm“^ The smooth curves are the theoretical results and 
the thinner, jagged lines are the experimental results. 


By doing measurements with different angles of inci¬ 
dence inside the prism, one can trace out the behavior of the 
edges of the bulk band and the position of the surface mode. 
In addition one can also use ordinary reflectivity. The 
results^^’^^ are in excellent agreement with the theoretical 
calculations shown in Figs. 1 and 2. Other recent reflectivity 
studies on FeF 2 in a different geometry also show excellent 
correspondence between theory and experiment. 

The properties of thin antiferromagnetic films, or of an¬ 
tiferromagnetic films coupled to ferromagnets in an ex¬ 
change biasing configuration may be quite different from 
those of bulk antiferromagnets. It is therefore of interest to 
see whether the infrared studies of bulk materials can be 
extended to thin films. In Fig. 6 we plot the ordinary infrared 
reflectivity (not ATR reflectivity) seen from a 1000 A FeF 2 
film on a Si substrate. If the linewidth is on the order of 500 
G, the signal is small. However, if the linewidth is only 50 G 
the signal is quite substantial with a change in reflectivity on 
the order of 15%. Linewidths in antiferromagnets can vary 
substantially depending on the quality of the crystal. Our 
bulk sample showed a linewidth on the order of 400-500 G 
at low temperatures. However some samples have been re¬ 
ported with linewidths an order of magnitude or more 
lower, 

The current FTIR system is sensitive to about a 1% 
change in reflectivity. If an antiferromagnetic film has a line- 
width on the order of 50 G, this would lead to the conclusion 
that one should be able to observe a signal from an antifer¬ 
romagnetic film with a thickness of about 100 A, Improve¬ 
ments in the signal to noise ratio might therefore easily allow 
much thinner films to be studied. Alternatively, one could 
form a superlattice where the unit cell contained, say, a 100 
A antiferromagnetic film. Ten repeats of this structure would 


0.45 I 


1000 X of FeF, on Si substrate 


0.40 


1 0.35 


0.30 


36.5 


^ 

1/ linAU/iHth ^ c;nn 


linewidth = 500 G 
linewidth = 200 G 


linewidth = 50 G 


37.0 37.5 

Frequency (cm'^) 


FIG. 6. Ordinary reflectivity from a thin FeF 2 film on a Si substrate for 
different linewidths. The applied field is 1.5 kG, and the angle of incidence 
is 45°. 


give 1000 A of antiferromagnet. In this case a signal should 
be observable even with the higher linewidths. 

What could be expected from studies of thin antiferro¬ 
magnetic films? We know that in ferromagnets surface an¬ 
isotropy fields or interfacial exchange fields can substantially 
change the surface spin wave frequency.^^ Measurements of 
this frequency can then be used to determine these surface 
and interface parameters. Initial calculations^^ show that the 
spin wave modes in antiferromagnets will also be sensitive to 
surface and interfacial properties. Thus IR probes, either with 
the FTIR system or with a narrow linewidth laser of thin 
antiferromagnetic films may be helpful in understanding the 
exchange biasing effect. 

This work was supported by EPSRC through Grant Nos. 
GR/G54139 and GR/J90831. The work of RFC was also 
supported by U.S. ARO Grant No. DAA H04-94-G-0253. 


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JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


I JUNE 1998 


Strain induced aiteration of the gadoiinium surface state 

C. Waldfried, D. N. Mcliroy, T. McAvoy, D. Welipitiya, and P. A. Dowben®* 

Department of Physics & Astronomy and the Center for Materials Research and Analysis, 

University of Nebraska-Lincoln, Lincoln, Nebraska 68588-01U 

E. Vescovo 

National Synchrotron Light Source, Brookhaven National Laboratoty, Upton, New York 11973 

The electronic structure of strained and unstrained Gd(OOOl) has been studied with photoemission, 
inverse photoemission, and spin-polarized photoemission. A shift of the occupied majority and 
unoccupied minority surface states has been observed as a result of the strain, consistent with the 
phase accumulation model. There is a strain induced shift of the minority spin surface state across 
the Fermi level. © 1998 American Institute of Physics. [80021-8979(98)28611-7] 


Surface states may experience a shift in binding energy 
due to strain,^ For magnetic surfaces the spin dependent shift 
of the surface majority and minority subbands near the Fermi 
level can result in a variation of the spin population at dif¬ 
ferent wave vectors k. This will have a substantial influence 
on the magnetic behavior of the surface. The subject of this 
article is the effect of strain on the electronic structure of the 
surface of gadolinium. We show consistency with the effects 
recently demonstrated by Neuhold and Horn^ on the surface 
of Ag(ni). 

The surface magnetism of gadolinium has been the sub¬ 
ject of controversy over the past years, mainly as a result of 
the proximity of the 6s surface states to the Fermi 

level. Strain substantially alters the electronic structure of 
gadolinium^”"^ and is expected to result in a shift of the sur¬ 
face state binding energies. We have been able to obtain 
■strained films of gadolinium, with an increased lattice con¬ 
stant of approximately 4% by growing gadolinium on the 
corrugated surface of Mo(112).^"'^ 

We investigated the occupied and unoccupied electronic 
structure of thin films of strained and unstrained Gd(OOOl). 
Spin-polarized photoemission experiments were carried out 
at the new U5UA undulator beamline of the National Syn¬ 
chrotron Light Source (NSLS) at the Brookhaven National 
Laboratory in Upton, NY. The details of the experimental 
setups are described elsewhere.^’^ Inverse photoemission 
spectra were acquired in a different UHV system^ in the 
isochromatic mode (^ct) = 9.4eV) with a Geiger-Miiller 
tube and an electron gun based on the Zipf design.^ Strained 
and unstrained thin films of Gd, 10-40 ML thick, were 
grown by slow thermal deposition on Mo(112) and W(llO) 
substrates, respectively. The surface and bulk character of 
the bands has been determined from chemisorption studies 
and photon energy dependence, while the symmetry of the 
bands has been ascertained from the light polarization depen¬ 
dence as described in detail elsewhere.^ 

The influence of strain on the surface electronic structure 
of Gd is illustrated in Fig. 1, which compares two normal 
emission photoemission spectra that were taken for strained 
and unstrained Gd(OOOl). Both spectra have been acquired 


“^Electronic mail: pdowben@unHnfo.unl.edu 


with a photon energy of 33 eV for films of similar nominal 
thickness of approximately 15 ML. The valence band of the 
strained Gd(OOOl) films is distinct from that of the relaxed 
films. The binding energy of the 5d, 6s strained bulk bands 
at 1.8 eV below Ef differs from the unstrained bulk bands 
observed at approximately 1.5 and 0.8 eV below Ep ai the 
surface Brillouin zone center. More significant, the narrow 
surface state near the Fermi level of the unstrained Gd(OOOl) 
is shifted towards higher binding energy and appears sub¬ 
stantially broadened. 

The origin of the clearly altered valence-band states and 
broader density of states near the Fermi level of strained Gd 
is revealed by the spin resolved electronic structure, shown 
in Fig. 2. The unstrained Gd(OOOl) valence band at the Bril¬ 
louin zone center (f) is characterized^ by Stoner-like ex¬ 
change split 5d bulk bands at binding energies of approxi¬ 
mately 1.5 (majority) and 0.8 eV (minority) and two sets of 



Binding Energy (eV) 


FIG. 1. Normal emission photoemission spectra for strained (bottom) and 
unstrained (top) films of Gd(OOOl), acquired with a photon energy of 33 eV. 
The inset shows a comparison of a strained (bottom) and unstrained (top) 
Ag(lll) surface from Ref. 1. 


0021-8979/98/83(11 )/6284/3/$15.00 


6284 


© 1998 American Institute of Physics 




J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Waidfried et al. 


6285 



Binding Energy (eV) 

FIG. 2. Spin-polarized photoemission spectra for strained (bottom) and un¬ 
strained (top) Gd(OOOl) at normal emission and approximately 145 K. The 
spectra were acquired with a photon energy of 34 eV. The inset schemati¬ 
cally plots the binding energy shifts of the surface (solid) and bulk (dashed) 
spin subbands as a function of increased expansive strain. 

spin majority and minority subbands of the surface on either 
side of the Fermi level. The occupied predominantly spin- 
mixed majority 6s surface state is located at ap¬ 

proximately 0.1 eV below Ef (Fig. 2) and the unoccupied 
minority counter part of the surface state at approximately 
0.3 eV above the Fermi level^ (Fig. 3) (though this is depen¬ 
dent on temperature well away from 

In the strained Gd films the bulk spin majority and mi¬ 
nority subbands are found at approximately 1.8 eV binding 
energy at F, with negligible Stoner-like exchange splitting.^ 
There are three features near the Fermi level (0 to 1 eV 
binding energy) in the valence band of the strained Gd films. 
Two features, the spin majority state at 0.7 eV below Ef and 
the spin minority state at 0.2 eV binding energy are Stoner- 



FIG. 3. The unoccupied density of states for strained (bottom) and un¬ 
strained (top) films of Gd(OOOl). The spectra were taken at approximately 
300 K. The data for the unstrained Gd has been extracted from Ref. 9. 
Surface and bulk features are indicated by the surface state (SS) and bulk 
state (BS), respectively. 


like exchange split surface bands.^ The surface character of 
these two states has been verified by their sensitivity to small 
amounts of adsorbates and their two dimensionality of state. 
Both surface sensitive features do not disperse with changing 
perpendicular momentum^ and are therefore confined to the 
two-dimensional plane at the surface. The third feature in the 
valence-band region near Ef, an additional bulk band of 
majority character, is located in the exchange splitting gap at 
approximately 0.4 eV binding energy ai TITc<0J, 

The two occupied bands closest to , the spin minority 
surface subband, and the spin majority bulk band are newly 
introduced into the occupied density of states as a result of 
the strain. Both bands are found in the unoccupied region for 
the unstrained Gd films as seen in Fig. 3. Expansive strain 
within the Gd films induces a “downward” shift of the un¬ 
occupied surface state across the Fermi level. This is consis¬ 
tent with the absence of the surface spin minority state (0.3 
eV above Ef)^ in the unoccupied density of states of the 
strained Gd films. The spin majority bulk band at 0.4 eV 
binding energy of the strained Gd film is postulated to origi¬ 
nate from the unstrained bulk band, located approximately 
1.5 eV above the Fermi level,^ at zone center, crossing the 
Fermi level about halfway across the zone in unstrained Gd, 
This shift in binding energy at F is illustrated in the inset of 
Fig. 2. More detailed studies of the occupied and unoccupied 
density of states are, nonetheless, necessary to confirm this 
postulate. 

From our data it is clear that the spin majority 
6s surface state is shifted from 0.2 eV binding energy for the 
unstrained Gd films to 0.7 eV in the strained Gd(OOOl). A 
similar downward shift of 0.5 eV is observed for the spin 
minority counterpart, which is unoccupied for the “relaxed” 
Gd(OOOl) and found at a binding energy of approximately 
0.2 eV below Ef due to strain (Fig. 2 inset). Concomitantly, 
the occupied spin minority (0.8 eV below Ef) and unoccu¬ 
pied spin majority (^1.5 eV above Ef) bulk bands of un¬ 
strained Gd experience large shifts of approximately 1.0 and 
1.9 eV, respectively. 

The shift to higher binding energies of the Gd surface 
states (majority and minority) under the influence of expan¬ 
sive strain is in agreement with the strain induced shifts of 
the surface state binding energy for Ag(lll),^ which is 
shown in the inset of Fig. 1. There, compressive strain results 
in the upward shift of the sharp Ag(lll) surface state across 
the Fermi level, where it is cut off by the Fermi function and 
undetectable with photoemission. In both cases the strained 
induced shift of the surface state(s) can be explained by the 
phase accumulation model. 

Surface states originate from electrons confined to the 
top most layer of the solid, trapped in between the bulk band 
gap and the surface potential. A simple one-dimensional (so- 
called “phase accumulation”) model^^”^'^ can be employed 
to roughly describe the surface state energy. This simple 
model considers the surface electron in a one-dimensional 
quantum well, confined by the image potential on the 
vacuum side and the bulk band gap on the crystal side. The 
surface state energy is then determined by the lowest allowed 
quantum mechanical solution of the electron wave function. 
The energy of the surface state thus varies proportionally to 





6286 J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Waldfried et al. 


Ifd^, with d being the width of the well. In the phase accu¬ 
mulation formalism, d is dependent, among others, on the 
bulk band edges^^ and the work function.^ Thus the strain 
induced shifts in binding energy of the surface states in ga¬ 
dolinium can be attributed to the altered majority and minor¬ 
ity bulk band gaps and the reduced work function of strained 
Gd, approximately 2.2 eV, as compared to 3.3 eV for the 
relaxed Gd film. 

Our results provide evidence that under expansive strain 
both spin components of the bulk bands are modified and 
results in a downward shift of the surface spin subbands. A 
change of the in-plane lattice constant of approximately 4% 
yields a surface state energy shift of 0.5 eV (Fig. 2 inset). 
The strain induced shifts of the bulk band edges (spin ma¬ 
jority and spin minority) of approximately 1 to 2 eV are 
substantially larger than those of the surface bands. The shift 
of each Gd surface state (one in the spin majority band struc¬ 
ture, the other in the spin minority band structure) is consis¬ 
tent with the observations and calculation for Ag(lll).^ 

This study shows that strain can significantly alter the 
spin-polarized electronic structure of a ferromagnetic system 
like gadolinium in much the same way as strain affects a 
nonmagnetic system like Ag(lll). In a ferromagnetic sys¬ 
tem, we need to consider each surface state spin component 
in the appropriate spin-resolved band structure. It is only 
apparent in the spin-resolved band structure how similar the 
influence of strain is in both Ag(lll) and Gd(OOOl). 


ACKNOWLEDGMENTS 

This work was supported by NSF through Grant Nos. 
DMR-92-21655, DMR-94-96131, and DMR-94-07933. The 
experiments were carried out at the National Synchrotron 
Light Source which is funded by the DOE and at the Syn¬ 
chrotron Radiation Center which is also funded by NSF. 

‘G. Neuhold and K. Horn, Phys. Rev. Lett. 78, 1327 (1997). 

^C. Waldfried, D. N. Mcllroy, and P. A. Dowben, J. Phys.: Condens. Mat¬ 
ter 9, 10 615 (1997). 

^C. Waldfried, D. Welipitiya, T. McAvoy, E. Vescovo, and P. A. Dowben, 
Phys. Rev. Lett, (submitted), 

Waldfried, D. N. Mcllroy, and P. A. Dowben, Phys. Rev. B 54, 16 460 
(1996); 56, 9973 (1997). 

^E. Vescovo et aly Activity Report 1996, Nat. Synch. Light Source, A-25 
(1997). 

^P. D. Johnson et aly Rev. Sci. Instrum. 63, 1902 (1992); J. Unguris, D. T. 
Pierce, and R. J. Calotta, Rev. Sci. Instrum. 57, 1314 (1986). 

^P. W. Erdmann and E. C. Zipf, Rev. Sci. Instrum. 53, 225 (1982). 

^D. Li, J. Pearson, S. D. Bader, D. N. Mcllroy, C. Waldfried, and P. A. 
Dowben, Phys. Rev. B 51, 13 895 (1995). 

^M. Donath, B. Gubanka, and F. Pa.ssek, Phys. Rev. Lett. 77, 5138 (1996). 
*^M. Bode, M. Getzlaff, S. Heinze, R. Pascal, and R. Wiesendanger, Phys. 
Rev. A (in press). 

‘*N. V. Smith, Phys. Rev. B 32, 3549 (1995). 

V. Smith, N. B. Brooks, Y. Chang, and P. D. Johnson, Phys. Rev. B 49, 
332 (1994). 

*^P. Ahlqvist, Solid State Commun. 31, 1029 (1979). 

^"^P. M. Echenique and J. B. Pendry, J. Phys. C 11, 2065 (1978). 

‘^R. Paniago, R. Matzdorf, G. Meister, and A. Goldmann, Surf. Sci. 336, 
113 (1995). 



JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER II 


1 JUNE 1998 


Effect of surface roughness on magnetization reversal of Co films 
on plasma-etched Si(100) substrates 

M. Li,®) Y.-P. Zhao, and G.-C. Wang 

Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, 

Troy, New York 12180-3590 

H.-G. Min 

Department of Physics, Hong-lk University, Seoul 121-791, Korea 

Co films '^970 A thick were deposited, simultaneously, on ten plasma-etched Si(lOO) substrates 
with various etch times t. The surface morphologies and magnetic properties of the Co films were 
measured by atomic force microscopy (AFM) and magneto-optic Kerr effect (MOKE) technique. 
The analysis of the AFM images shows that as the etch time t increased from 0 to 100 min, the 
vertical interface width w increased from ~5 to ~ 1400 A; the lateral correlation length | increased 
from ~300 to 10 500 A. The MOKE measurements provided the in-plane azimuthal angular 
dependence of the hysteresis loops and the change of loop shapes with the surface roughness. It was 
found that the magnetization reversal process changed with the surface roughness. Magnetization 
rotation dominated the magnetization reversal for the smoothest films. As the films roughened, the 
domain-wall pinning set in, eventually dominating the magnetization reversal for the roughest films. 
Additionally, the magnetic uniaxial anisotropy in the Co films disappeared as the roughness 
parameters increased. It was also found from MOKE that the surface roughness strongly affected the 
coercivity. © 1998 American Institute of Physics. [80021-8979(98)36911-X] 


It is known that surface/interface roughness of magnetic 
thin films and of superlattices influences magnetic properties, 
such as magnetic anisotropy, coercivity, magnetoresistance, 
and magnetic domain structure. Various works on the re¬ 
lationship between surface roughness and coercivity, of thin 
and ultrathin films, have been carried out."^"^ For examples, 
Malyutin et al^ investigated the effect of surface roughness 
on the coercivity of chemically etched NiFeCo films (200- 
1000 A thick) and found that the coercivity of the film in¬ 
creased with the increase of etch time. During the etching, 
the thickness of the magnetic film decreased and the surface 
roughness increased with etch time. Vilain et al.^ investi¬ 
gated the dependence of coercivity on the surface roughness 
for electrodeposited NiCo alloy films. For ultrathin films, 
Jiang et al^ investigated the coercivity of ultrathin Co films 
on Cu(lOO) substrate versus substrate roughness. The coer¬ 
civity of the 6-7 ML Co film increases from —70 Oe for 
deposition on an atomically flat Cu substrate, to — 170 Oe for 
deposition on a Cu substrate roughened by Ar'^ sputtering to 
a (vertical) interface width of —1.81 atomic-step heights. 
This demonstrates the sensitivity of coercivity on the surface 
roughness. 

In addition to the surface roughness, it is known that the 
thickness, the composition, the crystalline structure of the 
magnetic film, and the preparation conditions also determine 
the magnetic properties of the films. Therefore, to understand 
the interrelationship between roughness and magnetic prop¬ 
erties, other factors influencing the magnetic properties must 
be controlled. In the present study, we deposited —970 A Co 
films simultaneously (and thus identically) on ten plasma- 


^^Electronic mail: wangg@rpi.edu 


etched Si(lOO) substrates by thermal evaporation in high 
vacuum and studied the effect of the surface roughness on 
the magnetic properties of —970 A Co films. 

Ten n-type Si(lOO) substrates were etched by plasma¬ 
etching gases (CF 4 and 4% O 2 ) with an etch rate of 1500 
A/min to various degrees of roughness in a standard plasma¬ 
etching chamber. The etch times t were 0, 1,5, 10, 20, 30, 
40, 60, 80, and 100 min, respectively. The surface morpholo¬ 
gies of these roughened Si(lOO) substrates were imaged by 
atomic force microscopy (AFM) with a Si 3 N 4 tip. Then, 
these rough Si(lOO) substrates were arranged on a large sup¬ 
porting plate in another high-vacuum chamber. The Co at¬ 
oms were thermally evaporated from a crucible onto these 
ten Si(lOO) substrates simultaneously. The base pressure was 
5X10“^ Torr and the pressure increased to 5X10“^ Torr 
during deposition. A quartz crystal monitor indicated a depo¬ 
sition rate of — 0.8 A/s and — 970-A-thick Co films formed 
after about 20 min deposition. The starting substrate tem¬ 
perature was at the ambient temperature and the substrate 
temperature rose during the deposition due to the filament 
needed to heat the Co source. The characterizations were 
carried out in ambient air at room temperature. The surface 
morphology of the Co film was imaged by AFM. The hys¬ 
teresis loops were measured by the magneto-optic Kerr effect 
(MOKE) technique.^ 

All of the AFM images from AFM measurements 
showed islandlike features with a wide distribution of sizes 
and separations. Figure 1 shows four typical AFM images of 
the —970 A Co films deposited on the plasma-etched Si(lOO) 
substrates. As illustrated by the increasing scan size for suc¬ 
cessive etch time t, the average size and separation of the 
features increased with increasing etch time t. For etch 

© 1998 American Institute of Physics 


0021-8979/98/83(11 )/6287/3/$15.00 


6287 


6288 J. Appl. Phys., Vol. 83, No. 11,1 June 1998 



0 0.5 1 1.5 2pim 0 1 2 3 4 5|Jim 

t=1 min Nl5min 



0 4 8 12iim 0 10 20 30 40|Jim 

1=30 min t=60 min 


FIG. 1. Four grey-scale AFM images of '--970-A-thick Co films deposited 
on Si(lOO) substrates etched for times r=l, 15, 30, and 60 min. Note, the 
scan size increases. 



-150-75 0 75-150-75 0 75-150-75 0 75 150 
HiOe) 


FIG. 2. MOKE hysteresis loops at three in-plane azimuthal angles (0°, 50°, 
and 90°) for three ~970-A-thick Co films. 


times longer than 20 min, the islandlike features connected 
to form a networklike morphology. The roughness param¬ 
eters, the (vertical) interface width w, and the (lateral) cor¬ 
relation length ^ can be obtained by analyzing the height- 
height correlation function which can be calculated 

from AFM images.^ The vertical interface width w increased 
from ~5 to '--1400 A; the lateral correlation length ^ in¬ 
creased from '--300 to '^10 500 A. Table I lists the rough¬ 
ness parameters for different etch time t. 

The longitudinal hysteresis loops were measured for all 
of the Co films using an external magnetic field amplitude 
/7o=128 0e with a frequency /=1.4Hz. For a given 
sample, the loop was measured as a function of in-plane 
azimuthal angle (p from 0° to 360°, The results indicate that 
the easy magnetization direction of the Co films lay in the 
film plane for all the samples studied here. There was in¬ 
plane uniaxial magnetic anisotropy in the Co films for etch 
times f<60min, whereas there was no detectable in-plane 
magnetic anisotropy in the Co films with the etch time t 
= 60 and 100 min. 

The directions of the easy axis and the hard axis in the 
film plane were determined from the azimuthal angle depen- 


TABLE I. The surface roughness parameters (vertical interface width w and 
lateral correlation of Co films vs etch time t. 


?(min) 

>v(A) 

f(A) 

0 

5±1.5 

335±110 

1 

15±1.6 

310±105 

5 

30±3 

320±108 

10 

150±5 

677±213 

15 

172±9 

765 ±222 

20 

453 ±24 

2009±695 

30 

485±15 

2665 ±932 

40 

574±18 

3207±1160 

60 

859±30 

6795 ±2342 

100 

1376±15 

10475±3884 


dence of the loop shape. Figure 2 shows the hysteresis loops 
at different azimuthal angles for three typical samples with 
etch time /= 1, 15, and 60, min. For the samples with etch 
time t^5 min, the shape of the loop changed from square¬ 
like, to spindlelike, to almost a straight line as the in-plane 
azimuthal angle changes in the range of 0°-90°, The loop 
had a squarelike shape, a high coercivity and a high 
squareness S when the magnetic field was applied along the 
easy axis. When the magnetic field was applied along the 
hard axis direction, however, the loop was almost reversible; 
as a result, both S and were close to zero. This suggests 
that the magnetization reversal process was dominated by 
magnetization rotation, and that the contribution to the mag¬ 
netization reversal from domain wall motion was negligible 
for samples with f=0, 1, and 5 min. The uniaxial magnetic 
anisotropy field can be easily obtained from the hysteresis 
loops.^ 

For samples with etch time f=10, 15, 20, 30, and 40 
min, the twofold symmetry in the coercivity versus azi¬ 
muthal angle still existed, but all of the loop shapes were 
squarelike. The squareness lost its twofold symmetry, be¬ 
coming almost constant, independent of <p. Due to the in¬ 
creasing surface roughness, domain-wall pinning started to 
contribute to the coercivity. The magnetization reversal pro¬ 
cess was associated with both the domain wall motion and 
magnetization rotation. To make the magnetization reversal 
happen in these cases, the applied field H must overcome not 
only the domain-wall-pinning coercivity, but also the 
component of the magnetic anisotropy field in the applied 
field direction, which is H'a = H„ cos (p. This means that the 
combined magnetic field should at least equal //cw • There¬ 
fore, we have the following relation: 

Hl = H^ + H'^^-2HH'„cos(p, ( 1 ) 

where (p again is the in-plane angle between the applied 









J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Li et ai 6289 



FIG. 3. The easy axis coercivity and hard axis coercivity vs etch time for 
~970-A-thick Co films. The dashed curve is the fit using 


field and the easy axis of magnetization, and iF/' 
= (IKj^ /M^)cos (p. Letting and H=Hc, the mag¬ 

netization reversal will occur, and we have 

cos (2) 

By using this equation, we fitted the measured angular 
dependence of He for samples with 10, 15, 20, 30, and 40 
min, and obtained the magnetic anisotropy field and an¬ 
isotropy coefficient K ^^. 

For the samples with 40 min, the loop shape was 
squarelike, and there was no detectable in-plane magnetic 
anisotropy. At this point, the magnetization reversal was 
controlled mostly by the domain wall motion. 

The results of MOKE hysteresis loop measurements sug¬ 
gest that the magnetization reversal process in these Co films 
depended strongly on the surface roughness. With the in¬ 
crease of the surface roughness, the magnetization reversal 
process changed from the magnetization rotation {t 
<10 min) to a combination of magnetization rotation and 
domain-wall motion (10 min^f^40 min), and then to 
domain-wall motion (f>40 min). 

The coercivity determined from MOKE measurements is 
plotted in Fig, 3 versus etch time t and for samples with t 
<60 min, both the easy and hard axes coercivity are shown. 
The easy-axis coercivity was, in general, a monotonically 
increasing function of the interface width, except for a dip 
around ?~30 min. Specifically, the He increased slightly be¬ 
tween 13 and 15 Oe for t^5 min, peaked at —50 Oe for t 
= 15 min, came down to — 25 0e for f=30min, then in¬ 
creased again to —80 Oe for t = 60 min and —70 Oe for 100 
min. The hard-axis coercivity had a similar dependence on 
the etch time. The difference between easy axis coercivity 
and hard axis coercivity was due to the in-plane uniaxial 
anisotropy. The results indicated that He increased with the 
increase of the roughness. This is consistent with the predic¬ 
tion of He for a Bloch type of domain wall, for which He 
increases if the surface roughness increases for a given 


thickness.^ The overall decrease of the absolute values of He 
for t=20mm and ?=30min samples, as compared with 
those of the t= 10 min and t= 15 min samples, might be due 
to the network formation (as in Fig. 1), which would make 
wall movements easier. As the etch time t increased further, 
the roughness increased and the He increased again for t 
>40 min. We fitted the hard-axis coercivity, i.e., the 
domain-wall pinning coercivity by using He^=aw^l^^, 
which is shown in Fig. 3 by the dashed line,^ The roughness 
parameters used in the fit are the measured roughness param¬ 
eters listed in Table I. The fit parameters obtained are b 
= 2,40±0.05 and c= 1.00±0.01. The value of fit parameter 
a was an order of magnitude different in two etch time 
ranges: a”0.135±0.005 for r<20min and a = 0.019 
±0.005 for 20 min. This change coincides with the for¬ 
mation of the networklike features in the morphology after a 
20 min etch. This suggests a quantitative correlation between 
domain-wall coercivity and surface roughness. It is expected 
that, as the film thickness decreases, the enhancement of the 
coercivity due to surface roughness would be more dramatic. 

The origin of the in-plane uniaxial magnetic anisotropy 
is not clear yet. It might be related to the stress built up 
during the film deposition^® due to the different thermal ex¬ 
pansion coefficients of the substrate and of the Co film. From 
MOKE measurements, the uniaxial magnetic anisotropy 
decreased from 1.3X 10^ J/m^ for ?=0 min to 0 J/vo? (no an¬ 
isotropy) for t= 100 min with the increase of the etch time. A 
possible reason for the decrease in is that, when the sur¬ 
face became rougher, the stress between the Co film and the 
Si substrate was more easily relieved. Additionally, since the 
dispersion of the easy axis is expected to increase with the 
increase of the surface roughness, the uniaxial anisotropy 
would average out for differently oriented crystalline grains 
in a polycrystalline film. It is expected that when the mag¬ 
netic thin film gets thinner, the effect of the surface rough¬ 
ness on the magnetic properties will be more dramatic and is 
worth further systematic studies. 

This work was supported by the National Science Foun¬ 
dation. H,-G.M. was supported by Korea Research Founda¬ 
tion (KRF) 95-500-648 and KOSEF through ASSRC, Korea. 
The authors thank K. Mello for the help in the deposition of 
Co films, and John B. Wedding for reading the manuscript. 

^ Ultrathin Magnetic Structures I and //, edited by J. A. C. Bland and B. 
Heinrich (Springer, Berlin, 1994). 

Chang and M. H. Kryder, J. Appl. Phys. 75, 6864 (1994). 

^P. Bruno, G. Bayureuther, P. Beauvillain, C. Chappert, G. Lugert, D. 
Renard, J, P. Renard, and J. Seiden, J. Appl. Phys. 68, 5759 (1990). 

'‘V. I. Malyutin, V, E. Osukhovskii, Yu. D. Vorobiev, A. G. Shishkov, and 
V. V. Yudin, Phys. Status Solidi A 65, 45 (1981). 

^S. Vilain, J. Ebothe, and M. Troyon, J. Magn. Magn. Mater. 157, 274 
(1996). 

^Q. Jiang, H.-N. Yang, and G.-C. Wang, Surf. Sci. 373, 181 (1997). 

■^J.-P. Qian and G.-C. Wang, J. Vac. Sci. Technol. A 8, 4117 (1990). 
^H.-N. Yang, T.-M. Lu, and G.-C. Wang, Diffraction from Rough Surfaces 
and Dynamic Growth Fronts (World Scientific, Singapore, 1993). 

^R. F. Soohoo, Magnetic Thin Films (Harper and Row, New York, 1965). 
^®M. Prutton, Thin Ferromagnetic Films (Butterworths, Washington, 1964). 






JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Exploring magnetic roughness in CoFe thin fiims 

J. W. Freeland,®' V. Chakarian, K. Bussmann, and Y. U. Idzerda 

Naval Research Laboratory, Washington, D.C. 20375 

H. Wende 

Freie Universitdt Berlin, D-14195 Berlin-Dahlem, Germany 

C.-C. Kao 

National Synchrotron Light Source (NSLS), Brookhaven National Laboratory, Upton, New York 11973 

The behavior of chemical and magnetic interfaces is explored using diffuse x-ray resonant magnetic 
scattering (XRMS) for CoFe thin films with varying interfacial roughnesses. A comparison of the 
chemical versus magnetic interfaces shows distinct differences in the behavior of these two related 
interfaces as the chemical roughness is increased. Such changes appear to be correlated with the 
behavior of the magnetic hysteresis of the interface, measured by tracking the diffuse XRMS 
intensity as a function of applied magnetic field. © 1998 American Institute of Physics. 
[S0021-8979(98)17511-4] 


I. INTRODUCTION 

The influence of roughness on the properties of thin film 
magnetic structures is a question of current interest to many 
facets of the magnetism community. Current results have 
shown that direct measurements of magnetic roughness as 
compared to measurements of the chemical roughness indi¬ 
cate that these interfaces are compositionaly rough, but mag¬ 
netically smooth.Since the magnetotransport of these 
structures is strongly affected by interfacial scattering and in 
particular by magnetic disorder at the interface,chemical 
roughness may not be the appropriate parameter for correla¬ 
tion with the degradation of the magnetic properties. 

The formalism for the determination of the nature of 
chemical interfaces and surfaces using specular and off 
specular (diffuse) scattering is a well established field.^’^ 
However, to probe information about a magnetic interface 
one needs a significant magnetic scattering signal. One way 
of providing this is through the resonant enhancement of the 
magnetic and chemical scattering when an incident circular 
polarized photon is tuned to an absorption edge, known as 
x-ray resonant magnetic scattering (XRMS).^“^'^ Utilization 
of a circular polarized photon, like its absorption counterpart 
magnetic circular dichroism (MCD),^'^ generates the mag¬ 
netic scattering component. Recently XRMS has been ap¬ 
plied to the study of magnetic roughness. From both 
specular^ and diffuse^ studies of magnetic thin film structures 
comes evidence of differing chemical and magnetic inter¬ 
faces. 

To better understand the variation of magnetic versus 
chemical interfaces we have undertaken a study of thin CoFe 
films where an increasing chemical roughness was induced 
through the growth process. The results clearly show that the 
chemical and magnetic interfaces do not behave in the same 
manner as the root mean square (rms) chemical roughness is 
increased. Also, we will demonstrate the possibility of using 


®^Author to whom correspondence should be addressed: Naval Research 
Laboratory, NSLS Bldg. 725AAJ4B, Upton, NY 11973; electronic mail: 
freeland @ bnlls3 .nsls.bnl.gov 


variations in the magnetic diffuse intensity as a function of 
applied field as a probe of interfacial magnetic hysteresis. 

II. EXPERIMENT 

The reflectivity measurements were conducted at the 
NRL/NSLS Magnetic Circular Dichroism Facility located at 
beamline U4B of the National Synchrotron Light Source 
(NSLS).^^ Details of the experimental apparatus and mea¬ 
surement conditions are described elsewhere. To probe 
interface roughness via the diffuse intensity we performed a 
sample rocking curve where the detector angle {26) was kept 
fixed and the sample angle (co) was varied. In this configu¬ 
ration, a scan over a wave vector in the plane {qf) is per¬ 
formed while keeping the component perpendicular to the 
film {qf) approximately constant. To extract the magnetic 
information it is necessary to measure the helicity dependent 
scattering of the magnetic material (denoted as and /“). 
So the magnetic moment of the sample was reversed at each 
data point to determine and /“, which has been shown to 
be equivalent to alternating the photon helicity. 

The CoFe alloys thin films were prepared by the rf sput¬ 
tering facilities of Nonvolatile Electronics Inc. The samples 
were grown on atomically flat Si 3 N 4 substrates (roughness 
— 1.5 A rms) with the following structure: Cu(30A)/ 
Co95Fe5(50A)/Cu(.^A)/Si3N4. Due to growth dynamics the 
rms roughness of Cu grown on Si 3 N 4 increases dramatically 
as the thickness of the Cu buffer layer, x, is increased. Since 
the Cu buffer layer thickness can be controlled accurately, 
the roughness of the surface on which the CoFe is deposited 
can be tailored. For this study we utilized a series of four 
films with various Cu buffer layer thicknesses (x = 200, 400, 
800, and 1600 A) spanning a rms chemical roughness rang¬ 
ing from 2.5 to 32 A rms as measured by a Digital Instru¬ 
ments Dimension 3000 atomic force microscope (AFM) in 
tapping mode (resolution 10-50 A). Since the Cu cap layer 
is so thin, the topographical information provided by AFM 
should give an accurate measurement of the chemical rough¬ 
ness of the top CoFe/Cu interface. This will be important 


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Freeland et ai 


6291 



-0,004 -0.002 0.000 0.002 0.004 

%(A'b 


FIG. 1. Sample rocking curve measured at the Co edge (778 eV) for 
chemical [(/‘^ + /“)/2] and magnetic — contributions vs This 
scan was taken at a detector angle 20 of 9^ =0.062 A“*). Notice how the 
half width of the magnetic diffuse (Tyi^) is smaller than that of the chemical 
diffuse (Pc), indicating a longer correlation length, ^ for the magnetic in¬ 
terface. 

when we compare it with the diffuse scattering results be¬ 
cause the short mean free path of the photon at the L 3 edge^^ 
means that measurements made at grazing incidence (cu 
<10°) for a 50 A CoFe film probe predominately the top 
CoFe/Cu interface. 


30 

5 25 

S 20 

o 

^ 15 

I .0 

5 

0 

^ 1600 
^ 1500 
^ 1400 
^ 1300 

1 1200 
^ 1100 
g 1000 

900 


FIG. 2. Roughness parameters derived from the diffuse scattering data. Top 
panel: Chemical and magnetic rms roughness. Bottom panel: Chemical and 
magnetic correlation lengths. 



5 10 15 20 25 30 

AFM Roughness (A) 


III. RESULTS AND DISCUSSION 

Figure 1 shows the chemical [(I^ +/“)/2] and the mag¬ 
netic (7^ —/“) contributions from a sample rocking (diffuse) 
scan measured at the Co L 3 edge. The diffuse scan consists 
of a sharp specular peak around ^;c= 0 , with a broad under¬ 
lying diffuse component. Since roughness is the mechanism 
that channels flux from the specular peak into the diffuse 
component, values for the chemical and magnetic roughness 
(denoted as Cc and respectively) can be extracted by 
determining the fraction of total flux that resides in the dif¬ 
fuse part of the spectrum. This is accomplished by compar¬ 
ing the integrated areas of the specular [5'specuiar(Q)] vs dif¬ 
fuse [5diffuse(q)] components using'^ 

_ J^diffuse(q)6?^g|| _/jx 

/‘^diffuse(q)^ ^11‘1’/‘^specular(Q)^ 9^11 

where denotes integration over the (q^ ,qy) plane, and cr is 
the roughness perpendicular to the film plane. A second pa¬ 
rameter describing the roughness in the film plane, the lateral 
correlation length, is determined from the half width (F ^ 
and r of the diffuse portion of the sample rocking curves 
using a solution of diffuse structure factor (for a roughness 
exponent, h= 1 ):^’^ 

o 2 'n-exp[-(^,o-)^] 

‘^diffuse',*!)-' 2 

‘Iz 


00 


xX 

m= 1 


m\ 




Results of the analysis of our thickness series are shown in 
Fig. 2 for both chemical and magnetic data. 


The most important general result is the different behav¬ 
ior of both (7 and ^ for the chemical versus magnetic inter¬ 
faces. The magnetic roughness in this series of samples is 
'--20%~30% less than the chemical roughness. The same is 
seen for the behavior of the chemical versus magnetic corre¬ 
lation length (bottom panel of Fig. 2). This indicates that the 
magnetic interface is typically much smoother than the 
chemical interface both perpendicular to and in the plane the 
film. There is good agreement between the cr roughness pa¬ 
rameters extracted from the x-ray scattering and from the 
AFM values (the straight line of the top panel of Fig. 2). The 
small disagreements can be addressed through a more de¬ 
tailed analysis of the AFM roughness data, which is not 
shown here due to space limitations. 

An interesting application of this technique becomes 
possible upon examination of the the specular versus diffuse 
element specific magnetic hysteresis measured by XRMS 
(see Fig. 3). The reflected intensity as a function of applied 
field can be utilized as a measure of the magnetic hysteresis 
since the magnetic portion of the scattering tracks with the 
magnetic moment of the sample. Since the field dependence 
specular peak intensity gives a measure of the bulk magnetic 
hysteresis, we can use the diffuse signal, which only comes 
from the interfaces, to measure the interfacial magnetic hys¬ 
teresis. In Fig. 3 the clear difference in the coercive and 
saturation fields of spins at the interface indicates the differ¬ 
ent nature of the bulk versus interfacial magnetic environ¬ 
ment. For the x = 400 A film shown in Fig. 3 the difference 
in coercive fields was 3.5±0.5 Oe. This was confirmed by 
measuring at not only several different points in the diffuse, 
but also in the specular and diffuse at different detector 
angles. It is worth noting that the sample indicating the larg- 





6292 J. Appl. Phys., Vol. 83. No. 11, 1 June 1998 


Freeland et al. 



Applied Field (Oe) 

FIG. 3. Comparison of magnetic hysteresis measured by XRMS at specular 
(bulk) and diffuse (interface) points for the x=400 A film ((7AFM”iO-9 A). 
Differences, such as the coercive field , illustrate the different behavior 
of the bulk vs interfacial magnetic properties. 


est difference the between specular and the diffuse coercive 
field is also the one exhibiting a roughening of the magnetic 
interface as noted by the drop in and cr^ with respect to 
and cTc (see Fig. 2). 

In conclusion, our results distinctly show that the chemi¬ 
cal and magnetic interfaces can have a very different char¬ 
acter. In addition, by tracking the diffuse intensity as a func¬ 
tion of applied field we find a very different behavior of the 
interfacial spins, which appears to be correlated with varia¬ 
tions of the chemical versus magnetic interface. 


ACKNOWLEDGMENTS 

This work was supported by the Office of Naval Re¬ 
search. One of the authors (J.W.F.) is a NRC/NRL research 


fellow. Brookhaven National Laboratory is supported by the 
U.S. Department of Energy. 

*J. F. MacKay, C. Teichert, D. E. Savage, and M. G. Lagally, Phys. Rev, 
Lett. 77, 3925 (1996). 

^Y. U. Idzerda, V. Chakarian, and J. W. Freeland, Synch. Radiat. News 10, 
6 (1997). 

^S. Zhang and P. M. Levy, Phys. Rev. B 43, 11 048 (1991). 

Suzuki and Y. Taga, Phys. Rev. B 52, 361 (1995). 

^Z. J. Zang and M. R. Scheinfein, Phys. Rev. B 52, 4263 (1995). 

^S. K. Sinha, E. B, Sirota, S. Garoff, and H. B. Stanley, Phys. Rev. B 38, 
2297 (1988). 

^H.-N. Yang, G.-C. Wang, and T.-M. Lu, Diffraction From Rough Surfaces 
and Dynamic Growth Fronts (World Scientific, River Edge, NJ, 1993). 
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4099 (1985). 

^C. Kao, J. B. Hastings, E. D. Johnson, D. P. Siddons, and G. C. Smith, 
Phys. Rev. Lett. 65, 373 (1990). 

Kao, C. T. Chen, E. D. Johnson, D. P. Siddons, H. J. Lin, G. H. Ho, 
G. Meigs, J.-M. Brot, S. L. Hulbert, Y. U. Idzerda, and C. Vettier, Phys. 
Rev. B 50, 9599 (1994). 

'* J. M. Tonnerre, L. Seve, D. Raoux, G. Soullie, B. Rodmacq, and P. Wolf- 
ers, Phys. Rev. Lett. 75, 740 (1995). 

Chakarian, Y. U. Idzerda, C.-C. Kao, and C. T. Chen, J. Magn. Magn. 
Mater. 165, 52 (1997). 

*^J. W. Freeland, V. Chakarian, Y. U. Idzerda, S. Doherty, J. G. Zhu, J.-H. 
Park, and C.-C. Kao, Appl. Phys. Lett. 71, 276 (1997). 

Chakarian, Y. U. Idzerda, G. Meigs, C. T. Chen, and C. -C. Kao, in 
Synchrotron Radiation Techniques in Industrial, Chemical, and Materials 
Science, edited by L. J. Terminello, K. L. D’Amico, and D. K. Shuh 
(Plenum, New York, 1996), pp. 187-205. 

'^S. Hulbert, D. J. Holly, F. H. Middleton, and D. J. Wallace, Nucl. Instrum. 

Methods Phys. Res. A 291, 343 (1990). 

'^E. D. Johnson, C. -C. Kao, and J. B. Hastings, Rev. Sci. Instrum. 63, 1443 
(1992). 

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(1990). 

Y. U. Idzerda, C. T. Chen, H. -J. Lin, G. Meigs, G. H. Ho, and C. -C. Kao, 
Nucl. Instrum. Methods Phys. Res. A 347, 134 (1994). 

Chakarian, Y. U. Idzerda, and C. T. Chen, Phys. Rev. B (to be pub¬ 
lished). 







JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Soft x-ray resonant magnetic reflectivity study of thin films and multilayers 

J. M. Tonnerre L. Seve, A. Barbara-Dechelette, F. Bartolome, and D. Raoux 

Laboratoire de Cristallographic, CNRS/Universite Joseph Fourier, 

B. P. 166, 38042 Grenoble Cedex 9, France 

V. Chakarian 

Naval Research Laboratory, Code 6345, Washington, D.C. 20375 

C. C. Kao 

National Synchrotron Light Source, Brookhaven National Laboratory, Upton, New York 11973 

H. Fischer and S. Andrieu 

LPM, CNRS/Universite Nancy, 54506 Vandoeuvre, France 

O. Fruchart 

Laboratoire Louis Neel, CNRS/Universite Joseph Fourier, B.P. 166, 38042 Grenoble Cedex 9, France 

Soft x-ray resonant magnetic reflectivity measurements on thin films and multilayers in a transverse 
geometry using linear polarized photons are presented. Magneto-optic calculations taking into 
account the layer roughness allows us to reproduce all the experimental features of the angular and 
energy reflectivity curves as well as the asymmetry ratio in both cases. Application to Fej^Mni-j^ 
alloy films epitaxially grown on Ir(OOl) brings more insights on the magnetic transition occurring at 
x = 0.75. © 1998 American Institute of Physics. [80021-8979(98)49911-0] 


Magnetism in artificially made materials has become an 
area of intense activity. The study of magnetism of ultrathin 
films and multilayers has revealed new properties which are 
different from bulk materials and have technological poten¬ 
tial, especially in magnetic memories and magnetic based 
sensors. Since the devices to be implemented concern multi¬ 
layered and multielement systems, it is necessary to go be¬ 
yond the measurements of the macroscopic magnetic prop¬ 
erties and to separate out the magnetic signatures of the 
different species within the different layers. In order to se¬ 
lectively probe the magnetic contributions, we develop the 
use of the x-ray resonant magnetic scattering (XRMS), espe¬ 
cially in the soft x-ray range. 

XRMS, which is x-ray magnetic dichroism in a scatter¬ 
ing condition, presents the advantage of being atom and shell 
selective and then allows one to probe the magnetism of the 
different atomic levels of a specific element in a magnetic 
material.^’^ The angular dependence inherent to a scattering 
measurement brings furthermore the spatial selectivity. As 
XRMS is a two photon process, the effects related to mag¬ 
netic circular dichroism (XMCD) are observable not only 
with circular polarized photons but also with linear polarized 
ones.^’"^ Moreover, they are enhanced in diffraction condi¬ 
tions due to interference effects and, in that case, the mag¬ 
netization dependent contribution may be of the same order 
of magnitude as the nonmagnetic one.^ This has been shown 
by using artificial large period structures, like Ag/Ni and 
Ag/NiFe multilayers, in order to diffract photons of large 
wavelength (\^15 A at the Ni L 23 edges). These first ex¬ 
periments, where the energy dependence of an asymmetry 
ratio R = {I^-YI~) is measured, and I~ being 
two Bragg peak intensities collected for two opposite direc- 


^^Electronic mail: tonnerre@polycnrs-gre.fr 


tions of an applied magnetic field, allowed us on one hand to 
demonstrate the equivalence between the XMCD and the 
XRMS^ and on the other hand to determine the amplitude of 
the magnetic moment of both 3d transition metals in a binary 
alloyIn order to study thin films, which do not give Bragg 
peaks at small values, we have to turn to the analysis of 
magnetic specular reflectivity measurements. 

Following the success of XMCD measurements in the 
soft x-ray range, specular resonant magnetic reflectivity has 
been mainly measured using circular polarized incident pho¬ 
tons in a geometry similar to the longitudinal magneto-optic 
Kerr effect In the simulations, although general trends 
are well understood,^ some discrepancies still remain. One 
possible reason is related to the difficulty to take into account 
the roughness at the interfaces when both states of linear 
horizontal and vertical polarization of the photons are 
coupled and then to account for its effect on the change of 
the circular polarization rate at each interface. Therefore, we 
first focused on the development of the resonant magnetic 
reflectivity in the transverse magneto-optic Kerr effect ge¬ 
ometry, using linear p-polarized photons. The fact that the 
photon beam has only one polarization state allows us to 
straightforwardly extend the Vidal and Vincent formalism to 
treat the interface roughness, 

The measurements were conducted at the UAB beam 
line at the National Synchrotron Light Source. A vacuum 
compatible 9-29 spectrometer, working in the horizontal 
plane, was used.^^ The sample was magnetized by using a 
Bitter electromagnet capable of delivering a field up to 1400 
G perpendicular to the diffraction plane. First results were 
obtained from a bcc W(32 A)/Fe(91 A)AV(129 A) deposited 
by laser ablation on a AI 2 O 3 substrate. Figure 1(a) shows an 
angular scan where the reflected intensities and the asymme¬ 
try ratios R are collected at a selected energy in the vicinity 
of the L 3 Fe edge. Figure 2(a) displays an energy scan where 


0021 -8979/98/83(11 )/6293/3/$15.00 


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© 1998 American Institute of Physics 



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J. AppL Phys., Vol. 83, No. 11, 1 June 1998 


Tonnerre et a!. 



FIG. 1. Fixed energy angle scans (solid line, left side legend) and asymme¬ 
try ratio (open circles, right side legend) measured on a W/FeAV thin film in 
the vicinity of Fe L 3 edge (703.2 eV): experiment (a) and calculation (b). 


the angular position is kept fixed and the incident photon 
energy is scanned through the Fe L 23 edges. In this trans¬ 
verse geometry, the amplitude at maximum of R are typi¬ 
cally of the order of 5% to 15% depending on both the inci¬ 
dent angle and energy. Both scans depend on the strong 
resonance available at the L 23 edges and on the structural 
features of the layers: thickness and density of the layers as 
well as interface roughness. The energy scan is more sensi¬ 
tive to the spectroscopic aspect (amplitude of the magnetic 
moment) and the angular one to the structural aspect (ar¬ 
rangement of the moments). 

To analyze the data, we have developed a numerical 
calculation based on an optical approach, where the Max¬ 
well’s equation are solved in a matrix formalism. It allows us 
to reproduce all the features of the experimental curve [Figs. 
1(b) and 2(b)]. The main part is to calculate the dielectric 
tensor which has only diagonal terms in a cubic symmetry 
and to take into account the magnetic effects through nonva¬ 
nishing off-diagonal elements. Both the imaginary and real 
parts of the charge dielectric constant were derived from ab¬ 
sorption data and their Kramers-Kronig transformation, re¬ 
spectively. Their magnetic counterparts are determined in the 



Photon Energy (eV) 



690 700 710 .720 730 


D3 

o’ 


Photon Energy (eV) 


FIG. 2. Fixed angle energy scans (solid line, left side legend) and asymme¬ 
try ratio (open circles, right side legend) measured on a W/FeAV thin film at 
5° at the Fe L 27 , edges: experiment (a) and calculation (b). 


same way from XMCD data obtained from thin Fe films. 
That amounts to consider Mpe= 2.1 fiB as derived from sum 
rules.Since it is usually accepted that XMCD is propor¬ 
tional to the magnetic moment, we use a multiplying factor 
to reduce or increase the magnetic contribution to the reflec¬ 
tivity in order to fit our data. More details on the calculation 
will be given in an upcoming article.^ 

We turn next to the discussion of an example where soft 
x-ray resonant magnetic reflectivity has been used to inves¬ 
tigate the magnetic transition occurring in thin Fe;^Mni_;^ 
alloy films epitaxially grown on Ir(OOl). While bulk alloys 
present a fee structure and are antiferromagnetic (AF) over 
the whole range of composition, it has been shown that, in 
Fe^^Mni-^/Ir superlattices (SL), the alloy is body-centered 
tetragonal (bet) and exhibit a magneto-structural transition at 
x = 0.75 from a ferromagnetic state (j>0.75) to an antifer¬ 
romagnetic one (x<0.75).^^ In the present study, we fo¬ 
cused on two superlattices Feo.9Mno.|(27 A)/lr(18 A) and 
Feo.7Mno.3(27 A)/Ir(18 A), grown on a Ir buffer layer, whose 
concentrations have been chosen on each sides of the transi¬ 
tion. In the 70% Fe sample, the alloy layer is uniformly 
strained all through the stacking sequence of the superlattice 
in a bet structure with da- 1.23.^'^ In the 90% Fe sample, 
two phases have been identified. In the first phase, labelled 
SLl, the alloy and Ir layers undergo the influence of the Ir 
buffer layer and the alloy layer is bet with da = 1.16. In the 
second one, SL2, both layers have relaxed the strain imposed 
by the buffer layer and may be considered as free layers in 
mutual strain. In that case, the alloy tends to the Fe bcc 
structure with c/«=1.08. The analysis of a series of 
reciprocal-space maps of the diffracted intensities, collected 
around the (111) Bragg peak of the buffer layer for different 
grazing incident angles, allowed us to appreciate their pro¬ 
portion, which corresponds to 60% and 40%, respectively, 
and their localization.*^ These findings have been supported 
by the characterization of two thin alloy films of the same 
composition (x=0.7 and 0.9) with similar thicknesses (^30 
A) sandwiched between Ir layers, aimed at the determination 
of the structural properties of the alloy layers at the begin¬ 
ning of the elaboration process. This is of particular interest 
in order to separate out the magnetic properties of SLl and 
SL2. 

Figure 3 shows the energy dependence of R measured at 
15° on both multilayers around the Fe L 2 3 edges. The shapes 
of R are similar and they exhibit two resonances at the L 3 
(707 eV) and L 2 edge (720 eV). Fe atoms in the Fe 90% SL 
give rise to a strong asymmetry ratio of about 40% while for 
the Fe 70% SL, R values are at most 4%. This reduction of 
the magnetic signal of the Fe atoms is far beyond the change 
one would expect from its concentration reduction. The 
simulation of the energy dependence of R has been carried 
out using the structural parameters deriving from the struc¬ 
tural studies and by assuming that the alloy is a solid solution 
where the Fe atoms bear the same magnetic moment all 
through the layers. As in the preceding section, the magnetic 
moment of Fe is initially assumed to be 2.1 /jB. In the case 
of the Fe-rich SL, the calculation (solid line) fits quite well 
the experiment in Fig. 3(b). For the Fe 70% SL, it is required 
to reduce the dichroism signal by a factor 0.13 in 
















J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Tonnerre ef a/. 6295 




-{20 


60 


40 


690 700 710 720 730 740 690 700 710 720 730 740 
Photon Energy (eV) Photon Energy (eV) 


> 

B 

B 

n 


0 K 

O* 

-20 3 
•40 


FIG. 3. Energy dependent asymmetry ratio measured at 15° at the Fe L 2,3 
edges on FcojMnosAr (a) and FeogMno i Ar (b): experiment (open circles) 
and calculation (solid line). 


order to fit the data [Fig. 3(a)]. Therefore, we observe a 
transition for the Fe magnetic moment from 2.1 ±0.05 to 
0.27 ±0.05 jiiB. The uncertainties derive from the dispersion 
of the fitting parameters of reflectivity curves measured at 
other angular positions. It is worth recalling that the value for 
the Fe-rich SL is an averaged one since two phases have 
been evidenced in the SL. In order to separately determine 
the magnetic moment in the SLl phase, we measured the 
energy dependence of R for the thin Feo. 9 Mno.i films at dif¬ 
ferent angular positions. Using the same set of structural and 
magnetic parameters, we obtained a good agreement be¬ 
tween experiments and calculations. Figure 4(a) shows the 
asymmetry ratio values obtained at 26° while the ensemble 
of R measurements will be published in a full article. 
Again, a fairly good agreement has been obtained with a Fe 
magnetic moment of 2.1 /xB, leading us to conclude that the 
Fe atoms in SLl and SL2 carry about the same magnetic 
moments. Gathering the structural and magnetic informa¬ 
tions on the three different phases of the alloy thin films, we 
observe that the magnetic transition is related neither to the 



Photon Energy (eV) Photon Energy (eV) 


FIG. 4. Energy dependent asymmetry ratio measured on Ir/Feo.gMnoj/Ir 
thin film at 26° at the Fe L 2,3 edges (a) and at 20° at Mn L 2,3 edges (b): 
experiment (open circles) and calculation (solid line). 


hypothetical fee or bcc structure of the unstrained layer, nor 
to the Fe magnetic volume. It actually depends on the da 
value and the transition occurs for c/a = 1 . 2 ^^ which is in 
agreement with the theoretical prediction for a bet iron.^^ 

Work is under progress to understand the magnetic prop¬ 
erties of the Mn atoms. Figure 4(b) displays the weak mag¬ 
netic signal measured at the L 23 edges of Mn in the thin 
Feo. 9 Mno.i films. It shows that Mn atoms carry a net mag¬ 
netic moment. We observe the R spectrum has the same 
shape than that measured at the Fe L edges at the same 
incident angle. In order to determine the amplitude of the Mn 
magnetic moment as well as the coupling between Fe and 
Mn, we have to fit the R values. In the case of Mn, this is not 
so straightforward, since bulk Mn is antiferromagnetic and 
shows no circular dichroism. Here, the calculation is per¬ 
formed using the XMCD data from Mn [1 monolayer 
(ML)]/Fe(001),^^ where the coupling is found to be ferro¬ 
magnetic and the Mn magnetic moment estimated to be 
about 1.7 However, to fit the R values, it has been 

necessary to change the sign of the XMCD data used in the 
calculation, which implies to consider an AF coupling of Mn 
moments to the Fe ones. It appears that the amplitude of the 
XMCD allows us to simulate the amplitude of R and, hence, 
we estimate the Mn magnetic moment to be about 1.7 /xB. 

In summary, we have shown that XRMS in transverse 
mode allows to investigate quantitatively the magnetic prop¬ 
erties of thin films and multilayers. It turns out that it is 
possible to analyze small changes in the energy dependent 
magnetic contribution to the reflectivity. This allows us to 
measure weak magnetic moment (here 0.2 /xB) in a thin 
buried layer. A refinement procedure applied simultaneously 
to the angular and energy scans should give more insights 
about the amplitude of the moments, their distribution inside 
the layer, and likely about the magnetic roughness at inter¬ 
faces. Moreover, we show that large magnetic contributions 
to the reflectivity are available at large angles which should 
allow developments towards element specific imaging of 
magnetic domains. This approach could be useful for imag¬ 
ing the behavior of buried magnetic layers. 

The authors thank Y. Souche and F. de Bergevin for 
fruitful discussions on magneto-optic calculations. 

U. P. Hannon et al, Phys. Rev. Lett. 61, 1245 (1988); 62, 2644 (1989). 
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^C. C. Kao et al, Phys. Rev. B 50, 9599 (1994). 

^C. C. Kao et al, Phys. Rev. Lett. 65, 373 (1990). 

^J. M. Tonnerre et al, Nucl. Instrum. Methods Phys. Res. B 97, 444 
(1995). 

^J. M. Tonnerre et al, Phys. Rev. Lett. 75, 740 (1995). 

^L. Seve, Ph.D. thesis, Univesite Joseph Fourier, 1997 (unpublished). 

^V. Chakarian et al, J. Magn. Magn. Mater. 165, 52 (1997). 

^Y. U. Ydzerda et al. Synchrotron Radiation News 10, 6 (1997). 

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Andrieu et al, Europhys. Lett. 38, 459 (1997). 










JOURNAL OF APPLIED PHYSICS VOLUME 83, NUMBER 11 I JUNE 1998 

Dependence of anti-Stokes/Stokes intensity ratios on substrate optical 
properties for Brillouin light scattering from ultrathin iron films 

J. F. Cochran,M. From, and B. Heinrich 

Department of Physics, Simon Fraser University, Burnaby, British Columbia V5A IS6, Canada 

Brillouin light scattering experiments have been used to investigate the intensity of 5145 A laser 
light backscattered from spin waves in 20 monolayer thick Fe(OOl) films. The experiments have 
shown that the ratio of frequency upshifted light intensity to frequency downshifted light intensity 
depends upon the material of the substrate used to support the iron films. For a fixed magnetic field 
and for a fixed angle of incidence of the laser light this intensity ratio is much larger for an iron film 
deposited on a sulphur passivated GaAs(OOl) substrate than for an iron film deposited on a Ag(OOl) 
substrate. The data have been compared with a calculation that takes into account multiple scattering 
of the optical waves in the iron film and in a protective gold overlayer. The observations are in 
qualitative agreement with the theory, except for angles of incidence greater than 60°. © 1998 
American Institute of Physics. [80021-8979(98)37011-5] 


The ratio of upshifted scattered light intensity (anti- 
Stokes line) to downshifted scattered light intensity (Stokes 
line) in Brillouin light scattering experiments (BLS) per¬ 
formed on ultrathin magnetic films depends on the optical 
properties of the substrate that support the film.^ This is il¬ 
lustrated in Fig. 1 for BLS experiments performed on iron 
films 20 monolayers (ML) thick. Figure 1(a) shows scattered 
light intensity versus frequency shift for a 20 ML iron film 
grown on a Ag(OOl) single crystal by means of molecular 
beam epitaxy.^ The iron film was covered by 18 ML of gold. 
The BLS measurements were carried out ex situ. A magnetic 
field of 1.00 kOe was applied in the plane of the film and 
perpendicular to the plane of incidence of the incident 5145 
A laser light. The p-polarized laser light was incident at 45°, 
and the scattered light was collected in the backscattering 
configuration.^ The data shown in Fig. 1(b) were collected in 
the backscattering configuration for -polarized light"^’^ inci¬ 
dent at 45°, and using an applied magnetic field of 1.08 kOe. 
The iron film was 20 ML thick, and was grown by means of 
molecular beam epitaxy on a sulphur passivated GaAs(OOl) 
single crystal.^ The iron film was covered by 20 ML of gold 
and the BLS data were measured ex situ. It is clear from a 
comparison of Figs. 1(a) and 1(b) that (i) the ratio of up- 
shifted to downshifted scattered light intensity is quite dif¬ 
ferent for these two specimens; and (ii) the observed fre¬ 
quency shift is different for the two specimens. Both of these 
differences can be attributed to the effect of different sub¬ 
strates. The change in frequency between the two specimens 
can be primarily attributed to a difference in perpendicular 
uniaxial surface anisotropy, see Table I. The dependence of 
the intensity ratios on substrate material is a consequence of 
the dependence of the magnitude and phase of the optical 
electric field in the iron film on the optical properties of the 
substrate material. A 20 ML thick iron film is thin compared 
with the penetration depth of 5145 A light in iron, conse¬ 
quently the optical electric field amplitudes in the iron film 
depend very strongly on the optical properties of the 
substrate.^ 


“taectronic mail: jcochran@sfu.ca 


Data for thin iron films grown on Ag and GaAs sub¬ 
strates have been compared with calculations carried out us¬ 
ing the formalism described by Cochran and Dutcher.^ Rel¬ 
evant parameters used in the calculations are listed in Table 
I. The magnetic parameters listed in Table I give a good 



Frequency Shift (GHz) 


5 ’ 

-H 

§ aa 


'gO.6 


0,4 

>1 
4J 

n 0.2 

c 
0 ) 

tl 0 

5 -30 


-20 


-10 



(b) 1 



• • i • ■ 

i 

j 



:h- 1 

.08 ioe 



1 







L 



> 1 

> 1 

Hj 



rr 










10 


20 


30 


Frequency Shift (GHz) 


FIG. 1. Light intensity vs frequency shift for 5145 A light scattered from a 
20 ML thick Fe(OOl) film; the laser light was incident on the specimen at an 
angle of 45®. The scattered light was collected in the backscattering con¬ 
figuration, and intensities were normalized to the maximum intensity of the 
frequency upshifted peak, (a) Ag(001)/20 ML Fe/18 ML Au with a field of 
1.0 kOe applied in the film plane and directed along (100). (b) 
GaAs(00I)/20 ML Fe/20 ML Au with a field of 1.08 kOe applied in the 
specimen plane and directed along (110). In both cases the magnetic field 
was applied perpendicular to the plane of incidence of the laser light. 


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Cochran, From, and Heinrich 


6297 


TABLE I. Parameters used to calculate the frequencies and ratios of upshifted to downshifted scattered light 
intensities for the Ag(001)/20Fe/18Au and GaAs(001)/20Fe/20Au used for this work. The perpendicular 
uniaxial anisotropy energy was taken to have the form ergs/cc, where d is the iron 

film thickness and is the magnetization component perpendicular to the plane of the Fe film. 


Fe film: 

Thickness d—lO monolayers=28.6 A 

Saturation magnetization, 477M^ = 21.4 kOe 

Exchange stiffness parameter, A = 2.03X 10“^ 

Gilbert damping parameter, G= 10^ Hz 

Optical dielectric constant, 6= ( — 0.40, 16.44) 

Resistivity, p= l.OX 10“^ fl cm 

(a) Ag(001)/20Fe/18Au 

(b) GaAs(001)/20Fe/20Au 

Cubic anisotropy parameter, .fiT] =4.0X10^ ergs/cc 

Uniaxial anisotropy parameter, K^^ = 1.04 ergs/cm^ 

Effective cubic anisotropy parameter for H along (110), 
ii:i = 3.7X 10^ ergs/cc 

Uniaxial anisotropy parameter, Ky= 1.42 ergs/cm^ 

Au film: 

2.04 A per monolayer 

Optical dielectric constant, e=( —3.75, 2.75) 

Resistivity, p = 2.35X 10“^ 11 cm 

Ag substrate: 

Optical dielectric constant, 6=(- 10.70, 0.33) 

Resistivity, p= 1.59X 10"^ fi cm 

GaAs substrate: 

Optical dielectric constant, e=( 17.65, 3.19) 

Resistivity, p = 1 O cm 


description of the dependence of spin-wave frequencies on 
applied magnetic field, see Fig. 2. The optical dielectric con¬ 
stants listed for 5145 A light (2.41 eV) were obtained from 
Johnson and Christy (Iron,^ Silver^), Joenson et (gold), 
and Aspnes and Studna^^ (GaAs). 

The observed upshifted to downshifted intensity ratios 
are plotted as a function of applied magnetic field in Fig. 3 
for light incident at 45° on the specimens. The solid lines are 
intensity ratios calculated using the parameters listed in 
Table I. The data exhibit a decreasing intensity ratio with 
increasing magnetic field; this decrease with field is repro¬ 


duced by the calculations. However, the calculated intensity 
ratios tend to be smaller than the observed ratios, especially 
in the case of the GaAs substrate. The calculated intensity 
ratios are very sensitive to the amplitudes and phases of the 
optical electric field components in the iron film, and these 
field components in turn, especially their phases, are sensi¬ 
tive to the film thicknesses and the dielectric parameters used 
to describe them. 

The ratio of upshifted to downshifted light intensity has 
been investigated as a function of the angle of incidence of 
the light for fixed magnetic field. The results of angular mea- 


N 

sc 

o 


>1 

o 

c 

<D 

P 

cr 

0 ) 

u 

Pt4 



012345678 

Field (kOe) 



(b) 

(a) 


012 3 45678 

Field (kOe) 


FIG. 2. Spin-wave frequency vs applied magnetic field. The data were ob¬ 
tained from Brillouin light scattering experiments on 20 ML thick films with 
the field applied in the specimen plane. The angle of incidence of the laser 
light was 45°. X—Ag(001)/20 ML Fe(001)/18 ML Au. The field was ap¬ 
plied along the (100) direction; (a) calculated using the parameters listed in 
Table L +—GaAs(001)/20 ML Fe(001)/20 ML Au. The field was applied 
along the (110) direction; (b) calculated using the parameters listed in Table 
I. 


FIG. 3. The ratio of frequency upshifted to frequency downshifted Brillouin 
backscattered light intensity vs magnetic field applied in the specimen plane. 
The 5145 A laser light was incident at 45°. X—^Ag(001)/20 ML Fe(001)/18 
ML Au, the field was applied along (100); (a) calculated using the param¬ 
eters listed in Table I. +—GaAs(00iy20 ML Fe(001)/20 ML Au, the field 
was applied along (110); (b) calculated using the parameters listed in Table 
1. The vertical error bars correspond to an estimated 20% uncertainty in the 
data. 






6298 J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Cochran, From, and Heinrich 




0 0.5 1 1.5 2 2.5 

Wavevector {10®/cm) 


FIG. 4. The ratio of frequency upshifted to frequency downshifted Brillouin 
backscattered light intensity vs the in-plane component of the spin-wave 
wave vector for the specimen Ag(001)/20 ML Fe(001)/18 ML Au. A mag¬ 
netic field of 1.0 kOe was applied in the specimen plane along the (100) 
direction, and 5145 A laser light was used for the measurements. The solid 
line was calculated using the parameters listed in Table I. The vertical error 
bars correspond to an estimated 20% uncertainty in the data. 


FIG. 5. The ratio of frequency upshifted to frequency downshifted Brillouin 
backscattered light intensity vs the in-plane component of the spin-wave 
wave vector for the specimen. GaAs(001)/20 ML Fe(001)/20 ML Au. A 
magnetic field of 2.2 kOe was applied in the specimen plane along the (110) 
direction, and 5145 A laser light was used for the measurements, (i) Calcu¬ 
lated for a field of 1.0 kOe and (ii) calculated for a field of 2.2 kOe using the 
parameters listed in Table I. The vertical error bars correspond to an esti¬ 
mated 20% uncertainty in the data. 


surements on a specimen grown on a silver substrate are 
shown in Fig. 4, and results for an iron film grown on a 
GaAs substrate are shown in Fig. 5. The angular variation of 
the incident light is expressed in terms of the spin-wave 
wave vector component parallel with the film plane, Q 
= ( 47 r/A)sin (9, where X = 5145 A is the wavelength of the 
incident light and 6 is the angle of incidence. The data ex¬ 
hibit an increasing intensity ratio with increasing Q, i.e., 
with increasing angle of incidence. The calculations, indi¬ 
cated by the solid lines in Figs. 4 and 5, also display an 
increasing intensity ratio with increasing angle of incidence. 
According to theory, the intensity ratio varies with angle of 
incidence because of an interference between the scattered 
light originating from the optical electric field components in 
the iron film that are parallel and perpendicular to the film 
plane. In the limit of normal incidence the optical electric 
field in the iron film has only a component parallel to the 
plane, there is no interference effect, and therefore the up- 
shifted and downshifted intensity ratio must approach unity 
in the limit of Q-0, This expectation is borne out by the 
experimental observations. For reasons which we do not un¬ 
derstand, the intensity ratio data shown in Fig. 5, and ob¬ 
tained using an applied field of 2.2 kOe, are in better agree¬ 
ment with the ratios calculated for an applied field of 1 kOe 
[curve (i)] than with the curve calculated using a field of 2.2 
kOe [curve (ii)]. This appears to be a coincidence. However, 
the drop off in intensity ratio observed for Q lying between 
2.0 and 2.2X 10^ cm"^ {8 between 55° and 65°), and ob¬ 
served for both the silver substrates and the GaAs substrates, 
appears to be real. It may be caused by some unknown in¬ 
strumental effect. For the GaAs substrate the absolute inten¬ 
sity at 0=65° was also much reduced over that measured at 
0=55° contrary to theoretical expectations. The origin of 
this rather sudden drop off in scattered light intensity is un¬ 
known: no such effect was observed for specimens grown on 
silver substrates. It may be associated with the observed 
rough iron growth obtained using a GaAs substrate.^ A de¬ 
crease in intensity ratio at large angles of incidence runs 
counter to the rather sharp increase in the upshifted to down¬ 


shifted intensity ratio for Q approximately equal to 2.25 
X 10^ cm"^ reported by Moosmiiller, Truedson, and Patton 
for thin permalloy films sputtered on silicon.A monotonic 
dependence of the intensity ratio on angle of incidence of the 
laser light was reported by Camley et al.^ for 100 A thick 
polycrystalline iron films. 

The authors would like to thank S. Watkins for the sul¬ 
phur passivated GaAs substrates used in this work, and T. 
Monchesky for communicating to us the results of his 36 
GHz microwave measurements on 20 ML Fe films grown on 
these GaAs substrates. We would also like to thank the Natu¬ 
ral Sciences and Engineering Research Council of Canada 
for grants that supported this work. 

^M. G. Cottam, J. Phys. C 16, 1573 (1983). 

^Specimens were prepared in a layer-by-layer growth mode using molecu¬ 
lar beam epitaxy as described by B. Heinrich, Z. Celinski, J. F. Cochran, 
A. S. Arrott, and K. Myrtle, J. Appl. Phys. 70, 5769 (1991). 

^ J. R. Sandercock, in Topics in Applied Physics Vol. 51, Light Scattering in 
Solids III, edited by M. Cardona and G. Giintherodt (Springer, Berlin, 
1982), p. 173. 

"^In the backscattering configuration the intensity of the scattered light is the 
same for both p- and 5 -polarized incident light; see R. E. Camley and M. 
Grimsditch, Phys. Rev. B 22, 5420 (1980); also Ref. 5. 

^R. E. Camley, P. Griinberg, and C. M. Mayr, Phys. Rev. B 26, 2609 
(1982). 

^A buffer layer of GaAs was grown on a GaAs(OOl) wafer by means of 
metalorganic chemical vapor deposition and the resulting surfaces were 
passivated using a H 2 S treatment at 400 °C. The iron film was deposited 
on the sulphur passivated GaAs surface at room temperature by means of 
molecular beam epitaxy. The iron growth was rough and exhibited no 
RHEED oscillations. 

’j. F. Cochran and J. R. Dutcher, J. Magn. Magn. Mater. 73, 299 (1988). 
There is an error in the last term of on p. 309; the bracketed term 
should read {Hy + + not H, + 47rMg). 

^P. B. Johnson and R. W. Christy, Phys. Rev. B 9, 5056 (1974). 

^P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972). 

^®P. Joenson, J. C. Irwin, J. F. Cochran, and A. E. Curzon, J. Opt. Soc. Am. 
63, 1556 (1973). 

**D. E. Aspnes and A. A. Studna, Phys. Rev. B 27, 985 (1983). 

Moosmiiller, J. R. Truedson, and C. E. Patton, J, Appl. Phys. 69, 5721 
(1991). 






JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Critical Phenomena, Spin Norm Koon and 

Glasses, and Frustration Pedro Schottmann, Chairmen 


Magnetic phase diagrams of holmium determined 
from magnetoresistance measurements 

Jeffrey R. Gebhardt and Naushad Ali®' 

Department of Physics, Southern Illinois University at Carhondale, Carbondale, Illinois 62901 

The magnetic phase diagrams of holmium in the magnetic field-temperature plane have been 
determined using electrical resistance as a function of temperature and electrical resistance as a 
function of applied magnetic field (magnetoresistance). Two phase diagrams were constructed 
corresponding to magnetic fields applied along the a and c axes. For temperatures below 80 K and 
an applied field along the a axis, our H-T phase diagram agrees well with that of Jensen and 
Mackintosh. In a temperature range of 30-100 K we observe two transitions which correspond to 
the boundaries of the predicted helifan phase. However, at higher temperatures there are differences 
with the work of Willis et al, most notably in the behavior of the Neel temperature splitting. We 
observe a splitting of the Neel temperature above 1 T with one feature remaining nearly constant in 
temperature as the field is increased. For a c-axis applied field, our phase diagram is very similar to 
the results of Willis et al, a splitting of the Neel temperature transition above 0.5 T is observed. At 
temperatures below 18 K and magnetic field less than 1.5 T, an anomaly associated with a devil’s 
staircase is seen. © 1998 American Institute of Physics, [80021-8979(98)32811-X] 


The first detailed studies of the magnetic structures in 
holmium as a function of temperature and magnetic field, 
were performed by Koehler et al}'^ using neutron diffrac¬ 
tion. At temperatures below the Neel temperature (T^ 
= 132K), holmium orders antiferromagnetically with a he¬ 
lical structure propagating along the hexagonal c axis, and 
with moments lying in the basal plane. Below the Curie tem¬ 
perature (Tc^ 18 K), holmium restructures as a commensu¬ 
rate ferromagnetic cone phase. The spiral structures in the 
region Tc<T<Tf^ are in general incommensurate, however, 
a series of commensurate magnetic phases have been found, 
first by Gibbs et al^ using synchrotron radiation, and later by 
others.The commensurate structures in holmium are un¬ 
derstood in terms of the spin-slip model.^’^ The magnetic 
structures in a basal plane magnetic field were studied by 
Koehler et al^ who identified intermediate phases, termed 
fans, between the helix and the ferromagnetic phases. Re¬ 
cently, a structure between the fan and helix phases, which 
they called a helifan, was predicted by Jensen and 
Mackintosh^’^ using mean field calculations. Some experi¬ 
mental evidence of this structure is given by Ohsumi et al^ 
and Gebhardt et al Bulk magnetic properties such as mag¬ 
netization, Willis et al^^ and magnetoresistancehave 
also been used to determine magnetic phase transitions. In 
this article, we present the magnetic phase diagrams of hol¬ 
mium in the H-T plane for applied magnetic fields along the 
a and c axes using magnetoresistance measurements. 

Two single-crystal holmium samples, each in the shape 
of a long bar were prepared at Ames Laboratory. The first 
sample has an a-axis length of 10 mm and cross-sectional 


^^Corresponding author. 


area of 0.45 mm^, and the second, a c-axis length of 14.9 
mm and cross-sectional area of 0.95 mm^. The electrical re¬ 
sistance measurements were carried out using the conven¬ 
tional four probe method. A 30 mA longitudinal dc current 
was provided by a Keithley 220 constant current source, and 
the voltage measured using a Keithley 181 nanovoltmeter. A 
constant temperature and applied magnetic field was accom¬ 
plished by using the temperature control and superconduct¬ 
ing magnet of a Quantum Design SQUID magnetometer. For 
this study, two types of measurements were conducted: (i) 
the electrical resistance as a function of temperature (5-150 
K) at various constant applied magnetic fields (0-5.5 T) and 
(ii) the electrical resistance as a function of magnetic field, 
defined as magnetoresistance (MR), at various constant tem¬ 
peratures (2-150 K). 

A large number of electrical resistance {R) versus tem¬ 
perature (T) scans and magnetoresistance (MR) versus mag¬ 
netic field {H) have been carried out for magnetic fields 
applied along the a and c axes of Ho. In Fig. 1(a), a repre¬ 
sentative R vs T curve is shown for a field of 77^ 2 T applied 
along the a axis. The transitions are indicated by arrows. The 
magnetic transition temperatures are determined by a step 
change in the R vs T curve, or as a slope change in the R vs 
T curve. In the inset of Fig. 1(a), the transitions are clearly 
seen as large spikes in the slope of R vs T curve. The 
anomaly at 32 K corresponds to the transition from the fan to 
the ferromagnetic phase. The anomalies at 80 and 86 K 
bracket the helifan phase predicted by Jensen and 
Mackintosh.^ These two transitions are also clearly seen in 
MR vs H(H\\a) curves at a constant temperature. An ex¬ 
ample is given in Fig. 1(b) for a temperature of r=60K. 
The transitions show as step changes in the MR vs H curve 


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J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


J. R. Gebhardt and N. Ali 


Temperature (K) 

20 30 40 50 60 70 80 90 100 



FIG. 1. (a) Resistance vs temperature for a magnetic field of // = 2 T applied 
along the a axis. The inset shows the derivative of the curve. Arrows indi¬ 
cate magnetic transitions, (b) Resistance vs applied field at a con¬ 

stant temperature of T-60 K. The derivative is given in the inset. Arrows 
indicate magnetic transitions. 

and are indicated by arrows. The inset of Fig. 1(b) shows the 
[d(MR)/dH] vs H curve where the anomalies are visible in 
the slope change of the curve. By tabulating the transition 
temperatures in R wsT curves at a given magnetic field, and 
the transition fields in MR vs H curves at a given tempera¬ 
ture, we are able to construct the H-T phase diagram of 
holmium for a magnetic field applied along the a axis of Ho. 

Figure 2(a) shows a R vs 7 curve for a magnetic field 
applied along the c axis. The arrows indicate zero field 
anomalies at 7= 18, 20, and 24 K. These transitions are dif¬ 
ficult to see in the R vs 7 curve, but show up clearly in the 
slope of R vs 7 curve, which is shown in the inset of Fig. 
2(a). The arrow marked by an asterisk refers to an anomaly 
which is seen in all R vs 7 data in applied fields from 0 T up 
to 5.5 T and does not vary with temperature. The anomaly is 
not observed in MR vs H data and does not correspond to 
any known magnetic phase transition in Ho. Figure 2(b) 
shows a MR vs H(H\\c) curve at a temperature of 7==5 K. 
Although the data is quite noisy, a large transition at H 
= 1.25 T is clearly visible in both the MR vs //, and slope of 
MR vs H [Fig. 2(b) inset] curves. Again, by tabulating the 
transition temperatures and fields, we are able to construct 
the H-T phase diagram of holmium for a magnetic field 
applied along the c axis. 

The H~T phase diagram of Ho for applied field along 
the a axis is presented in Fig. 3. At lower temperatures, the 


Temperature (K) 

0 5 10 15 20 25 30 

1.000 


0.800 

a 

^ 0.600 

8 

c 

(0 

to 

g 0.400 
0^ 


0.200 


0.185 


0.180 


a 0.175 
<v 

C 0.170 

(D 

w 

to 

® 0.165 


0.160 


0.155 


FIG. 2. (a) Resistance vs temperature measured along the c axis in zero 
applied magnetic field and temperatures below 30 K. The inset shows the 
derivative of the curve. Arrows indicate magnetic transitions, (b) Resistance 
vs applied field (//||c), at a constant temperature of 7=5 K. The large step 
transition (arrow) shows as a spike in the derivative of the curve given in the 
inset. 


a. 


10 15 20 26 30 

Temperature (K) 

H = 0T 


-I—I—I—I—I—I—I—I—I—I—I- 


T = 5K 




. * X 

■ • - i 






0.0 0.5 1.0 1.5 2.0 2.5 


Field (T) 


Field (T) 


phase diagram is similar to that of Willis et determined 
from magnetization measurements. The inset of Fig. 3 shows 
our phase diagram for temperatures below 80 K and field 
below 2 T. This phase diagram is nearly identical to that of 
Jensen and Mackintosh^ (see Fig. 3), constructed from mean 



FIG. 3. //-7 phase diagram of single-crystal holmium for applied magnetic 
field along the a axis. Circular symbols (•) indicate data from R vs T 
measurements, and square symbols (■) indicate data from MR vs H mea¬ 
surements. Solid lines are a visual guide. The inset shows the H~T phase 
diagram for temperatures below 80 K. 








J. Appl. Phys., Vo!, 83, No. 11, 1 June 1998 


J. R. Gebhardt and N. Ali 


6301 



FIG. 4. H-T phase diagram of single-crystal holmium for applied magnetic 
field along the c axis. Circular symbols (•) indicate data from R T 
measurements, and square symbols (■) indicate data from MR vs H mea¬ 
surements. Solid lines are a visual guide. The inset shows the transition 
associated with the devil’s staircase in Ho. 


field calculations and a variety of experimental data. The 
only exception being a transition at 42 K which merges with 
the lower helifan line in higher fields. The magnetic struc¬ 
tures were labeled using the results of Jensen and 
Mackintosh.^ 

At higher temperatures, the phase diagram shows simi¬ 
larities to the phase diagram of Gebhardt et also con¬ 
structed from R T and MR vs H measurements, for ap¬ 
plied field along the b axis of Ho. The most striking 
similarity is the splitting of the Neel temperature anomaly, at 
r;v=132K, above 1 T. This anomaly splits into two parts 
with one feature changing very little with temperature at 
higher fields, while the other shifts towards lower tempera¬ 
tures and merges into the lower helifan transition at about 3 
T. An anomaly at 110 K shifts slightly to lower temperatures 
with increasing field until, above 2 T, when this shift be¬ 
comes more pronounced and it merges with the lower helifan 
line at 2.5 T, This behavior is similar to that reported by 
Willis et al (see Fig. 3 of Ref. 11). A transition at 98 K 
initially has a slight shift to higher temperatures in an in¬ 
creasing field, becoming more pronounced above 1 T and 
merging with the 110 K anomaly at 1.5 T. This result is 
consistent with that of Venter et al (see Fig. 14 of Ref. 5), 
however, the pronounced shift to higher temperatures above 
1 T is not evident in their phase diagram. This result also is 
in contradiction to the result of Willis et who see the 98 
K anomaly shifting to lower temperatures at higher fields. 

Figure 4 shows the phase diagram for a c-axis applied 
magnetic field. This phase diagram is very similar to the one 
of Willis et al (see Fig. 5 of Ref, 11) determined from mag¬ 
netization measurements. Zero field anomalies at 7= 18, 20, 
24, 42, 98, 110, and 131 K are observed. The anomaly at 
7^= 18 K shifts towards lower temperatures as the field is 
increased, reaching 1.5 T at our lowest attained temperature 
of 2 K. This transition is shown in the inset of Fig. 4. The 
dominant wave vectors in the regions above and below the 
transition are labeled using the results of Venter et al (see 


Fig. 8 of Ref. 5), who observed a similar transition using 
neutron scattering. Higher field transitions for temperatures 
below 15 K, separating the commensurate structures of a 
devil’s staircase, Cowley et aO^ could not be resolved in this 
study. The anomaly at 20 K has a slight shift to higher tem¬ 
peratures as the field is increased, until above 4 T when it 
splits into two parts. One part changing little with tempera¬ 
ture, while the other shifts towards higher temperatures in an 
increasing field. The 24 K transition shifts towards higher 
temperatures until around 3 T when this shift stops and the 
anomaly begins a slight shift to lower temperatures as the 
field is increased. Anomalies at 42 and 110 K were also 
detected and remain unchanged in fields up to 5.5 T. An 
anomaly at 98 K was also observed. This anomaly splits into 
two parts above 2 T, with one part showing little change in 
temperature as the field is increased, while the other shifts 
towards lower temperatures. As with fields applied along the 
a and b axes, for a c-axis applied field, the Neel temperature 
anomaly at7;v=131Kis seen to split into two parts. This 
split occurs in fields above 0.5 T which is lower than in the 
previous two cases. One feature does not change with an 
increasing field, whereas the other shifts towards lower tem¬ 
peratures, merging with the 110 K anomaly at 5 T. 

We have constructed the H~T phase diagrams of Ho for 
applied magnetic fields along the a and c axes using resis¬ 
tance versus temperature and magnetoresistance versus mag¬ 
netic field measurements. For temperatures below 80 K, our 
a-axis phase diagram agrees well with that of Jensen and 
Mackintosh.^ However, at higher temperatures there are dis¬ 
crepancies with that of Willis et al^^ Our c-axis phase dia¬ 
gram agrees well with the phase diagram of Willis et aO^ 

This study shows that even complicated magnetic phase 
diagrams can be established by simple magnetoresistance 
measurements. Such studies could be very useful for the lo¬ 
cation of temperature and field ranges for magnetic structure 
studies by neutron and or x-ray syncrotron scattering. 

This work was supported in part by a grant from Con¬ 
sortium for Advanced Radiation Source, University of Chi¬ 
cago, Chicago, Illinois. 


^W. C. Koehler, J. W. Cable, M. K. Wilkinson, and R O. Wollan, Phys. 
Rev. 151, 414 (1966). 

2w. C. Koehler, J. W. Cable, H. R. Child, M. K. Wilkinson, and E. 0. 
Wollan, Phys. Rev. 158, 450 (1967). 

^D. Gibbs, D. E. Moncton, K. L. D’Amico, J. Bohr, and B. H. Grier, Phys. 
Rev. Lett. 55, 234 (1985). 

"^R. A. Cowley and S. Bates, J. Phys. 21, 4113 (1988). 

^ A. M. Venter and Paul de V du Plessis, J. Phys. 9, 5167 (1997). 

Bohr, D. Gibbs, D. E. Moncton, and K. L. D’Amico, Physica (Utrecht) 
140A, 349 (1986). 

^J. Jensen and A. R. Mackintosh, Phys. Rev. Lett. 64, 2669 (1990). 

^J. Jensen and A. R. Mackintosh, J. Magn. Magn. Mater. 104-107, 1481 
(1992). 

^H. Ohsumi, K. Tajima, N. Wakabayashi, Y. Shinoda, K. Kamishima, and 
T. Goto, J. Phys. Soc. Jpn. 66, 1896 (1997). 

J. R. Gebhardt, R. A. Baer, and N. Ali, J. Alloys Compd. 250, 655 (1997). 

Willis, N. Ali, M. O. Steinitz, M. Kahrizi, and D. A. Tindall, J. Appl. 
Phys. 67, 5277 (1990). 

’^F. Willis and N. Ali, J. Alloys Compd. 181, 287 (1992). 

^^D. T. Marx and N. Ali, J. Alloys Compd. 207, 304 (1994). 

^^R. A. Cowley, D. A. Jehan, D. F. McMorrow, and G. J. McIntyre, Phys. 
Rev. Lett. 66, 1521 (1991). 



JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Magnetostatic critical point phenomena of ErIGa garnet 

Toshiro Tanaka®* and Kazuo Miyatani 

Department of Materials Science and Engineering, Ehime University, Bunkyocho 3, Matsuyama, 

790-8577 Japan 

The magnetostatic critical point phenomena of an ErIGa garnet, Er 3 (Feo.gGao. 2 ) 50 i 2 , single crystal 
sphere were investigated by a computer controlled vibrating sample magnetometer. Subtracting the 
induced large spin paramagnetic moment of Er^"^ from the measured values, allowed the 
Fe-sublattice magnetization to be extracted. data were used to analyze the critical 

phenomena by eliminating the low field data to avoid the effect of the magnetic inhomogeneity. The 
spontaneous magnetization and the zero-field susceptibility were obtained from the Arrot plot. The 
critical temperature and critical indices were obtained to be 7^ = 463.64 K, yS = 0.48±0.03, y 
= 1.1±0.1, and ^=3.1±0.1. These results agree well with the predicted values from the molecular 
field theory. The plot of the critical equation of states showed the same function as that 

found for Fe. Thus, was shown to satisfy the second-order phase transition based on the 

molecular field theory. © 1998 American Institute of Physics. [80021-8979(98)23011-8] 


I. INTRODUCTION 

One of the present authors (K.M.) investigated the mag¬ 
netostatic critical point phenomena of a yttrium-iron-garnet 
(YIG) single crystal^ using the directly measured critical 
temperature and the spontaneous magnetization Mq{T). 
In YIG, Y^"^ is a nonmagnetic ion and the magnetization is 
given by the ferrimagnetically coupled Fe^"^ sublattice mo¬ 
ments. The magnetostatic critical point phenomena were re¬ 
vealed to be close to those of the Heisenberg ferromagnet 
CdCr 2 Se 4 ^ and the metal ferromagnets Ni and Fe which we 
reported recently.^ 

The magnetization of the ErIG was explained by the 
ferrimagnetically coupled Fe^"^ sublattice moments, and Er^"^ 
sublattice moment weakly coupled with them."^ In this work, 
we substituted ErIG with Ga. The substituted nonmagnetic 
Ga^"^ diluted the Fe^^ sublattice magnetization and the mag¬ 
netic coupling was lowered. Then, the Er^"^ moment should 
become not negligible compared to the Fe^^"^ sublattice mo¬ 
ment. It is thus interesting to investigate the magnetostatic 
critical point phenomena with three sublattice moments. 


II. SAMPLE AND EXPERIMENTAL PROCEDURE 

A single crystal ErIGa garnet, Er 3 (Fei_^Ga;^.) 50 i 2 , 
sphere sample (od=3.326±001 mm) with a polished surface 
was obtained from a single crystal ingot prepared by a float¬ 
ing zone melting method using an IR imaging furnace at the 
RCA Laboratories. The sphere sample was annealed at 1273 
K for 10 h in air prior to the measurement. The Ga concen¬ 
tration X was estimated to be x = 0.2 from the lattice con¬ 
stant, the saturation magnetization at 0 K, and the density 
measurements. 

The magnetization along an easy direction was measured 
using a computer controlled vibrating sample magnetometer. 
The temperature of the sample was measured by the cali- 


‘‘^Electronic mail: tanaka@en2.ehime-u.acjp 


brated PlatineF^ thermocouple directly contacted with its 
surface. The experimental procedure basically followed our 
recent work.'^ 

III. RESULTS AND DISCUSSION 

The temperature dependence of the magnetization mea¬ 
sured at 8 kOe is shown in the inset of Fig. 1. The Curie 
temperature was about 7^. = 460K which was 100 K lower 
than the reported value of ErlG."^ The substituted Ga has thus 
lowered the average super exchange interaction between 
Fe^'*' sublattices. The constant field magnetization was mea¬ 
sured in detail from //^==0 Oe to 8 kOe at the temperatures 
between 440 and 520 K as shown in Fig. 1. The kink point 
which corresponds to the spontaneous magnetization was 
rounded on the curves contrary to the case of YIG^ and the 



Temperature (K) 


FIG. 1. The temperature dependence of the constant field magnetization 
near critical temperature. The inset shows the temperature dependence of 
magnetization measured at 8 kOe from 20 to 500 K. 


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J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


T. Tanaka and K. Miyatani 


6303 



Hgff / M (Oe cc/emu) 

FIG. 2. Arrot plot for the measured magnetization M. 



FIG. 3. Arrot plot for the Fe-sublattice magnetization 


magnetic transition was broadened. These facts suggest that 
this single crystal involves a magnetic inhomogeneity which 
may be caused by the local strain or imperfections associated 
with the substitution of Fe with Ga and that the low field data 
are significantly affected by this inhomogeneity. 

The Arrot plot, vs for the measured data M 

is shown in Fig. 2. was given by and n 

was obtained to be 0.3333 from the magnetization measure¬ 
ment. As is seen in the plot, is not proportional to 
even in high ifgff • This shows that the Landau theory for the 
second-order phase transition does not apply to the present 
system anymore. To understand the result, we assume that a 
large paramagnetic magnetization term of the Er^"^ spin 
A'Er^eff is involved in M. This term is commonly known to 
exist in rare-earth iron-garnet (RIG), and should not contrib¬ 
ute to the phase transition at . The experimental data M is 
expressed by 

M = M Fe+ MEr(Fe) + eff ’ (1) 

where M^t is the Fe^"^ sublattice magnetization and M^rCFe) 
is the Er^"^ sublattice magnetization induced by . 

The susceptibility of Er^"^ spin paramagnetism xet 
= C^^/(T- dp) was estimated from the paramagnetic sus¬ 
ceptibility X measured at T> is given by 

C/(r- Op) - (CFe+ C^rViT- Op). (2) 

Cpr was estimated by the ratio of the total Er^"^ and Fe^"^ spin 
magnetic moment in a formula unit. The Op was obtained to 
be - 10 K which was close to results of early work.^ Now, 
we can separate the Fe-sublattice magnetization 

M sub = ^Fe + ^ Er (T^) (3) 

by subtracting ;^Er^eff the experimental data M. 

The Arrot plot of M^ub was replotted in Fig. 3 for the 
high field data, 1 kOe, eliminating the low field data. 
Mgut, is then found to be proportional to The 

spontaneous magnetization Mq and the zero-field inverse 


susceptibility Xq^ were obtained by extrapolation to the 
Mgub axis and the //eff/^sub respectively. In Fig. 4, the 
temperature dependence of Mq and Xo^ is shown with 

MsubCT). 

The critical temperature was assumed to be 463.64 K 
from the T* vs T plot^ where T*=;^o ^(T)/(o'A'o ^(T)/^T). 
The critical indices p and % defined as Mo(r) = 6^ and 
= for ^^\T—Tc\ITc, were obtained to be 0.48 
±0.03 and 1.1 ±0.1, respectively. The critical index ^de¬ 
fined as was also determined to be 3.1 



450 455 460 465 470 475 480 


5000 


4000 


3000 


2000 


1000 


0 


3 

E 

(1) 


0) 

O 


X 


Temperature (K) 


FIG. 4. Temperature dependence of the spontaneous magnetization and 
zero-field susceptibility. The dotted lines indicate the constant field at 
1 Oe-8 kOe. 














6304 J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


T. Tanaka and K. Miyatani 


TABLE L Critical indices and critical temperature. 



p 

y 

S 

r,(K) 

Ref 

ErlGa garnet 

0.48 ±0.03 

1.1±0.1 

1+ 

p 

463.46 


YIG 

0.380± 0.005 

1.312± 0.008 

4.42±0.05 

551.35 

a 

Molecular 

0.5 

1 

3 


b 

field theory 

2)d Ising model 

0.312 

1.25 

5 


b 


^Reference 1. 
^Reference 6. 


±0.1. The critical indices and the Curie temperature were 
listed in Table I with those for YIG, and the theoretically 
predicted values.^ The present values do not agree with those 
for YIG, but are close to those predicted by the molecular 
field theory. 

The FC'Sublattice magnetization at 11^ = 2, 4, and 8 kOe 
were plotted in the form of vs M(7)/6^ to 

check the validity of the critical equation of state in 

Fig. 5. Msub below and above fell on the two separate 
curves, respectively. This suggests that Msub obeys a second- 
order phase transition, and shows the same function 

as that for Fe.^ 

In work on YIG,^ CdCr 2 Se 4 ,^ Ni,^’^ and Fe,^ Mq and 
;^Q ^ were determined directly from the extremely low field 
magnetization measurements. This allowed us to investigate 
the magnetostatic critical point phenomena without approxi¬ 
mation. In contrast to this, in the present work, we eliminated 
the low field data from M to avoid the influence of magnetic 
inhomogeneity which was enhanced in low fields. The mag¬ 
netostatic critical point phenomena can be explained ap¬ 
proximately by a molecular field theory. Present results show 
that the magnetization data at the critical region once the low 
field data was excluded satisfies a molecular field theory. 



FIG. 5. vs Mfe^ plot of for using 463.64 K in the 

temperature range from 463.14 to 479.14 K. 

ACKNOWLEDGMENT 

The authors express their thanks to J. Yamashita for his 
experimental collaboration during his master’s thesis work. 

^K. Miyatani and K. Yoshikawa, J. Appl. Phys. 41, 1272 (1970). 

^K. Miyatani, J. Phys. Soc. Jpn. 28, 259 (1970). 

^T, Tanaka and K. Miyatani, J. Appl. Phys. 82, 5658 (1997). 

^R. Pauthenet, Ann. Phys. (Paris) 3, 424 (1958). 

^J. S. Kouvel and D. S. Rodbell, J. Appl. Phys. 38, 979 (1967). 

^H. E. Stanley, Introduction to Phase Transitions and Critical Phenomena 
(Clarendon, Oxford, 1971), p. 47. 



JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Monte Carlo investigation of the eight-state Potts model 
on quasiperiodic tilings 

D. Ledue®^ 

Magnetisme et Applications, GMP UMR 6634 CNRS-Universite de Rouen, 76821 Mont-Saint-Aignan Cedex, 
France 

D. P. Landau 

Center for Simulational Physics, The University of Georgia, Athens, Georgia 30602 

J. Teillet 

Magnetisme et Applications, GMP UMR 6634 CNRS-Universite de Rouen, 76821 Mont-Saint-Aignan Cedex, 
France 

A Monte Carlo investigation of the eight-state Potts model on the two-dimensional (2D) 
quasiperiodic octagonal tiling with free boundary conditions is performed in order to determine the 
nature of a temperature-driven transition. It is shown that numerical data suffer from drastic free 
boundary effects that strongly disturb the probability distributions of the internal energy and, 
consequently, the scaling behavior of the specific heat. An alternative way consisting in analysing 
the core of the tilings is applied to pass over free boundary effects. This analysis combined with the 
Lee-Kosterlitz method allows one to evidence that the system undergoes a first-order transition as 
in 2D periodic lattices. The first-order type of scaling is observed for the maximum in the 
susceptibility of the core of the tilings but not for the maximum in the specific heat. © 1998 
American Institute of Physics. [80021-8979(98)23111-2] 


I. INTRODUCTION 

Recently, it has been shown by theoretical arguments 
that bond randomness will induce a second-order phase tran¬ 
sition in a system that would undergo a symmetry-breaking 
first-order phase transition. Since these arguments have 
been derived from an actual renormalization-group cal¬ 
culation^ and from a rigorous proof of the vanishing of the 
latent heat,^ Chen et al.^ have investigated the ability of ex¬ 
tensive Monte Carlo (MC) simulations to evidence such a 
prediction. They have considered the two-dimensional (2D) 
eight-state Potts model^ which undergoes a first-order transi¬ 
tion when it is pure. Applying finite-size scaling techniques, 
they concluded that, under bond randomness, the phase tran¬ 
sition changes from first to second order with 2D Ising ex¬ 
ponents. These new results have motivated us to study the 
eight-state Potts model on 2D quasiperiodic tilings^ which 
are less ordered than periodic lattices although they exhibit 
long range translational order. We have considered an oc¬ 
tagonal tiling (Fig. 1) because all octagonal tilings are locally 
isomorphic,^ that is, they exhibit identical phase transitions. 

II. BACKGROUND AND NUMERICAL SIMULATIONS 

The Hamiltonian of the ^-state Potts model is given by"^ 

9-^ (ij) 

where the spins Si , which are located at the vertices of the 
octagonal tiling, take on the values 1,...,^ and S is the Kro- 
necker delta function (in this study, ^ = 8 ). 


^^Electronic mail: Denis.Ledue@univ-rouen.fr 


The procedure is the importance-sampling MC method 
based on the standard single spin-flip Metropolis algorithm^ 
combined with the single histogram technique.^’^ Our simu¬ 
lations were carried out on finite octagonal tilings of Atot 
vertices with free boundary conditions. In order to investi¬ 
gate the free boundary effects, two kinds of systems (N ver¬ 
tices) have been considered: systems which are the whole 
tilings (A=Atot=329, 689, 1433, 2481, and 5497), and sys¬ 
tems which are the core of the tilings (A^0.13X ^^ 1 = 89 , 
329, and 705). This core is made up of the vertices which are 
located in a circle centered on the center of the tiling. Be¬ 
tween 5X10^ or 10^ Monte Carlo steps (MCS)/spin for 



A B C D E F 


FIG. 1. The octagonal tiling and the six local environments. 


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© 1998 American Institute of Physics 


6306 J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Ledue, Landau, and Telllet 


329 and 5X10^ MCS/spin for Niqi=5491 were per¬ 
formed (the first 2X10"^ MCS/spin were discarded for equili¬ 
bration). 

The nature of a phase transition can be, in principle, 
determined by looking at the size dependence of some ther¬ 
modynamic quantities in the vicinity of the transition tem¬ 
perature For example, the scaling forms^ for the 

specific heat and the susceptibility^^ in 2D systems are, at a 
first-order transition: 

and, at a second-order transition: 

where L-yjN is the linear dimension of the system, a, % 
and V are three infinite system critical exponents and t=\T 
-~Tc\ITc. However, a pseudodivergent correlation length in 
weak first-order transition can be responsible for a second- 
order type of scaling of thermodynamic quantities. A more 
powerful method of detecting first-order transitions by nu¬ 
merical simulations on finite systems is the Lee~Kosterlitz 
method^"^ which suggests to look at the size dependence of 
the free energy, Fi{E )=where PiiE) is the 
probability distribution of the internal energy. For a first- 
order transition, the free energy for large systems at T^iL) 
(the location of the maximum in the specific heat) exhibits a 
maximum ^^^(£" 2 ) between two wells of equal depth 
F/,(£i) = £l(^ 3 )* If Ihe free energy barrier, AFi=Fi{E 2 ) 
-Fi(Ei), grows with increasing system size, the transition 
will be first order in the thermodynamic limit, while the tran¬ 
sition will be second order if the barrier decreases with in¬ 
creasing size. In MC simulations using histogram techniques, 
the free energy barrier can be estimated by the reweighted 
probability distribution at 1^(1): 

^FL=ln[PdEl)/PL{E2)l 

It has been demonstrated that this method can identify un¬ 
ambiguously weak first-order transitions even when 
is the correlation length), at least for systems with periodic 
boundary conditions. 

III. RESULTS AND DISCUSSION 

In order to investigate the nature of the phase transition, 
we plotted the size dependence of the maximum in the spe¬ 
cific heat and the susceptibility on a log-log scale (Figs. 2 
and 3). Four different linear fits were performed using sys¬ 
tem sizes N^n^N^5491 with respectively A^min=329, 689, 
1433, and 2481. We were not able to conclude about the 
nature of the phase transition since the slope increases with 
(1.30±0.08, 1.40±0.09, 1.52±0.12, 1.61±0.21 for 
Cniax and 1.76±0.08, 1.8±0.1, 1.88±0.15, 1.93±0.23 for 
A^max) showing a nonanalytic behaviour for the two thermo¬ 
dynamic quantities. Then, one should keep in mind that, for 
a first-order transition, the behaviour can be observed 
only if L is larger than For example, the asymptotic regime 
of the 2D pure ten-state Potts model which is characterized 
by a small correlation length (^6 lattice spacings) is reached 
by L= 12. For the pure 2D eight-state Potts model, the cor- 



FIG. 2. Log-log plot of the size dependence of (the dashed line cor¬ 
responds to a linear fit; where not shown, the estimated error bars are 
smaller than the symbols). 


relation length is about 15 lattice spacings [^{q = %)^2.5 
X^(^= 10)].^^ So, if we assume that the correlation length 
is roughly the same in the octagonal tiling as in the square 
lattice, we should observe the L? behavior since in 

this study (7/max-5497). On the other hand, let us remind 
that the asymptotic regime of the 2D random-bond eight- 
state Potts model is reached approximately by L = 28.^ So, 
the asymptotic regime should be observed too if our system 
undergoes a second-order transition. In order to get more 
information, we plotted the probability distributions of the 
internal energy at Tc{L) that can be very useful to determine 
the nature of a transition (even if Unfortunately, 

they do not allow to conclude either. Indeed, for 1433, 
they look like single-Gaussian distributions which should 
suggest a second-order transition but they clearly exhibit a 



FIG. 3. Log-log plot of the size dependence of Xmax (ihe dashed line corre¬ 
sponds to a linear fit). 



J. AppI, Phys., Vol. 83, No. 11, 1 June 1998 


Ledue, Landau, and Teillet 6307 



FIG. 4. Probability distributions of the internal energy for A^=A^tot=689 at 
kT/J =0.^550 (single-Gaussian distribution) and for N=105 and A^jot 
=5497 at kTIJ=0.^130 (double-Gaussian distribution). 


shoulder for A^=2481 and 5497. These unusual shapes for 
the probability distributions suggest that our numerical data 
are strongly disturbed by free boundary effects. 

To clarify the question about free boundary effects, MC 
data from the simulations with A^^0.13XA^t^,t are presented 
below (analysis of the core of the tiling). For a given N, 
Cniax» and Xmax»increase with A^tot (Figs- 2 and 3) indicating 
that the internal energy and the order parameter fluctuations 
in the vicinity of the transition are more important as the free 
boundary effects lower. This can be seen on the probability 
distributions of the internal energy which evidence that low 
energy states corresponding to the ordered phases are occu¬ 
pied for the systems with but are missing if N = A^tot 

(Fig. 4). Moreover, the probability distributions look like 
double-Gaussian distributions. The estimated free energy 
barrier increases with size N [AF(A/= 89) = 0.08±0.03, 
AF(7V=329)-0.19±0.05, and AF(A/= 705) = 0.38±0,05] 
indicating that the phase transition is first order as in 2D 
periodic lattices. Note that the slope of the linear fit of the 
size dependence of C^ax and Xmax are, respectively, 1.37 
±0,03 and 2.02±0.02 (Figs. 2 and 3). So, the size depen¬ 
dence for Xmax is consistent with a first-order transition 
whereas the one for C^ax is difficult to explain. 

In order to estimate the infinite tiling transition 
temperature,^^’^^ we investigated the dependence of the loca¬ 
tion of Xmax vs for the three simulations with A^^0.13 
XNxo^. Two linear fits, using either the three data points or 
discarding the point N—S9, provided, respectively, kT^IJ 


=0.8745±0.0015 and 0.8757±0.0006 which are in good 
agreement. Note that these two estimates are also consistent 
with those obtained from the size dependence of the location 
of Cjnax* that is, /:rc//=0.875±0.001 and 0.8760±0.0007. 
So, the transition temperature of the eight-state Potts model 
on the octagonal tiling (mean coordinence {z} = 4) is slightly 
higher than on the square lattice (kT^/J-0.S513)^ This 
higher tendency to ferromagnetic ordering in quasiperiodic 
tilings has already been observed in previous studies on the 
Ising and Potts models. 

IV. CONCLUSION 

Our investigation on the eight-state Potts model on the 
2D quasiperiodic octagonal tiling has evidenced drastic free 
boundary effects in studying first-order transitions by MC 
simulations. These effects strongly disturb the probability 
distributions of the internal energy which do not exhibit two 
peaks in the vicinity of T^iL) as for systems with periodic 
boundary conditions. Rather than increasing the size of the 
tilings, an analysis of the energy probability distributions of 
the core of the tilings has been used to evidence a first-order 
transition, as in 2D periodic lattices. From MC data relative 
to the whole tilings, the behavior has not been observed, 
neither for C^ax for A'max^ probably because of free 
boundary effects. Quite surprisingly, MC data for the core of 
the tilings reveal different scaling behavior for Xmax ^^d C^ax 
(L^ behavior for Xmax ^ nonanalytic form for C^ax)- 

^ K. Hui and A. N. Berker, Phys. Rev. Lett. 62, 2507 (1989). 

^M. Aizenman and J. Wehr, Phys. Rev. Lett. 62, 2503 (1989). 

^S. Chen, A. M. Ferrenberg, and D. P. Landau, Phys. Rev. Lett. 69, 1213 
(1992); Phys. Rev. E 52, 1377 (1995). 

"^F. Y. Wu, Rev. Mod. Phys. 54, 235 (1982). 

^D. Gratias, Du Cristal a VAmorphe (Editions de Physique, Paris, 1988). 
^D. Levine and P. J. Steinhardt, Phys. Rev. B 34, 596 (1986). 

^N. Metropolis, A. E. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. 
Teller, J. Chem. Phys. 21, 1087 (1953). 

^A. M. Ferrenberg and R. H. Swendsen, Phys. Rev. Lett. 61, 2635 (1988); 
63, 1195 (1989). 

^A. M. Ferrenberg, in Computer Simulation Studies in Condensed Matter 
Physics 111, edited by D. P. Landau, K. K. Mon, and H. B. Schuttler 
(Springer, Heidelberg, 1991). 

^®M. E. Fisher, in Critical Phenomena, edited by M. S. Green (Academic, 
New York, 1971). 

^^M. E. Fisher and M. N. Barber, Phys. Rev. Lett. 28, 1516 (1972). 

^^M. S. S. Challa, D. P. Landau, and K. Binder, Phys. Rev, B 34, 1841 
(1986). 

^^P. Peczak and D. P. Landau, Phys. Rev. B 39, 11932 (1989). 

Lee and J. M. Kosterlitz, Phys. Rev. Lett. 65, 137 (1990). 

L. Black and V. J. Emery, Phys. Rev. B 23, 429 (1981). 

■^Y. Okabe and K. Niizeki, J. Phys. Soc. Jpn. 57, 16 (1988). 

^^E. S. Sorensen, M. V. Jaric, and M. Ronchetti, Phys. Rev. B 44, 9271 
(1991). 

Ledue, D. P. Landau, and J. Teillet, Phys. Rev. B 51, 12523 (1995). 
Ledue, Phys. Rev. B 53, 3312 (1996). 

Ledue, T. Boutry, D. P. Landau, and J. Teillet, Phys. Rev. B 56, 10782 
(1997). 


JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Exact renormalization group equation for systems of arbitrary symmetry 
free of redundant operators 

A. A. Lisyansky 

Department of Physics, Queens College of CUNY, Flushing, New York 11367 

D. Nicolaides 

Natural Sciences and Mathematics, Bloomfield College, Franklin Street, Bloomfield, New Jersey 07003 

A generalized exact renormalization group (RG) equation for the Ginzburg-Landau-Wilson 
functional of an arbitrary symmetry, containing invariants of all orders, with nonlocal vertices is 
derived. Unlike other RG equations which contain an infinite number of redundant operators, the 
equation derived is free of them. © 1998 American Institute of Physics. [80021-8979(98)32911-4] 


The new concepts brought about by the renormalization 
group (RG) theory in the 1970s helped one to understand 
critical phenomena at continuous phase transitions in mag¬ 
netic systems.^ Using RG theory, systematic perturbative RG 
expansions were developed to calculate critical exponents 
with a high accuracy.^’^ In addition to the perturbation 
theory, RG has been successful in deriving exact RG 
equations,"^ which not only provide a good insight of the 
theory, but also give a basis for developing new approxima¬ 
tion schemes.^“^ Working with exact RG equations is a dif¬ 
ficult task which has its origin in the fact that an exact RG 
equation contains an infinite number of redundant 
operators,which carry no physical meaning. Their ex¬ 
clusion from the RG equation is therefore a necessary but at 
the same time a complicated task, which requires imposing 
additional conditions. The problem of eliminating redundant 
operators for isotropic systems was considered in Ref. 8. In 
the present article we develop a new RG procedure appli¬ 
cable to arbitrary anisotropic systems. As a result we obtain 
an exact RG equation free of redundant operators. 

We start with the most general kind of Ginzburg- 
Landau-Wilson functional 


00 n 

H/[<p(q)]=S 2'-2U 2 

k = 0 J^|...92tai 

/ 2 * 

x(qi---.q2;fc)(227-)‘'5 2 q,- 


ai„..,a2k 

Sk 


2k 

xll ^“'(q,) 

i=\ 


( 1 ) 


Go{q,A) = q~^S{qVA^). (3) 

Here S(x) is a monotonic function with the properties S{x 
= 0)= 1 and lim^^oo 5'(3:)x'” = 0 for any m. 

We now perform two steps which are standard for RG. 
First, apply a Kadanoff transformation to thin out the origi¬ 
nal Hamiltonian by integrating those Fourier components 
^(q) corresponding to momenta within a spherical shell 
A(1“0<^<A in momentum space with ^<1. The 
Kadanoff transformation succeeds in bringing down the cut¬ 
off momentum to A(1 -^). Second, we rescale all the rest 
momenta in order to restore the original cutoff momentum 
A. 

Let us introduce the designation: 

Z= j D<pexp(-H[ip]) 

= Zo(exp(-H,[ip])}o,A^Zo(w[p]}o,A ’ (4) 

where 

Zo= j Dip exp(-Ho[<p]), (5) 

and the averaging is performed with respect to the 

functional //o[^] at a given value of A. Note that if ^(q) 
= <Pi(q) + (P2(q) and Go(<?,A)-Goi(^,Ai) +Go 2 (^,A 2 ), 
the following identity can be generated: 

(wM)oa=Zo' j D<pw[ip]exp(-Ho[ip]) 

= Zoi'Zo2 j Dip,Dip2W[iPi ,ip2] 


where ip is an n-component vector and f 
The vertices gj, have an arbitrary tensorial structure with 
respect to the space indices Let us define an RG proce¬ 
dure in the following way. We cut off all momentum inte¬ 
grals at an upper momentum A by adding to the functional 
Hj a term Hq 

( 2 ) 

where the propagator Gq is defined by 


Xexp(-//o[V’i.<P2]). (6) 

where 

D<p, exp -y \ Go,'(^,A,)|<P,(q)P ; 

[ J 

+ 2 J Go2'(?.A2)|<®2(q)P- 


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© 1998 American Institute of Physics 


J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


A. A. Lisyansky and D. Nicolaides 6309 


Choosing Goi(^,Ai) = Go(q',A(l-^)) with ^^1, makes „ „ 

the function G 02 of order Q) = 2 [ ^f “^( q) ] ^ \ q( 1 + ^) ] 

<5o2(^>A2) = Go(^,A)-Goi(^,Ai) 




<?Go(q',A) 

dk 


^2ih{q), 


h{q) = q ^A^ 


dSiq^lK) 

~dP 


( 8 ) 


Modes ^ 2 (q) those with momenta within a shell A (1 
~0<q<A which should be integrated out. To do so and 
have the first step completed we expand (w[^i ,^ 2 ]) in Eq. 
( 6 ) with respect to ^ 2 (q) to obtain 








where at present e"^(q) is an arbitrary tensor with the only 
condition e“^(q) = e^“( —q). Then we apply the above 
transformation to (w[^q)])o,A(i-|) of Eq. (10). After keep¬ 
ing terms of the lowest order in ^ and using the relationship 
w[^] = exp(-/f£^]) we derive the RG equation for Hj, 


(m'[«’])o.a=-Zoi'Zo2‘ J D<piDtp2 
Sw[q>{\ 


w[(p{] 




1 f y _ i 

2 J qq^ a,(3 1 




(q)^<pf(q') 


x?’2(q)?>2(q')+--- 


exp(-ffo[<Pi.^2])- 


H,[ip\ = Vd 


dV 


•-I- 


7/2 

^ J q a 


’7““(q) 


T [E ’7“^(q)Go^?.A)9“(q)<p^(-q) 

^ Jqa,p 

fl 

J qa.p 


f qa,^ 

d(p“iq) 


d + 2 27“^(q) 


^q 


2 

SHi[<p] 

d<pP(q) 


I 


2 

h(q) 


9“(q) + 5“^q 


(9) 

xX 

a 

1 

1 — 1 

r-^ 

Having in mind the Gaussian nature of ^o[^i ^^ 2 ] only even 
terms in the above expansion survive. Keeping terms of the 
lowest order with respect to ^ the integration yields 

lS(p^(q)S(p^(-q) S(p^(q) S(p^(-q)j 




Here 77 "^(q) is defined as 


(14) 


Xw[^(q)]) , (10) 

' 0,A(l-f) 

where the averaging (••.)o,A(i-J) is performed with respect 
to the functional 

Ho[<p,A(l-e]=^ fGo\q,A(l-m<P(q)i^- (11) 

Consequently, the right-hand side of Eq. (10) contains effec¬ 
tively only modes with A(1 -1). The first step of the RG 
transformation has been completed. 

For the second step, we must rescale the momentum to 
restore the original cutoff A through transformation q 
==q'(l-~0. This rescaling changes //o[A] to 
— ^)] as follows: 

Ho[<p,A(l-^)]=j f Go‘(?,A(l-^))Mq)p, 

( 12 ) 

(l-£\d+2 r 

ffol<P,A]= -2-J^Go'(?-A)|^[q(l-^)]p. 

However, we must restore this change since it is essential to 
the restoration of A. We do so by substituting ^(q). 


77“^(q)=5“^(d+2)-2€“^(-q). (15) 

Equation (14) is an exact RG equation for functional (1). It 
contains an arbitrary function ? 7 "^(q). Note that if we 
choose ? 7 ®^(q )^0 then the resulting simplified RG equation 
will be similar to the traditional ones, and as in those cases it 
will contain redundant operators. Not being physical, these 
operators must be eliminated by developing a proper proce¬ 
dure. Our goal is to find the correct choice of the tensor 77 "^ 
which will make the RG Eq. (14) free of redundant opera¬ 
tors. Explicitly, Eq. (14) generates different vertices g^^(q). 
Some of the ^-dependent part of this renormalization can be 
incorporated into Gq of the functional Nq . This means that 
the cutoff A is affected which should, however, remain un¬ 
changed. To avoid so, we define 77 "^(q) such that it cancels 
out the ^-dependent renormalization of the vertex gf^(q). 
To achieve this, we use Eq. (14) to write explicitly the 
change of vertices corresponding to zeroth and first or¬ 
der in (p"(q) 9 ^(~q). Then we require that is momen¬ 
tum independent initially and must remain so after the trans¬ 
formation so that Hq which controls the cutoff remains 
intact. This requirement finds a momentum dependent ex¬ 
pression for the tensor ? 7 “^(q). First, we extract an explicit 
equation for the vertex gi(q) from Eq. (14), 



6310 J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


A. A. Lisyansky and D. Nicolaides 


d 




dq 


25«r_ ,^«r(q) 

gr(q) + S 


-2E gr((l)8fmiq), (16) 

r 

where 

g«/3r^(q) = 3 [ hip)gf^\q-q,p,-v). (17) 

Jp 

We can now split Eq. (16) into two equations: one for gjo, 
which is the momentum independent part of ^}(q), and an¬ 
other for g;(q)=gi(q)-iio, 

gii=^ [2S"^-rm]gj^+^ 

y 7 


-2E g^JgJ^Hoy, 

7 


(18) 


g'“^(q)=-77“^(q)Go'(^,A) + 2 

7 




g7^{q)-[v‘^-^{q)-v‘^m]gj§ 

+Q»^yyiq)-Q-^yy{0)-2g‘^o^gj§[hiq) 
-/i(0)]-2[groV/^(q) + g'“"(q)gro^ 

+ /i“"(q)g'/^(q)]M^)}. (19) 

Using Eq. (19) we can define the function such that 

the derivative of gj(q) is equal to zero. This means that if 
the vertex gi(q) of the initial functional Hj is a constant then 
a ^-dependent part of this vertex will not be generated and 
the functional //q will be intact within the renormalization 
procedure. The requirement gi(q) = 0 implies that 



,7“/5(q)=77“^(0)-2 

V 


,7“’'(0)Go‘(g,A) 


+ 2 [2[hiq)-hmg%^gJ^-Q‘^''y^{q) 

7 

+ C“''^’'(0)]j[gro + Go'(9,A)5‘'^]-'. (20) 

Equation (20) defines the momentum dependent part of 
the function ? 7 '^^(q). We still have to define components 
of the tensor ^/"^(O). We can use these values to simplify 
the RG equation and clarify the physical meaning of To 
do this, let us diagonalize the vertex |io the initial func¬ 
tional Hi . This can always be done without loss of general¬ 
ity. The diagonal components of this tensor are trial critical 


temperatures for the corresponding components of the order 
parameter ^(q). However, as one can see from Eq. (18), even 
if the nondiagonal part of the tensor does not exist in the 
initial functional, it will be generated within the renormaliza¬ 
tion process. We can use the arbitrariness of tensor 77 “^ to 
keep the tensor diagonal. In order to do this, let us split 
Eq. (18) into two separate equations, for diagonal and non¬ 
diagonal parts of the vertex g"(f. Defining 
_|_ ( 1 _ 

r"^=(2-77^)r^+2^(0)-2(O2/i(0); (21) 


7 


-2 


7 


yOi7y>7{i 


h{Q), 


( 22 ) 


where 77 “, 2 “ and are diagonal and nondiagonal 

elements of tensors 77 “^ and respectively, 

77“^(0) = (5“^77“+(1 - ^^) 


2 <2“^''’'(q) = ^“^G“(q) + (l-^“^)e“^(q)- (23) 

7 

Now by choosing 

2“^/7-^, (24) 

it is guaranteed that if the initial functional does not contain 
nondiagonal parts of the vertex g i , then this vertex remains 
diagonal after the renormalization. If at last we require that 
the expansion of does not contain terms, then the 

diagonal part of the tensor ? 7 "^( 0 ) is 

7“=^[Q“(q)-2/i(^)(r“)%=0. (25) 

Function ? 7 "^(q) is now completely defined and there is no 

more freedom in the exact RG Eq. (14), therefore it must 
contain no redundant operators. The physical meaning of the 
function 77 '*'^ is suggested by Eq. (21): at the stable fixed 
point of the functional ( 1 ), 77 " is equal to the critical expo¬ 
nent 77 of the corresponding critical mode (p". 


^S.-K. Ma, Modern Theory of Critical Phenomena (Benjamin, New York, 
1976). 

^S. G. Gorishny, S. A. Larin, and F. V. Tkachov, Phys. Lett. A 101, 120 
(1978). 

C. Le Guillon and J Zinn-Justin, J. Phys. (France) 48, 19 (1987). 

G. Wilson and J. Kogut, Phys. Rep. 12, 75 (1974). 

^G. R. Golner and E. K. Reidel, Phys. Lett. 58A, 11 (1976). 

^E. K. Reidel, G. R. Golner, and K. E. Newman, Ann. Phys. (N.Y.) 161, 
178 (1985). 

^G. R. Golner, Phys. Rev. B 33, 7863 (1986). 

^Yu. M. Ivanchenko and A. A. Lisyansky, Phys. Rev. A 45, 8525 (1992). 
^Yu. M. Ivanchenko, A. A. Lisyansky, and A. E. Filippov, Phys. Lett. A 
150, 100 (1990). 

^®F. J. Wegner and A. Hougton, Phys. Rev. A 8, 401 (1973). 

^‘T. L. Bell and K. G. Wilson, Phys. Rev. B 10, 3935 (1974). 

’^F. J. Wegner, in Phase Transitions and Critical Phenomena, edited by C. 
Domb and M. S. Green (Academic, New York, 1976), Vol. 6, p. 7. 



JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER II 


I JUNE 1998 


Random-exchange and random-field Ising model-like behaviors 

in F6 o.482^0.52^2 

E. P. Raposo®' 

LaboratSrio de Fisica Teorica e Computacional, Universidade Federal de Pernambuco, 50670-901, Recife, 
PE, Brazil and Lyman Laboratory of Physics, Harvard University, Cambridge, Massachusetts 02138 

M. D. Coutinho-Filho 

LaboratSrio de Fisica Teorica e Computacional, Universidade Federal de Pernambuco, 50670-901, Recife, 
PE, Brazil 

By using a local mean-field microscopical numerical approach, we investigate the role of frustration, 
random vacancies, and magnetic field cycles on the random-exchange and random-field Ising 
model-like behaviors of the diluted antiferromagnet Feo, 48 ^% 52 F 2 - The analysis includes studies on 
microscopic configurations, distribution of local effective fields, and the crossover exponent <^, 
which were found to be in good agreement with the experimental results. © 1998 American 
Institute of Physics. [80021-8979(98)23211-7] 


Much progress has been achieved^ in the last few years 
on the characterization of the phase diagram of the insulating 
diluted antiferromagnet (DAF) Fe^Zni_^F 2 . Nevertheless, a 
complete understanding of the relative influence of its micro¬ 
scopic ingredients, namely, the local density fluctuations, the 
presence of a small magnetic frustration, and the short range 
of the spin interactions, is still lacking. In the following, we 
investigate the roles of these elements in the presence of 
magnetic field cycles by using a local mean field (LMF) 
microscopical numerical approach.^’^ 

The DAF compound Fe;,.Zni_;j.F 2 has a strong single-ion 
anisotropy in the easy-magnetization direction which makes 
it a nearly ideal experimental realization of an Ising system."^ 
All its important microscopic ingredients can be found in the 
DAF Hamiltonian in the presence of a uniform magnetic 
field H, 

E (1) 

a.s,} ' ' 

where 5, = ±2 (Fe'''^), ^=0, 1, and I is summed over the 
three short-range exchange interactions between nearest 
neighbors in a centered tetragonal lattice. By fitting the Neel 
temperature which marks the onset of the AF phase for the 
pure system, Tj^(x= 1)^78 K, we fixed the exchange con¬ 
stants so that the experimental ratios ji= J 1 /J 2 — ~0.013 
and 73 — 73 / 72 =+0-053 measured for the pure compound 
FeF 2 are kept unaltered.^ Disorder and frustration are present 
respectively in the form of local density fluctuations due to 
the random quenched substitution of magnetic ions Fe"^^ by 
nonmagnetic ones Zn'*'^ (“vacancy” sites), and in the pres¬ 
ence of a small frustrated super-exchange planar interaction 
73 with respect to the dominant AF coupling 7 * 2 . 

The LMF method^’^ consists in solving iteratively the 
self-consistent equations involving the thermally averaged 
spins, m^G[“ 2 , 2 ], 

mi=={Si)T=2tmh{hi/KsT}, g;=l, (2) 


“^Electronic mail: raposo@cmt.harvard.edu 


where the local field effectively seen by this spin is 

The numerical procedure starts by choosing an initial ran¬ 
dom configuration in the high-temperature (T 

= 150 K) paramagnetic (PM) phase. The system is then 
cooled in a rate A7= 0.05 K and, at each temperature, Eqs. 
(2) and (3) are iterated for every magnetic site until a con¬ 
vergence criterium^’^ is satisfied. The cooling procedure is 
repeated until reaching the minimum temperature 7= 2 K 
from which the system is heated by using the same amount 
A 7, and then the measurements are done. We have followed 
the experimental procedures in FQj^Zni^^F 2 as close as pos¬ 
sible. In a zero-field cycle (ZFC) the system is cooled in H 
= 0 to the minimum temperature and a magnetic field is 
applied along the heating process. On the other hand, in a 
field cycle (FC) both cooling and heating procedures are per¬ 
formed in the presence of H. We simulate bcc lattices with 
two sublattices of 30^ sites each and periodic boundary con¬ 
ditions. In order to eliminate any possible dependence of the 
results on some initial configuration, we average over 50 
independent samples {5,-,(^}. 

The compound Feo. 48 Zno. 52 F 2 presents a random- 
exchange Ising model (REIM)-like behavior at zero field.^’^ 
In H¥^0, it experiences^’^ a field-induced crossover upon 
ZFC from the REIM to the random-field Ising model 
(RFIM)-like behavior. The LMF results indicate^ that the 
combined action of random vacancies and magnetic field in¬ 
duces an AF long-range order (LRO) that exist up to the 
neigborhood of the critical temperature, and is essentially 
constituted by two large slightly-interacting interpenetrating 
structures with AF internal arrangements, each one occupy¬ 
ing approximately half of the sample, in agreement with 
some very recent experiments.^’^ The domain walls are 
strongly pinned along the vacancies^ and can minimize the 
energy cost by avoiding as much as possible to embody frus¬ 
trated magnetic bonds so that a different picture emerges 


0021-8979/98/83(11)/6311/3/$15.00 


6311 


© 1998 American Institute of Physics 



6312 J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


E. P. Raposo and M. D. Coutinho-Filho 



HT) 


FIG. 1. (a) Few isolated clusters (full squares) represent spins reversed by a 
ZFC magnetic field, H=IT, with respect to the //=0 frustrated configu¬ 
ration close to the ground state, TITf^{x— 1) = 0.06. Odd (even) horizontal 
lines correspond to consecutive layers of sublattice A (B). (b) Correspon¬ 
dent local effective field distribution F(/i,) of one sublattice. The nonfrus- 
trated case is presented in the inset. 

with respect to the usual Imry-Ma argument,^ including the 
existence of fractal domains. 

The microscopic states for low and moderate ZFC fields 
are similar to those obtained in //= 0, except for the presence 
of some small isolated clusters, as also experimentally 
probed.^’^ In Fig. 1(a), two consecutive layers (one of each 
sublattice) randomly chosen in the bulk of the system are 
projected onto a plane so that spins belonging to the sublat¬ 
tice A {B) are displayed by squares in the odd (even) hori¬ 
zontal lines. Full squares represent reversed spins in the frus¬ 
trated systems after H—\T ZFC, relative to the H=0 case 
at the very proximity of the ground state, T/T^{x=l) 
= 0.06. Figure 2(a) displays the associated field distributions 
for one sublattice of these samples, with the nonfrustrated 
case shown in the inset. A very similar picture is also found 
in /f=0. Furthermore, we notice that frustration plays an 
important role for the nucleation process upon ZFC by in¬ 
ducing the presence of competitive local fields. Indeed, the 
presence of frustration introduces more important changes on 
the properties of the system than low and moderate magnetic 
fields do after ZFC. 

On the other hand, a FC procedure at x = 0.48 leads to a 
very distinct domain state without AF LRO at low tempera¬ 
tures even for low fields.^® In Fig. 1(b), a very small field 
//= 1 G was applied upon FC and the differences with re¬ 
spect to the zero-field configuration at TITf^{x— 1) = 0.06 are 
represented by full squares. Figure 2(b) displays the associ¬ 
ated field distributions for one sublattice. Notice from Fig. 
2(b) that frustration is unimportant in the FC regime. 

The field-induced crossover upon ZFC from the REIM 



-20 0 20 


h,(T) 

FIG. 2. (a) Even a very low magnetic field // = 1 G upon FC induces a 
remarkably distinct low-7 configuration (differences indicated by full 
squares) relative to the AF LRO //=0 and ZFC states. The correspondent 
local effective field distributions of one sublattice are depicted in (b) for the 
frustrated and nonfrustrated (inset) cases. 

to the RFIM-like behavior is described by the crossover ex¬ 
ponent 

(4) 

Above, the same scaling dependence experimentally^^ and 
numerically^^ seen for the critical and equilibrium 

[7eq(^)] lines is accounted by considering both cases, 
Ti(H) = T,{H) and In the former, T* 

= r^(x = 0.48), whereas in the latter T* is the highest tem¬ 
perature below which the total magnetizations measured af¬ 
ter ZFC and FC begin to differ. The LMF results for the 
exponents in the presence of frustration, (f)^^ 1,28±0.06 and 
1-30±0.08, nearly agree with the experimentaland 
Monte Carlo^^ ones, (^^1.40-1.46, if the range of concor¬ 
dance between independent measurements is considered. No¬ 
tice that the equivalent scaling dependence in the critical and 
equilibrium lines is also probed by the LMF method. It is 
remarkable that the exponents do not depend (within the er¬ 
ror bars) on the presence of frustration for both and 

Tc{H) lines. Figure 3 displays the numerical data along with 
the best-fitting curves and the most generally accepted ex¬ 
perimental value, <^=1.42.^’^^ The LMF approach causes an 
enlargement of the region where the and T^iH) lines 

differ. We have also observed a reentrant behavior in T^^H) 
for extremely low fields, H<0.01 T, as detailed in the inset 
of Fig. 3(b). However, the absence of experimental data in 
this range of fields prevent us to comment on the reality of 
this reentrance. It would be interesting to probe it in the real 
compound. 

From the H ws T diagrams one can also speculate about 
the irreversibility and stability of the AF LRO at jc = 0,48. In 




J. App!. Phys., Vol. 83, No. 11, 1 June 1998 


E. P. Raposo and M. D. Coutinho-Filho 6313 




FIG. 3. (a) Critical and (b) equilibrium lines at a:= 0.48. The respective 
best-fitting plots 1.28 and ^=1.3 are shown along with the experimental 
value ^=1.42 (see Ref. 1) characteristic of the RFIM-like behavior. Inset in 
(b) displays the numerical reentrance observed for very low magnetic fields, 
^<0.1 T. 


the free energy surface, irreversibility is related to the dis¬ 
placement or disappearance of local minima due to changes 
in H or T} After ZFC to a low-temperature state, when the 
uniform magnetic field is turned on and kept fixed, the sys¬ 
tem initially exhibits an irreversible AF phase whose LRO is 
broken down when the critical line TdH) is crossed during 
the heating process. The system thus enters an irreversible 
close-PM regime in which spin correlations still exist.^ Be¬ 
low Tc{H) the difference between the ZFC and FC measures 
means that the FC domain state cannot reach its equilibrium 
configuration within the characteristic LMF or experimental 
times. In this sense only the ZFC states are quasi- 


equilibrated. On the contrary, in the vitreous intermediate 
phase, Tc{H)<T<T^{H), it has been shown^ that the 
domain-like states without fully developed AF LRO have 
less free energy than those ones associated with the AF LRO. 
The high-T reversible behavior is restored only after crossing 
the line above which the equilibrium measurements 

from both ZFC and FC procedures coincide. 

Finally, we would like to mention that the consistency of 
the LMF results was also attested by applying the same nu¬ 
merical procedure for the system at x = 0.25. The value 
obtained,^^ 3.8±0.6, is in good agreement with the ex¬ 

perimental one, 0=3.4±O.2, measured^ for Feo. 25 ZRo. 75 F 2 > 
which is associated with the presence of a spin-glass-like 
phase without AF LRO. The independence of frustration in 
the crossover exponents has been also observed. 

One of the authors (E.P.R.) would like to acknowledge 
the hospitality of the Condensed Matter Theory group at 
Harvard University. The authors are deeply grateful to D. P. 
Belanger for many stimulating discussions. This work was 
supported by CNPq, FINEF, CAPES, and FACEPE (Brazil¬ 
ian Agencies). 

* For recent reviews, see D. P. Belanger, in Experiments on the Random 
Field Ising Model, edited by A. P. Young (World Scientific, Singapore, 
1997), and references therein. See also, D. P. Belanger and A. P. Young, 
J. Magn. Magn. Mater. 100, 272 (1991); W. Kleemann, Int. J. Mod. Phys. 
7 , 2469 (1993). 

^C. M. Soukoulis, K. Levin, and G. S. Grest, Phys. Rev. Lett. 48, 1756 
(1982); Phys. Rev. B 33, 7659 (1986), and references therein. 

^E. P. Raposo, M. D. Coutinho-Filho, and F. C. Montenegro, Europhys. 
Lett. 29, 507 (1995). 

"^M. T. Hutchings, B. D. Rainford, and H. J. Guggenheim, J. Phys. C 3 , 307 
(1970); A. R. King, V. Jaccarino, T. Sakakibara, M. Motokawa, and M. 
Date, Phys. Rev. Lett. 47 , 117 (1981). 

^D. P. Belanger, S. M. Rezende, A. R. King, and V. Jaccarino, J. Appl. 
Phys. 57 , 3294 (1985); S-J. Han, D. P. Belanger, W. Kleeman, and U. 
Nowak, Phys. Rev. B 45 , 9728 (1992). 

^E. P. Raposo and M. D. Coutinho-Filho (unpublished). 

^D. P. Belanger, J. Wang, Z. Slanic, S-J. Han, R. M. Nicklow, M. Lui, C. 
A. Ramos, and D. Lederman, Phys. Rev. B 54, 3420 (1996). 

®P. Poliak, W. Kleemann, and D. P. Belanger, Phys. Rev. B 38, 4773 
(1988). 

^Y. Imry and S. K. Ma, Phys. Rev. Lett. 35, 1399 (1975). 

Nowak and K. D. Usadel, Phys. Rev. B 39 , 2516 (1989); 43 , 851 
(1991); 44 , 7426 (1991); 46 , 8329 (1992); Physica A 191 , 203 (1992). 
Although is the most generally accepted experimental value (see 

Ref. 1), some of the reported crossover exponents in different measure¬ 
ments are: <;6=1.40±0.05 [A. R. King, V. Jaccarino, D, P. Belanger, and 
S. M. Rezende, Phys. Rev. B 32 , 503 (1985)], <^=1.42±0.03 [I. B. Fer¬ 
reira, A. R. King, and V. Jaccarino, J. Appl. Phys. 69 , 5246 (1991)], 
(;6=1.44±0.04 [W. Kleemann, A. R. King, and V. Jaccarino, Phys. Rev. B 
34 , 479 (1986)], and <^=1.46±0,02 [M. Lederman, J. Hamman, and R. 
Orbach, J. Appl. Phys. 69 , 5249 (1991)]. The equivalence (within error 
bars) between the values of cj) measured from critical and equilibrium lines 
has been always probed. 

^^E. P. Raposo and M. D. Coutinho-Filho, J. Appl. Phys. 81, 5279 (1997). 





JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Magnetic structures of the triangular lattice magnets 
AFe(S 04)2 (A=K, Rb, Cs) 

H. Serrano-Gonzalez 

School of Chemistry, University of Birmingham, Edgbaston, Birmingham, B15 2TT, United Kingdom 

S. T. Bramwell®>'‘’> 

Department of Chemistry, University College London, Christopher Ingold Laboratories, 20 Gordon Street, 
London WCIH OAJ, United Kingdom 

K. D. M. Harris®' and B. M. Kariuki 

School of Chemistry, University of Birmingham, Edgbaston, Birmingham, BI5 2TT, United Kingdom 

L Nixon and I. P. Parkin 

Department of Chemistry, University College London, Christopher Ingold Laboratories, 20 Gordon Street, 
London WCIH OAJ, United Kingdom 

C. Ritter 

Institute Max von Laue-Paul Langevin, BP 156, F-38042 Grenoble 09, France 

In the crystal structures of CsFe(S 04 ) 2 , RbFe(S 04 ) 2 , and KFe(S 04 ) 2 , the magnetic Fe^"^ ions form 
a triangular array in well separated layers. CsFe(S 04)2 and RbFe(S 04)2 may be regarded as 
realizations of the highly frustrated triangular lattice antiferromagnet, whereas KFe(S 04)2 is a 
suspected realization of the row model. The latter model is characterized by two couplings 7' and 
7, and for 777>0.5 forms a helical spin structure with an incommensurate repeat distance. The 
regular triangular lattice magnet may be described by the row model with 7'= 7, and its “120®” 
spin structure may be regarded as a special case of this helical structure. We have determined the 
low temperature (1.3 K) magnetic structures adopted by CsFe(S 04 ) 2 , RbFe(S 04 ) 2 , and KFe(S 04)2 
by powder neutron diffraction. CsFe(S 04)2 and RbFe(S 04)2 adopt the expected 120 ° helical spin 
structure of the triangular lattice magnet, but KFe(S 04)2 does not adopt the expected 
incommensurate helical structure of the row model. Rather, it adopts a sine wave modulated 
structure. Possible reasons for this behavior are discussed. © 1998 American Institute of Physics, 
[80021^8979(98)50511-7] 


The triangular lattice antiferromagnet^ is the prototypical 
two-dimensional frustrated magnet. It exhibits a wealth of 
unusual properties, such as novel critical exponents,^ large 
quantum fluctuation effects,^ and anomalous percolation 
properties."^ Recently we showed that the materials with lay¬ 
ered crystal structures related to that of the mineral Yavapai- 
ite KFe(S 04)2 are of interest as realizations of a model quasi- 
two-dimensional triangular lattice antiferromagnet.^ With 
regard to their magnetic properties, the Yavapaiite materials 
can be classified into two major groups, depending on the 
symmetry of the triangular net occupied by the magnetic 
atoms. The materials in the first group, which includes 
CsFe(S 04)2 and RbFe(S 04 ) 2 , have an equilateral triangular 
lattice, and approximate very well to the two-dimensional 
Heisenberg model antiferromagnet on the triangular lattice. 
Those in the second group, which includes KFe(S 04 ) 2 , have 
an isosceles triangular (i.e., centered rectangular) lattice. 
They may thus be considered realizations of the “row” 
model.^“^ The relationship between the regular triangular lat¬ 
tice model and the row model is illustrated in Fig. 1; in the 
regular triangular lattice model all magnetic bonds are of the 
same strength (7), whereas in the row model “horizontal” 


“^Authors to whom correspondence should be addressed. 
‘’^Electronic mail: s.t.bramwell@ucl.ac.uk 


bonds are of different strength (7') to the remaining bonds 
(7). Zhang et al^ and Kawamura^ have studied the XY row 
model and shown that for 777>l/2 the ground state is a 
spin helix propagating along the row direction, with period 
determined by the ratio 777. The regular triangular lattice, 
with 777= 1, may be regarded as a special case of the row 
model, in which the turn angle of the helix is 120 °; however, 
for general 777, the period of the helix is incommensurate 
with the lattice. The stacked row model, with unfrustrated 
interlayer coupling, was introduced by Kawamura^ to ex¬ 
plain the magnetic structure of RbMnBr 3 .^ However, the 
model can potentially be used to describe any C-centered 
spin lattice in which a^b^3. Thus, the class of C-centered 
orthorhombic compounds MXO 4 , such as MnS 04 ^^ and 
^-CrP 04 ,^^ may also be regarded as realizations of this sys¬ 
tem; they indeed exhibit the expected incommensurate heli¬ 
cal structure. 

In this work we determine the low temperature magnetic 
structures adopted by the title compounds, and compare 
these with theoretical expectations for the row and triangular 
models. The magnetic susceptibility versus temperature 
curves of all three compounds show anomalies in the region 
of 4-5 K,^ which can be attributed to magnetic ordering 
transitions. Using the DIB powder diffractometer at the In- 
stitut Max von Laue—Paul Langevin, Grenoble, France, we 


0021 -8979/98/83(11 )/6314/3/$15.00 


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© 1998 American Institute of Physics 



J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Serrano-Gonzalez et ai 


6315 




FIG. 1. (a) The regular (equilateral) triangular lattice, showing a unit cell 
(shaded area with vectors a and b; (b) the row model lattice, in which 
horizontal bonds (double lines) have a different strength to other bonds 
(single lines). In the crystal structures of CsFe(S 04)2 and RbFe(S 04)2 the 
magnetic Fe ions occupy a lattice of the type shown in (a), whereas in the 
crystal structure of KFe(S 04)2 the magnetic Fe atoms occupy a lattice of the 
type shown in (b). In (b) the primitive unit cell shown (shaded area with 
vectors a and b) describes the magnetic structure of KFe(S 04 ) 2 . The lattice 
sites labeled O, A, and B are referred to in the text. 


have measured diffraction patterns both above ordering 
transition^^ and at 1.3 K, and subtracted these to create a 
magnetic-only diffraction pattern (in this temperature range 
thermal effects on the nuclear diffraction pattern are negli¬ 
gible). All the magnetic diffraction patterns show Bragg 
peaks arising from three-dimensional magnetic order. Mag¬ 
netic structures were determined using the GSAS^^ and 
FULLPROF^"^ program packages, assuming a pseudo-Voigt 
line shape, and zero point corrections and scale factors de¬ 
rived from fits to the nuclear structure. The magnetic form 
factor for Fe^"^ was calculated from Ref. 15. 

Crystallographic data for the three title compounds are 
given in Table I. In the case of CsFe(S 04)2 and RbFe(S 04 ) 2 , 
the magnetic diffraction pattern was indexed on a unit cell 
with a„ = b^ = aV3, c„ = 2c, «„ = )S„ = 90°, r„ = 60°, 

TABLE I. Crystallographic data for CsFe(S 04 ) 2 , RbFe(S 04 ) 2 , and 
KFe(S 04 ) 2 . The magnetic Fe^"^ ions occupy the (0,0,0) position in each 
case, and so the Fe sublattice is uniquely defined by the centering symbol 
(P or C) of the space group. For full crystallographic details see Ref. 5. 


Compound 

Space group 

Lattice parameters 

CsFe(S 04)2 

RbFe(S04)2 

KFe(S04)2 

P3 

P3 

CUm 

0 = ^=4.8612(5) A, c = 8.7081(l) A (20 K) 
a = ()=4.8189(5) A, c = 8.2248(2) A (8 K) 
a = 8.0926(8) A, fe = 5.1401(5) A, c = 7.8026A, 
)8= 95.155(11)° (15 K) 


30000 


20000 


10000 


0 


FIG. 2. Fit of the magnetic model described in the text to the experimental 
magnetic-only powder diffraction pattern of CsFe(S 04)2 at 1.3 K. The fig¬ 
ures show experimental (+ marks), calculated (upper solid line), and differ¬ 
ence (observed—calculated, lower solid line) magnetic diffraction profiles. 

where a, b, and c denote the crystallographic unit cell pa¬ 
rameters. The diffraction data are well described by a model 
in which the spins form a three sublattice “120°” structure 
in the basal (ab) plane, and there are two basal planes per 
magnetic unit cell. Spins in adjacent layers are rotated by an 
angle <^, which was found to have the value 180° ± 10° for 
CsFe(S 04)2 and 150° ± 10° for RbFe(S 04 ) 2 . Note that pow¬ 
der neutron diffraction cannot give the in-plane spin direc¬ 
tion for the high symmetry structures of CsFe(S 04)2 and 
RbFe(S 04 ) 2 . The refined values of the magnetic moments 
were />6=4.2±0.2for CsFe(S 04)2 and /x=4.5±0.2 
for RbFe(S 04 ) 2 , which are close to the maximum expected 
value jui=5 fjig for Fe^"^. The fit to the experimental magnetic 
diffraction pattern for CsFe(S 04)2 is shown in Fig. 2. 

In the case of KFe(S 04 ) 2 , the magnetic Bragg peaks 
could be indexed on the unit cell illustrated in Fig. 1(b). This 
cell is primitive in the basal ab plane, but contains two basal 
planes along the c axis. 

With respect to this unit cell, the magnetic Bragg peaks 
could all be indexed by the wave vector (0.73, —0.73, 0). 
This implies that neighboring spins along the row direction 
are approximately antialigned, but that the antiferromagnetic 




FIG. 3. Sine-wave modulated magnetic structure used to describe the mag¬ 
netic diffraction pattern of KFe(S 04 ) 2 , as described in the text. The figure 
shows two “rows” in the a b plane of the KFe(S 04)2 structure (not drawn 
to scale), with the projection of the magnetic structure into the a b plane. 
The spins shown lie along the [ 1, 1, 1/2] and [ - 1, -1, — 1/2] directions, 
which are denoted as (+) or (—) on the diagram. The spin amplitude is 
modulated along [1,—1,0] (indices refer to the unit cell shown in Fig. 1). 
Note that the spins in the upper row may look more strongly modulated than 
those in the lower row, but in fact the modulation is the same. In the 
adjacent layer the spins similarly lie along either [1, 1, —1/2] or [-1, 
- 1 , 1 / 2 ]. 





6316 J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Serrano-Gonzalez et al. 


i 

1 

- A^fA 1 / 

1 Mil 1 11 1 1 Hill iiiiiiiiii II mil III mill III III iiiiiiiiiiiiiiiiii 


pn Tin 4n sn go 70 80 


FIG. 4. Fit of the magnetic model described in the text and shown in Fig. 3 
to the experimental magnetic-only powder diffraction pattern of KFe(S 04)2 
at 1.3 K. The figures show experimental (+ marks), calculated (upper solid 
line), and difference (observed—calculated, lower solid line) magnetic dif¬ 
fraction profiles. 


rows are modulated with a long repeat distance which is 
incommensurate with the crystal structure (ratio of periodici¬ 
ties approximately equal to 0.73). The modulation may be of 
the sine wave or helical type, but the indexing imposes se¬ 
vere limitations on the possible magnetic models. All plau¬ 
sible models were tested. Helical structures were tested first, 
and it was found that none of these described the data, even 
assuming an elliptical, rather than circular, helix (and 
thereby introducing an extra fitting parameter). In contrast, 
one particular sine wave modulated model was found to de¬ 
scribe the magnetic diffraction pattern well, with a maximum 
magnetic moment of 43±0.2/jLsy again close to the maxi¬ 
mum expected value for Fe^"^. In this model, shown in Fig. 
3 , the spins in a given layer are uniaxial, but the spin axis 
alternates from layer to layer. Thus, in the first layer the 
spins lie along ±[1,1,1/2] and in the second layer they lie 
along ±[“ 1,“ 1,1/2]. The spin amplitude is modulated per¬ 
pendicular to this direction along [1,- 1,0], i.e., the row di¬ 
rection, as shown in Fig. 3. The fit of the model to the ex¬ 
perimental data is illustrated in Fig. 4. 

These results may be discussed in terms of the Heisen¬ 
berg row model. It is easy to show that its 7=0 ground state 
is coplanar, and is the same as that of the XY row model.^’^ 
For JIJ'<2, this consists of a helical spin structure with a 
magnetic unit cell consisting of two rows, and an incommen¬ 
surate repeat distance along the row direction. This magnetic 
structure minimizes the energy of every elementary triangu¬ 
lar plaquette of spins OAB, where spins A and B lie in the 
same row and spin O lies in the adjacent row [see Fig. 1(b)]. 
Let 6o, 6^ denote the orientation, in the XY plane, 

of the spins on sites O, A, and B, respectively. If Oq is set 
equal to 0°, then — cos~\j/2J') and — 

The wave vector of this magnetic structure, referred to the 
primitive unit cell defined in Fig. 1, is {0^/360°, — 0^/360°). 


The magnetic structures of CsFe(S 04)2 and RbFe(S 04)2 
have 0q=0°, 6^-120°, and ^^ = 240°, corresponding, as 
expected, to J/J' = l. The magnetic structure adopted by 
KFe(S 04)2 has wave vector (0.73, —0.73, 0), corresponding 
to JfJ'^0.25. However, rather than adopting this 

helical structure, KFe(S 04)2 adopts a sine wave modulated 
structure with the same wave vector. This structure can be 
derived from the expected helical structure by suppression of 
one of its two orthogonal spin components. The adoption of 
this partially disordered spin structure is consistent with the 
fact that helical structures cannot develop in a system with 
lower than tetragonal symmetry at a second order phase 
transition.In fact, Solyom^^ showed that for the C-centered 
orthorhombic structure of MnS 04 , the helical spin structure 
can only arise via three second-order transitions. The obser¬ 
vation of a sine wave modulated structure well below the 
ordering temperature in KFe(S 04)2 is nevertheless surpris¬ 
ing, as it implies both substantial anisotropy to fix the spin 
direction, and also large-amplitude spin fluctuations persist¬ 
ing to low temperature. The origin of this spin structure 
leaves an intriguing problem for future investigation. 


ACKNOWLEDGMENT 

It is a pleasure to thank Dr. J. P. Attfield for bringing to 
our attention the work on the C-centered orthorhombic 
compounds.^®’’^ 


‘K. Kawamura and S. Miyashita, J. Phys. Soc. Jpn. 53, 4138 (1984); S. 
Miyashita, J. Phys. Soc. Jpn. 55, 3605 (1986); S. Miyashita and H. Shiba, 
J. Phys. Soc. Jpn. 53, 1145 (1984); S. Miyashita and H. Kawamura, J. 
Phys. Soc. Jpn. 54, 3385 (1985). 

^H. Kawamura, Phys. Rev. B 47, 3415 (1993). 

^P. W. Anderson, Mater. Res. Bull. 8, 153 (1973). 

Harrison and T. E. Mason, J. Appl. Phys. 67, 5424 (1990). 

^S. T. Bramwell, S. G. Carling, C. J. Harding, K. D. M. Harris, B. M. 
Kariuki, L. Nixon, and I. P. Parkin, J. Phys.: Condens. Matter 8, LI23 
(1996). 

^W. M. Zhang, W. M. Saslow, and M. Gabay, Phys. Rev. B 44, 5129 
(1991). 

^H. Kawamura, Prog. Theor. Phys. Suppl. 101 , 545 (1990). 

^M. E. Zhitomirsky, Phys. Rev. B 54, 353 (1996). 

^C. J. Glinka, V. J. Minkiewicz, D. E. Cox, and C. P. Khattak, AIP Conf. 
Proc. 18 , 659 (1973). 

‘^G. Will, B. C. Frazer, G. Shirane, D. E. Cox, and P. J. Brown, Phys. Rev. 
A 140, 2139 (1965). 

P. Attfield, P. D. Battle, and A. K. Cheetham, J. Solid State Chem. 57, 
357 (1985). 

^^The diffraction patterns were measured at the following temperatures: 

CsFe(S04)2, 20 K; RbFe(S04)2, 8 K; KFe(S04)2, 15 K. 

^^A. C. Larson and R. B. Von Dreele, Los Alamos Laboratory Report No. 
LA-UR-86-748, 1987. 

'"^J. Rodriguez-Carvajal, “fullprof: A program for Rietveld Refinement 
and Pattern Matching Analysis,” Abstracts of the Satellite Meeting on 
Powder diffraction of the XV Congress of the International Union of 
Crystallography, Toulouse, France, 1990 (unpublished), p. 127. 

‘^E. J. Lisher and J. B. Forsyth, Acta Crystallogr. A27, 545 (1971). 

*^G. Shirane, Acta Crystallogr. 12, 282 (1959). 

^^J. Rossat-Mignod, Methods of Experimental Physics: Neutron Scattering 
(Academic, New York, 1987), Vol. 3, p. 131. 

'^J. S6lyom, Physica (Amsterdam) 32, 1243 (1966). 



JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Phase transition and phase diagram of the J^-J 2 Heisenberg model 
on a simple cubic lattice 

C. Pinettes and H. T. Diep 

Laboratoire de Physique Theorique et Modelisation, Universite de Cergy-Pontoise 2, Avenue Adolphe Chauvin, 
95302 Cergy-Pontoise Cedex, France 

By extensive standard and histogram Monte Carlo simulations, we show that the magnetic phase 
transition is of first order in the frustrated J\-J 2 Heisenberg model on a simple-cubic lattice. 
Despite the infinite ground-state degeneracy, the system is shown to retain only the collinear spin 
configurations at low temperatures. © 1998 American Institute of Physics. 

[80021-8979(98)38211-0] 


I. INTRODUCTION 

Various properties of frustrated spin systems have been 
extensively investigated during the last 15 years. ^ Neverthe¬ 
less, several questions remain controversial. In particular, the 
nature of the phase transition from a noncollinear ground 
state (GS) to the paramagnetic state is not yet understood at 
present. 

In a frustrated system with vector spins {XY or Heisen¬ 
berg), the frustration is uniformly distributed on all spins, 
generally causing a noncollinear GS with very high or infi¬ 
nite degeneracy. Some well-known examples are the antifer¬ 
romagnetic face-centered cubic (fee) lattice,^’^ the so-called 
fully frustrated simple-cubic (SC) lattice,"^ the antiferromag¬ 
netic hexagonal-close-packed (hep) lattice,^ the stacked tri¬ 
angular antiferromagnets,^ the two-dimensional Villain XY 
model,^ and the XY model on the check-board lattices.^ This 
great degeneracy with a noncollinear ground state gives rise 
to both a rich behavior on the finite temperature properties 
such as the nature of ordering and on the phase transition. 

The purpose of this work is to study the frustrated SC 
lattice with antiferromagnetic nearest neighbors (NN) and 
next-nearest-neighbor (NNN) interactions, Ji and J 2 , re¬ 
spectively. We are particularly interested in the frustrated 
region of the phase diagram, when J 2 is strong. Extensive 
Monte Carlo (MC) simulations, including histogram calcula¬ 
tions, have been performed to clarify the nature of the order¬ 
ing and of the phase transition. 

II. MODEL 

For this purpose, we consider a classical Heisenberg 
model with the Hamiltonian 

E ■/2S,-S,-, (1) 

{ij) m) 

where S/ is a vector spin of unit length occupying the /th 
lattice site and the sums () and {{)) run over NN and NNN 
pairs, respectively. All interactions are antiferromagnetic 
(>0). Hereafter, the energy and temperature will be mea¬ 
sured in units of . 

For Heisenberg spins, the classical ground state can be 
determined numerically by an iterative procedure minimiz¬ 
ing the local energies until the internal energy is stabilized.^ 


It is given as follows: for 0<72^0.25 , the classical GS is 

the antiferromagnetic structure. For 0.25 J\<J 2 the classical 
GS has an infinite degeneracy, apart from the global rotation. 
It is divided into eight sublattices, the elementary cubes con¬ 
taining two tetrahedra formed by the NNN sites and stacked 
as in Fig. 1(a). The spin configurations a, b, c, and d of the 
NNN tetrahedra are those of the elementary tetrahedra in the 
GS of the fee antiferromagriets:^ each NNN tetrahedron is 
characterized by two angles, 6, formed by two up spins (or 
two down spins) and formed by the plane containing the 
two up spins and the plane containing the two down spins 
(see Ref. 2). The three collinear configurations (one line up, 
one line down) are particular GS configurations in this range 
of parameters [see Fig. 1(b)]. 

We have performed standard MC simulations using the 
sample sizes of 12^-18^ spins with periodic boundary 
conditions. Starting from a random spin configuration as the 
initial condition for the MC simulations, we have calculated: 
the internal energy per spin U, the specific heat per spin Cy, 
the magnetic susceptibility per spin (a), and the average sub¬ 
lattice magnetization , as functions of temperature T. At a 
given r, 10 000 MC steps per spin have been discarded for 
equilibrating and 10 000 MC steps per spins have been used 
for averaging. Random initial conditions and such long runs 




(a) (b) 

FIG. 1. (a) The general GS spin configurations for 0.25 J\<J 2 - R is de¬ 
composed into two NNN tetrahedra, defined by the void and solid circles. 
The spin orientations of the four sublattices a, b, c, and d are the same as in 
the antiferromagnetic face-centered cubic lattice: it is given by two angles 6 
and ^ (see Ref. 2). (b) The collinear configurations (one line up, one line 
down) are particular GS configurations for 0.25 J\<J 2 ■ There are two other 
equivalent configurations with lines along the two other directions of the 
cubic lattice. 


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J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


C. Pinettes and H. T. Diep 



FIG. 2. Phase diagram of the SC -Jj lattice in the space iTJ 2 fJ\)- 
and III design antiferromagnetic, collinear [see Fig. 1(a)], and paramagnetic 
phases, respectively. First-order transitions are shown by black circles for 
0.25 J\<J 2 ’ Void circles indicate second-order transitions for 0<J2 
<0.25 J,. The dashed line indicates the critical value J 2 lJ\ = 025, 

were used in order to detect the nature of ordering at finite T 
as seen below. 

III. RESULTS 

Figure 2 displays the phase diagram in the phase space 
For 0</2<0-25 Jx , there is a second-order tran¬ 
sition from the antiferromagnetic structure to the paramag¬ 
netic state at finite temperature. When 0.25 Ji<J 2 , there is a 
first-order like transition between the infinitely degenerated 
GS and the paramagnetic state. At the limit ^1 = 0 or 
= 00, the Sc lattice is decoupled into two independent fee 
sublattices. The different physical quantities are shown in 
Fig. 3 in this range of parameters. They all show a disconti¬ 
nuity at Tc=033 for J 2 !Ji = 0.26. In order to confirm the 
nature of the phase transition, we have used the histogram 
MC simulations.^ We discarded 500 000 MC steps per spin 
for equilibrating and calculated the energy histogram P(E) 
at the transition temperature over the next one million MC 
steps. P(E) is shown in Fig. 4 where two peaks are observed 
at 70 = 0.330 for J 2 lJx = 0.26. This bimodal distribution is a 
clear evidence of the first-order character of the transition 
suggested above. Note that long run is necessary to observe 
the two-peak structure. Less than one million MC steps per 
spin, the two peaks are not equally developed. 

Another interesting point in Fig. 2 is the nature of order¬ 
ing at low temperature in the frustrated range 0.25 7i <72 • ^ 
natural way to find the nature of ordering at finite tempera¬ 
ture is to use the heating procedure from a disordered state 
and to analyze the spin structure. We used in our runs as 
order parameters the three staggered magnetizations defined 
for the collinear configuration shown in Fig. 1(a) and the two 
other equivalent configurations with lines along the two 
other directions of the cubic lattice. The results show (see 
Fig. 5) that just below 7^ the system is ordered in one of 
these three collinear configurations. Thermal (or quantum) 
fluctuations lift the degeneracy and select collinear configu¬ 
rations. This verifies the conjecture by Henley,in analogy 
with what was called “order by disorder” in the Ising case,^^ 
as the Heisenberg fee antiferromagnets,^’^ the hep anti- 
ferromagnets,^ and the stacked triangular antiferromagnets.^ 


-u 

1.475 

1.25 

1.025 



c 


0.6 

0.4 

0.2 

0 

0 


FIG. 3. Thermodynamical quantities as functions of temperature T for 
J 2 /7j = 0.26. (a) On the left-hand scale, the internal energy per spin U (void 
circles) and on the right-hand scale, the specific heat per spin Cy (black 
circles); (b) on the left-hand scale, the average sublattice magnetization 
(void circles) and on the right-hand scale, the magnetic susceptibility per 
spin (;^') (black circles). The full curves are a fit to the MC data. The vertical 
arrows indicate rc=0.33. 


Finally, let us notice that the first-order transition be¬ 
tween the collinear phase and the paramagnetic phase can be 
explained as follows: in the collinear configuration, the infi¬ 
nite degeneracy is reduced to three (apart from the global 

P(E) 

0.0016 


0.0012 


0.0008 


0.0004 


<%> 

10 


5 



FIG. 4. The energy histogram P(E), E being the total energy, for J 2 ^J\ 
= 0.26 at a temperature very close to the transition temperature, Tq 
= 0.330. The energy E is given for the total number of spins A^= 18'^. The 
bimodal distribution is a signature of a first-order transition. 





J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


C. Pinettes and H. T. Diep 6319 



FIG. 5. The three staggered magnetizations defined for the collinear con¬ 
figuration shown in Fig. 1(a) are reported as functions of temperature T for 
J 2 IJ\ = 0.4. The full curve is a fit to the MC data. 


rotation) since there are three ways to choose the antiparallel 
spin pairs in a tetrahedron. This threefold degeneracy is 
reminiscent of the three-state Potts model in three dimen¬ 
sions which is known to undergo a first-order transition. This 
may be the origin of the first-order line observed here, as in 
the Heisenberg fee antiferromagnets^’^ and the hep 
antiferromagnets.^ 

Nevertheless, the nature of the phase transition in non- 
eollinear spin systems (ineluding helimagnets) is not yet 
clear since some of them exhibit first-order^’^’^’^ character 
and others show a second-order transition unknown univer¬ 
sality class. ^ 

IV. CONCLUSION 

In conclusion, we note that the different thermodynami¬ 
cal quantities determined as functions of temperature suggest 


a first-order character of the phase transition in the frustrated 
J\~J 2 simple-cubic lattice with vector spins. This first-order 
character is confirmed by histogram MC simulations. Fi¬ 
nally, we have shown that there is an order by disorder effect 
in these systems: the thermal fluctuations lift the infinite de¬ 
generacy and select collinear configurations. 


ACKNOWLEDGMENT 

The “Laboratoire de Physique Theorique et Modelisa- 
tion” is an “equipe postulante” (EP 0127) of CNRS. 


^ Magnetic Systems with Competing Interactions {Frustrated Spin Systems), 
edited by H. T. Diep (World Scientific, Singapore, 1994). 

^T. Oguchi, H. Nishimori, and Y. Taguchi, J. Phys. Soc. Jpn. 54, 4494 
(1985). 

T. Diep and H. Kawamura, Phys. Rev. B 40, 7019 (1989); C. Henley, 
J. Appl. Phys. 61, 3962 (1987); W. Minor and T. Gielbultowicz, J. Phys. 
(Paris) 49, C8-1551 (1988). 

"^P. Lallemand, H. T. Diep, A. Ghazali, and G. Toulouse, J. Phys. Lett. 46, 
L-1087 (1985); H. T, Diep, A. Ghazali, and P. Lallemand, J. Phys. C 18, 
5881 (1985). 

^H. T. Diep, Phys. Rev. B 45, 2863 (1992). 

^D. Loison and H. T. Diep, Phys. Rev. B 50, 16453 (1994); T, Bhatta- 
charya, A. Billoire, R. Lacaze, and Th. Jolicoeur, J. Phys. 14, 122 (1994); 
E. H. Boubcheur, D. Loison, and H. T. Diep, Phys. Rev. B 54, 4165 
(1996). 

”^B. Berge, H. T. Diep, A. Ghazali, and P. Lallemand, Phys. Rev. B 34, 
3177 (1986), and references therein. 

^E. H. Boubcheur, R. Quartu, H. T. Diep, and 0. Nagai, Phys. Rev. B 
(submitted). 

^A. M. Ferrenberg and R. H. Swendsen, Phys. Rev. Lett. 61, 2635 (1988); 
63, 1195 (1989). 

'^C. Henley, J. Appl. Phys. 61, 3962 (1987); Phys. Rev. Lett. 62, 2056 
(1989). 

J. Villain, R. Bidaux, J. P. Carton, and R. Conte, J. Phys. (Paris) 41, 1263 
(1980). 



JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Spin fluctuations and thermal expansion of La(NixAli_;f)i 3 
amorphous alloys 

A. Fujita®* and K. Fukamichi . 

Department of Materials Science, Graduate School of Engineering, Tohoku University, 

Sendai 980-77, Japan 

The influences of spin fluctuations on the magnetization M and thermal expansion for 
La(Nij^Ali_^)i 3 amorphous alloys have been investigated. The spontaneous magnetization obeys a 
^ 2 ^ 4/3 relation and the coefficient ^ is concerned with the dynamical spin fluctuation spectrum. 
The spontaneous volume magnetostriction in the ferromagnetic state appears due to the thermal 
variation of the local spin amplitude. The change in the linear thermal expansion coefficient in 
paramagnetic temperature regions is caused by the saturation of amplitude of the spin fluctuations. 
© 1998 American Institute of Physics. [80021-8979(98)23311-1] 


Recently, influences of spin fluctuations on magnetic 
properties in amorphous weakly itinerant ferromagnetic al¬ 
loys have been extensively studied.In amorphous alloys, 
the magnetic properties are changed by the concentration 
without the limitation of stoichiometry in contrast with that 
in crystalline compounds.^ Therefore, the characteristics of 
spin fluctuations can be studied more closely in connection 
with the stability of the ferromagnetic state. Strictly speak¬ 
ing, however, it should be noted that the atomic short-range 
order varies with the concentration in amorphous alloys^ and 
the recent theoretical studies point out that the stability of 
ferromagnetism is drastically influenced by the change of the 
atomic short-range order.^’^ The structure of La(Ni^Ali„j^.)i 3 
amorphous alloys can remove the problem mentioned above, 
namely, the local structure in the present amorphous alloys is 
well defined by the icosahedral clusters consisting of Ni and 
A1 atoms as observed in NaZni 3 -type crystalline compounds 
in a wide concentration range. The present amorphous al¬ 
loys are useful, therefore, to investigate explicitly spin fluc¬ 
tuation characteristics. 

La(Ni;^Ali_;^.)i 3 (0.90^x^0.95) amorphous alloys were 
prepared by high-rate dc sputtering on a water-cooled Cu 
substrate. The substrate was mechanically removed before 
the magnetization measurement. The temperature and mag¬ 
netic field dependences of the magnetization were measured 
with a SQUID magnetometer. 

Temperature dependence of the spontaneous magnetiza¬ 
tion M(0,r) for x = 0.925 and 0.95 is plotted in the form of 
in Fig. 1. The value of M(0,r) is deduced 
from the isothermal magnetization M{H,T) curves. The lin¬ 
ear relation is observed in the temperature range above about 
TJ2 for x = 0.95 and 0.3 for jc = 0.925. According to the 
theory on exchange enhanced spin fluctuations with mode¬ 
mode coupling, the relation is explained as a result 

of a strong renormalization effect of paramagnon-like modes 
of spin fluctuations to the magnetic free energy.The 
coefficient ^ in the relation is associated with the 

dynamical properties of spin fluctuations and expressed by 
the following expression^"^’^^: 


^taectronic mail: afujita@material.tohoku.ac.jp 


1/3, (1) 

where K is the constant and the parameters and Tq char¬ 
acterize the dispersion of the static ( 7 -dependent susceptibil¬ 
ity and the dynamical spin fluctuation spectrum. The follow¬ 
ing relation between these parameters and magnetization 
curve is derived by assuming that the sum of amplitudes of 
thermal and zero-point spin fluctuations is conserved at finite 
temperatures.^^ 

^ksTlP] 

- 2 c(-) — - = ( 2 ) 

where and fig are the Boltzmann constant and the Bohr 
magneton, respectively, equals 2 M( 0 , 0 ), and c is 0 . 335 . 
The parameters and Tq for the present amorphous alloys 
have been evaluated from the Arrott plots in our previous 
paper^ by using Eq. (2). In Fig. 2, the coefficients ^ for x 
=0.90, 0.925, and 0.95 are plotted against \I{T^Tq^), and 
the proportional relation is confirmed. Therefore, the relation 
(1) is well established in the present amorphous alloys. It 
should be emphasized that the relations ( 1 ) and ( 2 ) are valid 
even in amorphous alloys, although these were originally 
applied to crystalline systems. 



FIG. 1. Temperature dependence of the spontaneous magnetization plotted 
in the form of/W(0,7)^-7*'® for La(Ni^AI| _^)i 3 (a: = 0.95 and 0.925) amor- 
phous alloys. 


0021-8979/98/83(11 )/6320/3/$15.00 


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© 1998 American Institute of Physics 




J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


A. Fujita and K. Fukamichi 6321 



FIG. 2. The coefficient ^ plotted against \I{T^T][^) for La(Ni^Ali_;p)i 3 
amorphous alloys. The parameters , and Tq are explained in the text. 

Thermal variation of the amplitude of spin fluctuations is 
reflected on the thermal expansion.Figure 3 shows the 
temperature dependence of the spontaneous volume magne¬ 
tostriction o)^{T) for x = 0.925 and 0.95. The value of 
o)m{T) is obtained from the comparison between the ob¬ 
served and hypothetical nonmagnetic thermal expansion 
curves, as shown in the inset in Fig. 3. The hypothetical 
nonmagnetic thermal expansion curve, represented by a 
dashed line, is obtained from the Griineisen relation with 
referring the Debye model and the free-electron model for 
phonon and electron contribution, respectively. The Debye 
temperature 6q is assumed to be the same value of 
= 280 K for La(Fe;^Ali 13 amorphous alloys obtained from 
the Brillouin scattering.^^ The magnitude of a)^(r) continu¬ 
ously decreases with increasing temperature and smears 
around the Curie temperature. Such behavior is an indication 
that the amplitude of local spin density varies with tempera¬ 
ture and continuously decreases up to the Curie 
temperature.Detailed influence of spin fluctuations on 
will be discussed elsewhere. 

Theories on spin fluctuations in itinerant ferromagnets 
predict that the amplitude of spin fluctuations increases with 
the temperature and the thermal variation of spin fluctuations 
gives a positive contribution to the thermal expansion coef¬ 
ficient in paramagnetic temperature ranges.Figure 4 



FIG, 3. Temperature dependence of the spontaneous volume magnetostric¬ 
tion (ii^{T) for La(Ni;rAli_;c)i 3 (;c=0.95 and 0.925) amorphous alloys. The 
inset shows the thermal expansion curve of x — 0.95, together with a hypo¬ 
thetical dashed curve in a nonmagnetic state. The Curie temperature is in¬ 
dicated by the arrows. 



Temperature ( K ) 

FIG. 4. Temperature dependence of the linear thermal expansion coefficient 
for La(Ni;fAli_;r)i 3 amorphous alloys in the paramagnetic temperature re¬ 
gion. The inset shows the temperature dependence of the inverse magnetic' 
susceptibility for x = 0.90 and 0.925. The characteristic temperature T* is 
given by the arrows. 

shows the linear thermal expansion coefficient (TEC) in 
paramagnetic temperatures for x —0.95, 0.925, and 0.90. For 
itinerant weakly ferromagnets, the contribution of spin fluc¬ 
tuations to TEC, , is represented as 

dSliT) 

am=KCm . (3) 

where S\{T) is the mean square of the amplitude of local 
spin fluctuations, and k are the magnetovolume coupling 

coefficient and the compressibility, respectively.^^ Generally 
speaking, S\ increases linearly and hence is almost con¬ 
stant in weakly itinerant ferromagnets.^The electron 
contribution is proportional to the temperature.^^ In the tem¬ 
perature region higher than the Debye temperature, the pho¬ 
non contribution to TEC behaves as the Dulong-Petit law. 
As mentioned in the preceding section, the Debye tempera¬ 
ture of the present amorphous alloys is assumed to be 280 
Therefore, TEC around room temperature should in¬ 
crease monotonically with the temperature. However, as seen 
in Fig. 4, a change in the increase occurs in all the curves, 
shifted to lower temperatures with decreasing x. Because of 
an apparent concentration dependence, the origin of this 
anomaly neither is phonons nor electrons but spin fluctua¬ 
tions. Thus, the anomalous temperature dependence of s\ 
occurs in paramagnetic temperature ranges. 

The information on the paramagnetic spin fluctuations in 
itinerant weakly ferromagnets can be obtained from tempera¬ 
ture dependence of paramagnetic susceptibility.^^ The in¬ 
verse magnetic susceptibility Mx is proportional to and a 
linear ±ermal variation of S\ gives a Curie-Weissrlike be¬ 
havior even in itinerant ferromagnets.^The inset in Fig. 4 
shows the temperature dependence of the inverse magnetic 
susceptibility for x = 0.90 and 0.925. For the present amor¬ 
phous alloys, Hx becomes convex upwards just above 
and subsequently shows an upturn.^ The curving of Mx con- 





6322 J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


A. Fujita and K. Fukamichl 


vex upwards is interpreted as a significant increase of S\. 

A sudden increase in the slope of Hx suggests that the mag¬ 
nitude of arrives at its upper limit because of charge 
neutrality.^^’^^ After the amplitude of spin fluctuations is 
saturated at the upper limit value, the spin fluctuations give 
no contribution to lix, resulting in a large slope of Mx due to 
the directional fluctuations of magnetic moments. The start¬ 
ing temperature of the saturation phenomenon, T*, is ob¬ 
tained from the intersection of the straight lines before and 
after the change in the slope as indicated by the arrows in 
Fig. 4. Apparently, TEC changes its magnitude at around 
7*, revealing that the saturation of the amplitude of spin 
fluctuations is its origin. 

In summary, the influences of spin fluctuations on the 
magnetization and thermal expansion are observed in 
La(Nij^Ali_^)i 3 amorphous alloys. In the ferromagnetic 
state, the relation appears and the coefficient ^ is 

closely correlated with the spin fluctuation spectrum. The 
spontaneous volume magnetostriction is caused by the ther¬ 
mal variation of the local spin amplitude. The linear thermal 
expansion coefficient in paramagnetic temperature regions 
changes its magnitude due to the saturation of the amplitude 
of spin fluctuations. 

The present work was partially financed by a Grant-in- 
Aid for Scientific Research from Ministry of Education, Sci¬ 
ence, Sports and Culture, Japan, No. (B) (2) 08455287. One 


of the author (A.F.) would like to thank the JSPS Research 
Fellowships for Young Scientists. 


* A. Fujita, T. H. Chiang, N. Kataoka, and K. Fukamichi, J. Phys. Soc. Jpn. 
62, 2579 (1993). 

^A. Fujita, K. Fukamichi, H. A. Katori, and T. Goto, J. Phys.: Condens. 
Matter 7, 401 (1995). 

^A, Fujita, K. Suzuki, K. Fukamichi, Y. Obi, and H. Fujimori, Mater. 
Trans., JIM 36, 852 (1995). 

^V. S. Amaral and B. Barbara, J. Magn. Magn. Mater. 140-144, 2011 
(1995). 

^A. L. Dawson and D. H. Ryan, Phys. Rev. B 54, 12238 (1996). 

^P. D. Babu and S. N. Kaul, J. Phys.: Condens. Matter 9, 3625 (1997). 
’a. Fujita, M. Matsuura, and K. Fukamichi (unpublished). 

^H. Tanaka and S. Takayama, J. Phys.: Condens. Matter 4, 8203 (1992). 
^Y. Kakehashi, Phys. Rev. B 43, 10820 (1991). 

‘^A. Fujita, K. Fukamichi, E. Matsubara, and Y. Waseda (unpublished). 
‘^T. Moriya and A. Kawabata, J. Phys. Soc. Jpn. 34, 639 (1973); 35, 669 
(1975). 

'^K. Makoshi and T. Moriya, J. Phys. Soc. Jpn. 38, 10 (1975). 

'^T. Moriya, Spin Fluctuations in Itinerant Electron Magnetism (Springer, 
Berlin, 1985). 

”^Y. Takahashi and T. Moriya, J. Phys. Soc. Jpn. 54, 1592 (1985). 

'^G. G. Lonzarich and L. Taillefer, J. Phys. C 18, 4339 (1985). 

'^Y. Takahashi, J. Phys. Soc. Jpn. 55, 3553 (1986). 

'^T. Moriya and K. Usami, Solid State Commun. 34, 95 (1985). 

'^A. Yoshihara, Y. Shimada, T. H. Chiang, and K. Fukamichi, J. Appl. 

Phys. 75, 1733 (1994). 

*^S. Ogawa, Physica B & C 119, 68 (1983). 

^^T. Moriya and Y. Takahashi, J. Phys. Soc. Jpn. 45, 397 (1978). 

^'T, Moriya, Solid State Commun. 26, 483 (1978). 



JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Magnetic relaxation in Gao.6Mo2S4 spinel 

T. Taniyama®' and I. Nakatani 

National Research Institute for Metals, Tsukuha 305-0047, Japan 

Magnetization measurements on Gao. 6 Mo 2 S 4 cluster compound of modified spinel were performed 
at temperatures from 2 to 30 K. Temperature irreversibility of the magnetization develops just below 
the ferromagnetic transition temperature. Relaxation isotherms of the thermoremanent 
magnetizations can be described by a superposition of a stretched exponential and a constant term, 
and shows distinctive aging effects. This implies the presence of the orientational spin freezing in 
the ferromagnetic regime of the Gao. 6 Mo 2 S 4 . © 1998 American Institute of Physics, 
[80021-8979(98)50611-1] 


The molybdenum cluster compound Ga;^.Mo 2 S 4 (x 
=0.5-0.67) demonstrates fruitful magnetic properties owing 
to the tetrahedral molybdenum clustering induced by the or¬ 
der of Ga atoms and vacancies on the tetrahedral sites in 
spinel structure.^"^ In this kind of compound, imperfections 
of the Ga-vacancy ordering yields significant modification of 
electronic properties. Recently, Sahoo et al reported the sig¬ 
nature of variable-range hopping between the localized states 
of clusters induced by such imperfections."^’^ However, com¬ 
paratively little attention has been paid to the magnetic prop¬ 
erties intrinsically affected by the random atomic arrange¬ 
ment. 

The intrigue magnetic properties due to such random 
effects can be sensitively probed by the thermoremanent 
magnetization (TRM). In particular, time evolution of the 
TRM gives distinguishable dynamic response caused by the 
different physical mechanism. Thus, we employ the time de¬ 
pendent TRM measurements on the Gao. 6 Mo 2 S 4 to elucidate 
the magnetic nature in the view of the randomness. In this 
article, we present temperature irreversibility of the magne¬ 
tization and waiting time dependence of the magnetic relax¬ 
ation in the ferromagnetic regime. 

The method of sample preparation has been described in 
our previous article.^ The x-ray diffraction pattern was in¬ 
dexed on the basis of the lower symmetric spinel structure 
(space group F43m) having a = 9.737 A and revealed a ho¬ 
mogeneity of the prepared sample. With decreasing tempera¬ 
ture, splitting of the /zOO diffraction peaks was observed be¬ 
low the temperature of 43 K, reflecting the structural 
transition from a space group F43m io R3m. The is consis¬ 
tent with the results previously reported by Shamrai et al}’^ 
The pellet used for the x-ray diffraction measurement was 
cut into a size of 1 mmX 1 mmX5 mm for the magnetic mea¬ 
surements. Magnetic data were collected using a magneto¬ 
meter (PPMS, Quantum Design) at temperatures from 2 to 
30 K. Temperature dependent magnetizations were measured 
with increasing temperature under both zero field cooled 
(ZFC) and field cooled conditions. The time dependent TRM 
was recorded over four decades of observation time after 
switching off the cooling magnetic field. 

Figure 1 shows the temperature dependent magnetization 


^^Electronic mail: taniyama@hagi982.nrim.go.jp 


and the ac susceptibility at temperatures from 2 to 30 K. The 
ZFC magnetization exhibits a shallow maximum structure 
and the maximum temperature shifts towards lower tempera¬ 
tures as the magnetic field increases. The temperature irre¬ 
versibility of the magnetization also develops just below the 
ferromagnetic transition temperature , which has been de¬ 
fined to be 17.4 K by the previous nonlinear susceptibility 
measurements.^ The significant irreversibility and the peak 
structure of the temperature dependent magnetization are 
typical of the disordered materials, e.g., spin glasses and ran¬ 
dom ferromagnets. We note that the magnetic feature of the 
Gao 6 M 02 S 4 is quite similar to that of the reentrant ferromag¬ 
netic semiconductor of the indium-doped chalcogenide spi¬ 
nel CdCr 2 Se 4 :In.^ 

Relaxation isotherms were collected after a sequence of 
waiting for a time of ^^^=60 s at the measurement tempera¬ 
ture and switching off the cooling fields of 50 Oe and 1 kOe, 
from which the temperature dependent relaxation rates (Fig. 
2 ) are extracted simply using the logarithmic relaxation de¬ 
cay form: 

M = Mo”Slogt, ( 1 ) 



FIG. 1. Temperature dependent zero field cooled and field cooled magneti¬ 
zation in a field of 50 Oe. Temperature dependent ac susceptibility in a 
modulation field of 2 Oe is also depicted. 


0021-8979/98/83(11 )/6323/3/$15.00 


6323 


© 1998 American Institute of Physics 



6324 J. Appi. Phys., Vol. 83, No. 11, 1 June 1998 


T. Taniyama and I. Nakatani 



7( K ) 


FIG. 2. Temperature dependent relaxation rate S and initial magnetization 
Mq in a cooling field of (a) 50 Oe and (b) 1 kOe. 

where the S is the relaxation rate and Mq is the initial mag¬ 
netization. Although the maximum in the temperature depen¬ 
dent relaxation rate shifts towards lower temperatures with 
increasing magnetic fields, the normalized relaxation rate 
S/Mq hardly shows the field dependence. 

Figure 3 illustrates the relaxation dynamics for two ex¬ 
treme waiting times t^r= 60s and %= 10 800 s, at 15 K on a 
logarithmic time scale. In contrast to the concave up profile 
for %= 60 s, the relaxation isotherm concaves down after 
waiting for t^= 10 800 s in a magnetic field. Such behavior 
has been frequently observed in the reentrant ferromagnet 
and the relaxation isotherms can be represented by a super¬ 
position of a stretched exponential and a constant term:^’^ 

M-Mq + Mi exp[--(f/r)^“'*]. (2) 

The additional constant term has been interpreted on the ba¬ 
sis of the reliable picture introduced by Gabay and 
Thoulouse,^® in which the longitudinal spontaneous magne¬ 
tization coexists with the freezed transverse spin component. 
Within this framework, we fit the experimental data using 
Eq. (2) over the entire observation time scale (Fig. 3). The 
best fit parameters are listed in Table I. The values of the 
fitted parameters r and n closely correspond to those of 
FeNiMn reentrant ferromagnet.^^ 


1.08 


1.06 

00 

I 1-04 

3 

£ 

Z 1.02 
§ 

1.00 


0.98 

10 ^ 10 ^ 10 ^ 10 ^ 
time (sec) 

FIG. 3. Time dependent thermoremanent magnetization recorded at 15 K 
after a sequence of waiting for a time and switching off the cooling 
magnetic field of 50 Oe. The solid lines are fitted curves in terms of a 
superposition of a stretched exponential and a constant term. 


Mitchler et al carefully investigated the analytical func¬ 
tional forms of the relaxation isotherm in the random ferro¬ 
magnet PdFe and the reentrant ferromagnet CrFe, and found 
that the relaxation responses are divided into two groups: a 
power law and a stretched exponential decay. The former 
functional form accurately represents the relaxation of the 
random ferromagnets such as PdFe, while the latter case 
characterizes the orientational collapse into random spin con¬ 
figurations in the reentrant ferromagnet. Further, the reen¬ 
trant phase exhibits the system age dependent relaxation al¬ 
though the random ferromagnet shows no measurable aging 
effects on the relaxation dynamics reflecting the equilibrium 
aging limit. In the present case, the relaxation isotherms are 
represented by a stretched exponential superposed on a con¬ 
stant term and show the discernible aging effects. This per¬ 
suasively indicates that the glassy freezing occurs in the fer¬ 
romagnetic phase of the Gao. 6 Mo 2 S 4 , although the presence 
of the aging effects on the relaxation isotherms does not offer 
a definitive criterion for distinguishing the microscopic spin 
configurations in the disordered materials. 

It is not clear whether or not the orientational collapse 
simultaneously evolves as the ferromagnetic ordering is es¬ 
tablished. In our previous article, the ferromagnetic transition 
temperature was determined to be 17.4 K based on the non¬ 
linear susceptibility measurements.^ The obtained transition 
temperature exactly coincides with the temperature below 
which the dc susceptibility MIH exhibits the field depen¬ 
dence as shown in Fig. 1. On the contrary, the irreversibility 
in a field of 50 Oe develops below a slightly lower tempera- 


TABLE I. Best-fit parameters to a stretched exponential in Eq. (2). 


% (s) 

Mq (emu/cm'^) 

Mi (emu/cm^) 

t(s) 

n 

60 

0.99 

0.12 

135 

0.76 

10 800 

0.91 

0.22 

39 000 

0.87 





J. AppL Phys., Vol. 83, No. 11, 1 June 1998 


T. Taniyama and I. Nakatani 6325 


ture of 16.5 K. If we assign the glassy freezing with the onset 
of the irreversibility, the freezing process may sequentially 
occur after the ferromagnetic transition. Although one may 
suspect that the irreversibility temperature possibly ap¬ 
proaches the Tc with reducing the applied field, we empha¬ 
size the coincidence between the irreversibility temperature 
and the peak temperature of the ac susceptibility in zero bias 
field. Thus, our picture of the sequential collapse into the 
randomly orientational spin configurations is plausible. 

Finally, we make a brief comments on the origin of the 
spin-glass-like dynamics. As we have stated before, the mag¬ 
netic disorder would be mainly driven by the random molyb¬ 
denum clustering due to the imperfection of the Ga-vacancy 
ordering. However, we have to claim the instability of the 
cubic lattice structure at 43 K. Shamrai et al proposed the 
displacement of the molybdenum atoms to form a M 03 com¬ 
plex with a shorter distance in the low-temperature R3m 
phase and suggested the resultant mixed type of interactions, 
i.e., indirect exchange interaction and superexchange interac¬ 
tion between molybdenum ions. Thus, the distortion of the 
crystal lattice should be partly responsible for the frustrating 
interactions which promote the glassy behaviors in the 
GaQ 5]V[o2S4. 

We summarize the magnetic feature of the Gao. 6 Mo 2 S 4 


deduced from the magnetic measurements. The random ori¬ 
entational freezing is inferred from the temperature irrevers¬ 
ibility and the relaxation dynamics described by a superpo¬ 
sition of a stretched exponential and a constant term, which 
is further reinforced by the specific aging effects in the fer¬ 
romagnetic regime. In order to get the convincing evidence 
for the spin configurations, further microscopic measure¬ 
ments such as neutron scattering or nuclear magnetic reso¬ 
nance measurements are required. 


^ A. K. Rastogi, A. Berton, J. Chaussy, R. Toumier, M. Potel, R. Chevrel, 
and M. Sergent, J. Low Temp. Phys. 52, 539 (1983). 

^V. Shamrai, H. Madge, T. Mydlarz, and G. Leitus, J. Low Temp. Phys. 
49, 123 (1982). 

W. F. Shamrai and G. M. Leitus, Sov. Phys. Solid State 29, 1312 (1987). 

Sahoo and A. K. Rastogi, J. Phys.: Condens. Matter 5, 5953 (1993). 
^S. Lamba, A. K. Rastogi, and D. Kumar, Phys. Rev. B 56, 3251 (1997). 
^T. Taniyama and I. Nakatani, J. Magn. Magn. Mater. 177-181, 263 
(1998). 

^M. Lubecka, L. J. Maksymowicz, R. Szymczak, and W. Powroznik, Phys. 
Rev. B 55, 6460 (1997). 

®P. D. Mitchler, R. M. Roshko, and W. Ruan, Philos. Mag. B 68, 539 
(1993). 

^G. Sinha, R. Chatterjee, M. Uehara, and A. K. Majumdar, J. Magn. Magn. 
Mater. 164, 345 (1996). 

*°M. Gabay and G. Thoulouse, Phys. Rev. Lett. 47, 201 (1981). 

Li, R. M. Roshko, and G. Yang, Phys. Rev. B 49, 9601 (1994). 


JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Nanocrystalline and Gordon E. Fish, 

Amorphous Soft Materials Chairman 


New bulk amorphous Fe-(Co,Ni)-M-B (M=Zr,Hf,Nb,Ta,Mo,W) alloys with 
good soft magnetic properties 


Akihisa Inoue, Tao Zhang, and Hisato Koshiba 

Institute for Materials Research, Tohoku University, Katahira 2-1-1, Aoba-ku, Sendai 980-77, Japan 

Akihiro Makino 

Central Research Laboratory, Alps Electric Co. Ltd., Higashi-Takami 1-3-5, Nagaoka 940, Japan 

We have found that an amorphous phase with a wide supercooled liquid region reaching 85 K 
before crystallization is formed in Fe™(Co, Ni)~(Zr, Nb, Ta)-B, Fe-Co-(Zr, Nb)-(Mo, W)-B and 
Co-Fe-Zr-B systems. The high stability of the supercooled liquid enabled the production of bulk 
amorphous alloys with diameters up to 5 mm by copper mold casting. These amorphous Fe-(Co, 
Ni)-M-B alloys exhibit good soft magnetic properties, i.e., saturation magnetization of 0.95 to 1.1 
T, low coercivity of 1 to 8 A/m, Curie temperature of 560 to 590 K and low magnetostriction of 
8- 14X 10“^. The effective permeability of the Co-based alloys exceeds 25 000 at 1 kHz and keeps 
high values above 5000 at the high frequency of 1 MHz. The permeability at 1 MHz is much higher 
than those for any kinds of soft magnetic materials. The frequency at which the imaginary part of 
permeability shows a maximum is also about 1 MHz. The success of synthesis of new Fe- and 
Co-based amorphous alloys with good soft magnetic properties and high glass-forming ability is 
promising for future development of a new type of soft magnetic material. © 1998 American 
Institute of Physics. [S0021 -8979(98)47111-1] 


It is well known that Fe- and Co-based amorphous alloys 
exhibit good soft magnetic properties. The soft magnetic 
properties have been characterized as the achievement of 
high saturation magnetization for Fe-based alloys and high 
permeability (/x^) and zero magnetostriction for Co-based 
alloys.^ However, these soft magnetic amorphous alloys have 
usually been prepared in a thin sheet from with a thickness 
below 50 /xm and in a wire form with a diameter below 120 
ixm? The small maximum thickness resulting from the low 
glass-forming ability has prevented the further extension of 
application fields as magnetic materials. Consequently, great 
effort has been devoted to search new ferromagnetic amor¬ 
phous alloys with higher glass-forming ability for the last 
two decades. Recently, Inoue et al. have succeeded in find¬ 
ing a number of amorphous alloys with high glass-forming 
ability in Ln-Al-TM,^ Mg-Ln-TM,"* Zr-Al-TM^ and 
Pd-Cu-Ni-P® (Ln=lanthanide metal, TM=transition metal) 
systems and in preparing bulk amorphous alloys with maxi¬ 
mum diameters up to about 72 mm by copper mold casting.^ 
Although these bulk amorphous alloys have been limited to 
the nonferrous alloys without ferromagnetism, the findings 
of the above-described bulk amorphous alloys have enabled 
the derivation of the three empirical rules for achievement of 
large glass-forming abilityThat is, (1) multicomponent 
alloys systems consisting of more than three elements, (2) 
significant difference in atomic size ratios above 12% among 
the main constituent elements, and (3) negative heats of mix¬ 
ing among their elements. Based on the three empirical rules, 
we have subsequently searched ferromagnetic Fe- and Co¬ 
based amorphous alloys with large glass-forming ability 


leading to the production of bulk amorphous alloys. As a 
result, we have found that multicomponent Fe-(Co, Ni)-(Zr, 
Nb, Ta)-B, Fe-Co-(Zr, Nb)-(Mo, W)-B and Co-Fe-(Zr, 
Nb)-B amorphous alloys exhibit a wide supercooled liquid 
region reaching 80 K before crystallization*^”’*^ and can be 
produced in a cylindrical form with diameters up to about 5 
mm by copper mold casting.*"* This is believed to be the first 
evidence on the preparation of ferromagnetic Fe- and Co¬ 
based bulk amorphous alloys. This paper aims to present the 
composition range in which amorphous alloys in Fe-(Co, 
Ni)„]V[-B (M=Zr, Hf, Nb, Mo, W) systems, are formed 
either by copper mold casting or by melt spinning and to 
examine the compositional dependence of the thermal stabil¬ 
ity and magnetic properties of the Fe- and Co-based amor¬ 
phous alloys. 

Multicomponent alloys with composition 
Fe 56 Co 7 Ni 7 Zr 10 B 20 . F^56Cu7Ni7Zr8Nb2B2o» 

Fe 6 oCo 8 ZrioMo 5 W 2 Bi 5 , and Co56Fei6Zr8B2o were prepared 
by arc melting a mixture of pure metals and pure B crystal in 
an argon atmosphere. These compositions were chosen be¬ 
cause of the appearance of a supercooled liquid region of 35 
to 85 K. From these prealloyed ingots, cylindrical samples 
with a constant length of about 50 mm and different diam¬ 
eters in the range of 0.5 to 6 mm were prepared by injection 
casting of the molten alloy into copper molds with cylindri¬ 
cal cavities. For comparison, amorphous ribbons with a cross 
section of 1 X 0.02 mm^ were produced by melt spinning. 
The amorphicity was examined by x-ray diffractometry and 
optical microscopy (OM). The OM sample was etched for 10 
s at 293 K in a solution of 0.5% hydrofluoric acid and 99.5% 


0021 -8979/98/83(11 )/6326/3/$15.00 


6326 


© 1998 American Institute of Physics 




J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Inoue et al. 


6327 




LiBitadiiiifeiii! 

FIG. 1. Outer morphology and surface appearance of cast 
Fe 6 oCo 8 ZrioMo 5 W 2 Bi 5 alloy cylinders with diameters 3 and 5 mm. 


distilled water. The specific heat associated with glass tran¬ 
sition, supercooled liquid region and crystallization was 
measured at a heating rate of 0.67 K/s with a differential 
scanning calorimeter (DSC). Saturation magnetization (7^) 
and coercivity (77^) under a field of 800 kA/m were mea¬ 
sured at room temperature with a vibrating sample magneto¬ 
meter (VSM). Hysteresis B-H loop under a magnetic field of 
1.6 kA/m was also measured for the melt-spun ribbons with 
a B-H loop tracer. Permeability was evaluated in a 
frequency range of 1 to 10"^ kHz with an impedance ana¬ 
lyzer. Saturated magnetostriction (X^) was measured under a 
field of 240 kA/m by a three-terminal capacitance method. 
Curie temperature (T^) was determined by extrapolating the 
I~T curve in the constant coupling approximation manner. 
Electrical resistivity measurement was made by the four- 
probe method at room temperature. 



FIG. 2. DSC curves of the cast amorphous Fe 56 Co 7 Ni 7 Zr 8 Nb 2 B 2 o, 
Fe 6 oCo 8 ZrioMo 5 W 2 B, 5 , and Co5<5Fe)6Zr8B2o alloys. 


TABLE I. Maximum sample thickness (tmax) thermal stability {Tg , 
and Tg/Tjjj') of the Fe 5 gCo 7 Ni 7 Zr|QB 2 o, Fe 5 gCo 7 Ni 7 ZrgNb 2 B 20 r 
Fe 6 oCo 8 Zr,oMo 5 W 2 B] 5 , and Co 56 Fe] 6 Zr 8 B 2 o amorphous alloys. 


Alloy 

Maximum 

sample thickness Thermal stability 


r,(K) 

Ar,(K) 

T IT 

1 gi 1 

ES56C07N i 7 Zr 1 qB 20 

2 

814 

73 

0.60 

Fe5gCo7Ni7Zr8Nb2B2o 

2 

828 

85 

- 

F 656 Co 7 Zr 10 M 05 W 2 B 15 

6 

898 

64 

0.63 

CO56B®16Zr8B20 

- 

839 

39 

- 


Figure 1 shows the outer morphology of the bulk 
Fe 6 oCo 8 ZrioMo 5 W 2 Bi 5 cylinders with diameters of 3 and 5 
mm. These samples have smooth surface and metallic luster. 
No contrast of a crystalline phase is seen over the outer sur¬ 
face. The x-ray diffraction patterns showed a main halo peak 
with a wave vector Kp{ = 47r sin 6/X) around 29.6 nm"^ and 
no crystalline peak is observed even for the 5 mmcf) sample. 
The optical micrographs of the cross section of the two 
samples also revealed a featureless contrast in an etched state 
using a hydrogen fluoride acid. These results indicate that the 
bulk cylinders are composed of an amorphous phase in the 
diameter range up to 5 mm. It is to be noticed that the maxi¬ 
mum thickness (^max) is about 3 times larger than the largest 
value (2 mm for Fe 72 Al 5 Ga 2 PioC 6 B 4 Si 2 ,) for Fe-based amor¬ 
phous alloys reported up to date. Figure 2 shows the DSC 
curves of the bulk amorphous Fe 56 Co 7 Ni 7 Zr 8 Nb 2 B 2 o and 
Fe 6 oCo 8 ZrioMo 5 W 2 Bi 5 cylinders of 1 to 3 mm in diameter 
and Co 56 Fei 6 Zr 8 B 2 o of 1 mm in width. These amorphous 
alloys exhibit the sequential transition of glass transition, su¬ 
percooled liquid and crystallization. The supercooled liquid 
region, defined by the difference between the glass 

transition temperature (Tg) and the onset temperature of 
crystallization (T^) is as large as 39 to 85 K and the crystal¬ 
lization from the supercooled liquid occurs through a distinct 



FIG. 3. Frequency dependence of real (/x.') and imaginary (/x") parts of 
permeability for amorphous Co 56 Fei 6 Zr 8 B 2 o alloys of 1 mm in width sub¬ 
jected to annealing for 600 s at 750 and 800 K. 









6328 J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Inoue et al. 


TABLE II. Magnetic properties (/,, at 1 kHz and of Fe 56 Co 7 Ni 7 Zr,oB 2 o, Fe 56 Co 7 Ni 7 Zr 8 Nb 2 B 2 o, and 

Co 56 Fei 5 Zr 8 B 2 o amorphous alloys. 


Alloy 



Soft magnetic properties 



/.(T) 


/A,(lkHz) 

M,(1MHz) 

X.dO-'*) 

r,(K) 

F'^56Co7Ni7Zr 10 B 20 

0.96 

2.0 

19 100 

- 

10 

594 

Fe56Co7Ni7Zr8Nb2B2o 

0.75 

1.1 

25 000 

- 

13 

531 

Co56Fei6Zr8B2o 

0.77 

8.3 

17 100 

5500 

14 

- 


exothermic reaction. The crystallites were identified to con¬ 
sist of a-Fe, Fe 2 Zr, FegB, MoB, and W 2 B phases for the 
Fe 6 oCo 8 ZrioMo 5 W 2 Bi 5 sample heated to the temperature just 
above the exothermic peak. Thus, the crystallization is due to 
the simultaneous precipitation of the five crystalline phases. 
This crystallization mode is in agreement with that^ for other 
bulk amorphous alloys. The largest is 85 K for 
Fe 56 Co 7 Ni 7 Zr 8 Nb 2 B 2 o, being larger than the largest values 
(57 to 67 K) for Fe-(A1, Ga)-(P, C, B, and nonfer- 

rous Pd- and Pt-based amorphous alloys.*^ ’^ 

Table I summarizes the and TgfT^ of the 

Fe-(Co, Ni)-M-B amorphous alloys. We also evaluated the 
reduced glass transition temperature (Tg/T^). The was 
1420 K for Fe 56 Co 7 Ni 7 ZrioB 2 o and 1416 K for 
Fe 6 oCo 8 ZrioMo 5 W 2 Bi 5 and the TglT^ was evaluated to be 
0,60 for the former alloy and 0.63 for the latter alloy. Con¬ 
sidering that TglTf^ is 0.54 for FcgoP 12 ^ 454 ^^ and 0,57 for 
Fe 73 Al 5 Ga 2 PiiC 4 B 4 Sii,^^ the present TglT^ values are be¬ 
lieved to be the highest among all Fe-based amorphous al¬ 
loys. 

Figure 3 shows the real and imaginary parts of perme¬ 
ability (/x' and (jJ'), respectively, as a function of frequency 
(/) for the Co 56 Fei 6 Zr 8 B 2 o amorphous ribbon of 1 mm 
width. The />t' of the Co 56 Fei 6 Zr 8 B 2 o ribbon keeps high val¬ 
ues of 17 100 to 5500 in the high frequency range up to 1 
MHz and decreases with a further increase in frequency to 10 
MHz. It is to be noticed that the frequency at which the 
maximum /x" is obtained for the ribbon is as high as about 1 
MHz. The ) data indicate that the Co-Fe-Zr-B alloy 
can keep high yu' values up to 1 MHz of the maximum /x" 
point. The yu' value is much higher than those for the 
Fe-Si-B amorphous ribbon with the same width of 1 mm 
over the whole frequency range. Furthermore, the ji' values 
of the Co 56 Fei 6 Zr 8 B 2 o alloy is higher than those for the 
Co-Fe-Ni-Mo-Si-B amorphous alloy with zero in the 
high frequency range above 10 kHz. The electrical resistivity 
(Prt) of the Co 56 Fei 6 Zr 8 B 2 o alloy is 1.70 yLtOm, which is 
higher as compared with 1.34 yu fl m for Co 7 o, 3 Fe 4 7 BioSii 5 , 
1.37 yLcflm for Fe 78 Bj 3 Si 9 (METGLAS 2605S-2) and 
1.42 ytxam for the Co-Fe-Ni-Si-B METGLAS 2714A 
alloy. Consequently, the excellent high-frequency perme¬ 
ability for the present alloys is probably due to the decrease 
in eddy current loss resulting from the higher It is con¬ 
cluded that the present Co-based amorphous alloys have 
good soft magnetic properties and high stability of super¬ 
cooled liquid against crystallization. 

Table II summarizes the yu-^ at 1 kHz and 

for the new amorphous Fe-(Co, Ni)-M-B alloys. These 
amorphous alloys exhibit good soft magnetic properties in an 


annealed (800 K, 300 s) state, i.e., high of 0.74 to 0.96 T, 
low //^ of 1.1 to 3.2 A/m, high of 12 000 to 25 000 and 
low of lOX 10“^ to 14X 10”^. The and ytt. are supe- 
rior to those for conventional Fe-Si-B amorphous ribbons, 
presumably because of the lower • 

Finally, the reason for the large and for the 
Fe-based amorphous alloys is discussed in the framework of 
the three empirical rules for the achievement of high glass¬ 
forming ability. The base composition is the Fe-Zr-B sys¬ 
tem which satisfies the three empirical rules. The addition of 
Nb, Ta, Mo, and W is effective for the increase in the degree 
of the satisfaction of the empirical rules. That is, the addition 
of these elements causes the more sequential change in the 
atomic size in the order of Zr^Nb>W>Mo>Fe>Co>B as 
well as the generation of new atomic pairs with various nega¬ 
tive heats of mixing. In the supercooled liquid in which the 
three empirical rules are satisfied at a high level, the topo¬ 
logical and chemical short-range orderings are enhanced, 
leading to the formation of a highly dense random packed 
structure with low atomic diffusivity. The largest ATj,. is 85 
K for Fe56Co7Ni7Zr8Nb2B2o and 35 K for Co56Fei6Zr8B2o 
and the reaches 5 mm for Fe 6 oCo 8 Zr|oMo 5 W 2 Bi 5 . Fur¬ 
thermore, these bulk amorphous alloys exhibit good soft 
magnetic properties. These novel characteristics allow us to 
expect that the new Fe- and Co-based bulk amorphous alloys 
are used as engineering materials. 


^Materials Science of Amorphous Metals, edited by T. Masumoto (Ohmu, 
Tokyo, 1982). 

^M. Hagiwara, A. Inoue, and T. Masumoto, Met. Trans. A 13, 373 (1982). 

^A, Inoue, T. Zhang, and T. Masumoto, Mater. Trans. JIM 30, 965 (1989). 

'^A. Inoue, K. Ohtera, K. Kita, and T. Masumoto, Jpn. J. App!. Phys., Part 
2 27, L2248 (1988). 

^A. Inoue, T. Zhang, and T. Masumoto, Mater. Trans. JIM 31, 177 (1990). 

^A. Inoue, N. Nishiyama, and T. Matsuda, Mater. Trans. JIM 37, 181 
(1996). 

^ A. Inoue, T. Zhang, and T. Masumoto, J. Non-Cryst. Solids 156-158, 473 
(1993). 

®A. Inoue, Mater. Trans. JIM 36, 866 (1995). 

^A. Inoue, Mater. Sci. Forum 179-181, 691 (1995). 

’‘^A. Inoue, Mater. Sci. Eng. A 226-228, 357 (1997). 

A. Inoue and J. S. Gook, Mater. Trans. JIM 36, 180 (1995). 

’^A. Inoue and J. S. Gook, Mater. Trans. JIM 36, 1282 (1995). 

’^A. Inoue and J. S. Gook, Mater. Trans. JIM 37, 32 (1996). 

^"^A. Inoue, Y. Shinohara, and J. S. Gook, Mater. Trans. JIM 36, 1427 

(1995). 

^^A. Inoue, A. Takeuchi, T. Zhang, A. Murakami, and A. Makino, IEEE 
Trans. Magn. 32, 4866 (1996). 

'^H. S. Chen, Mater. Sci. Eng. 25, 151 (1976). 

S. Chen, J. Appl. Phys. 9, 3289 (1978). 

^^A. Inoue and R. E. Park, Mater. Trans. JIM 37, 1715 (1996). 

*^C. H. Smith, Rapidly Solidified Alloys, edited by H. H. Liebermann (Mar¬ 
cel Dekker, New York, 1993), p. 617. 



JOURNAL OF APPLIED PHYSICS VOLUME 83, NUMBER II I JUNE 1998 

Influence of Si addition on thermal stability and soft magnetic properties 
for Fe-AI-Ga-P-C-B glassy alloys 

T. Mizushima and A. Makino 

Central Research Laboratory, Alps Electric Co., Ltd., 1-3-5 Higashitakami, Nagaoka 940, Japan 

A. Inoue 

Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-77, Japan 

The thermal stability of the supercooled liquid region (AT^), defined by the difference 
between crystallization temperature {Tf) and glass transition temperature (7^), and soft 
magnetic properties were investigated for Fe 7 oAl 5 Ga 2 Pi 2 . 65 -;cC 5 . 75 B 4 . 6 Si;c(-^ = 0“4) and 
Fe 77 Al 2 .i 4 Gao. 86 Pii-;cC 5 B 4 Si^(:t = 0-3) glassy alloys. The thermal stability, glass forming ability 
and effective permeability at 1 kHz are improved with the replacement of P by 1-3 at. % Si 
for Fe7oAl5Ga2Pi2.65-xC5.75B4.6Sijc and by 1-2.6 at. % Si for Fe 77 Al 2 .i 4 Gao. 86 Pii-xC 5 B 4 Si^. The 
A 7^ and the maximum thickness for glass formation (fmax) reach maximum values of 60 K and 280 
yum, respectively, for Fe 7 oAl 5 Ga 2 Pi 2 . 65 -xC 5 . 75 B 4 6Si;^ and 34 K and 220 yum, respectively, for 
Fe 77 Al 2 .i 4 Gao. 86 Pii-xC 5 B 4 Si;,. at Si(at. %)/(Si(at. %)+P(at. %))=0.24. Core losses for 
Fe 77 Al 2 .i 4 Gao. 86 P 8 . 4 C 5 B 4 Si 2 6 glassy alloy is much lower than that for amorphous Fe-Si-B alloy at 
the sheet thickness more than 70 pm. Therefore, it can be said that the Fe-Al-Ga-P-C-B-Si 
glassy alloys are useful for inductive applications because of their bulky shape and good soft 
magnetic properties. © 1998 American Institute of Physics. [80021-8979(98)47211-6] 


Since the discovery of good soft magnetic properties for 
Fe-based amorphous alloys,the development of thicker 
ferromagnetic amorphous alloy sheets has been desired for 
further extension of application fields for these alloys. The 
thicker sheets have been also desired because the reduction 
of lamination process for transformers and/or inductors is 
expected by using thicker sheets. Furthermore, lamination 
factor will be improved with use of thicker sheets. However, 
to date, it has been known that the preparation of amorphous 
sheets with thicknesses over 100 pm was very difficult be¬ 
cause of the necessity of high cooling rates resulting from 
their low glass-forming ability.^ Recently, bulk glassy alloys 
have been formed in multicomponent Mg-,'^’^ Ln-,^’^ Zr-,^“^^ 
and Pd-^^ based (Ln=lanthanide metal) alloy systems. These 
bulk glassy alloys have a wide supercooled liquid region 
above 60 K before crystallization. There is a clear tendency 
for the glass-forming ability to increase with increasing 
A Ty .. The above mentioned glassy alloys always satisfy the 
following three empirical rules^^“^^ for achievement of a 
large glass-forming ability; i.e., (1) multicomponent alloy 
systems consisting of more than three elements, (2) signifi¬ 
cantly differential atomic size ratios above about 12% among 
the main constituent elements, and (3) negative heats of mix¬ 
ing among their elements. Based on the three empirical rules, 
we have searched for new Fe-based glassy alloys with a wide 
supercooled liquid region before crystallization. As a result, 
we have already reported that the Fe-based glassy alloy 
sheets with thicknesses up to 190 pm were prepared by us¬ 
ing a melt spinning technique in Fe-(A1, Ga)-(P, C, B, Si) 
where the three group elements satisfied the three empirical 
rules. We have tried to further investigate the composition 
to prepare a much thicker sample. This paper investigates the 
influence of Si addition on the thermal stability of the super¬ 
cooled liquid region and the soft magnetic properties for Fe- 


Al-Ga-P-C-B glassy alloys with various Fe concentrations 
and possibility of producing a thick glassy alloy sheet with 
good soft magnetic properties. 

Multicomponent Fe7oAl5Ga2Pi2.65-;cC5.75B4.6Si;c(3: 
= 0-4) and Fe 77 Al 2 .i 4 Gao. 86 Pii-xC 5 B 4 Si;,(x = 0-3) alloys 
were used in the present study because the highest perme¬ 
ability (/^e) at 1 kHz and the largest saturation magnetization 
{(Ts) for alloys having a supercooled liquid region 
in the Fe-Al-Ga-P-C-B system were obtained for 
Fe7oAl5Ga2Pi2.65Q.75B4.6 Fe77Al2.i4Gao86PllC5B4, 

respectively.^^ The alloy ingots were prepared by induction 
melting the mixtures of pure Fe, Al, and Ga metals, pre¬ 
melted Fe-P and Fe-C and pure crystalline boron in an ar¬ 
gon atmosphere. Rapidly solidified alloy sheets with various 
thicknesses ranging from 15 to 320 pm were prepared, 
through the control of roll velocity, by a single roll melt 
spinning method. The amorphous nature was confirmed by 
x-ray diffraction. The thermal stability associated with the 
glass transition, the supercooled liquid region and crystalli¬ 
zation were examined by differential scanning calorimetry 
(DSC) of a heating rate of 0.67 K/s. The magnetic properties: 
saturation magnetization (cr^), coercive force {Hf}, perme¬ 
ability {pf) at 1 kHz, saturation magnetostriction (X^) and 
core loss (W) were measured at room temperature with a 
vibrating sample magnetometer (VSM), sl B-H loop tracer, 
an impedance analyzer, a three-terminal capacitance appara¬ 
tus and a single sheet tester (SST), respectively. 

Figure 1 shows the DSC curves for the melt- 
spun F^7oA^l5C^a2Pi2.65-A:Q75B4.6SiA:(-^“0-4) and 
Fe 77 Al 2 .i 4 Gao. 86 Pii-;cQB 4 Si;j.(x = 0-3) alloy sheets with a 
thickness of about 30 pm as a function of Si content. One 
can see an increase in specific heat (endothermic reaction) 
due to a glass transition, followed by a supercooled liquid 
region for the samples containing jc = 0 to 3 at. % for 


0021 -8979/98/83(11 )/6329/3/$15.00 


6329 


© 1998 American Institute of Physics 



6330 J. Appl. Phys., Vol. 83, No. 11,1 June 1998 


Mizushima, Makino, and Inoue 



FIG. 1. Changes in DSC curves for the FcyoA l 5 Ga 2 Pi 2 . 65-.^^5 7584 68 !^ and 
Fe 77 Al 2 .i 4 Gao, 86 Pn-jcC 5 B 4 Sijf alloy sheets with a thickness of about 30 /Ltm 
as a function of Si content. 


^^ 70 ^ 15 ^^ 2 ^ 12 . 65 -^:^ 5 . 75 ^ 4 . 6 ^ 1 ^: X —Oat. % for 

Fe 77 Al 2 .i 4 Gao. 86 Pii-xC 5 ^ 4 Sijc and then an exothermic reac¬ 
tion, indicating that crystallization of the amorphous phase 
takes place through a single stage. The latter leads to simul¬ 
taneous precipitation of more than two kinds of crystalline 
phase, including a-Fe, Fe 3 B, Fe 3 P, Fe 2 B, and Fe 3 C. A su¬ 
percooled liquid region and two exothermic peaks due to the 
two-stage crystallization are observed for the samples con¬ 
taining 4 at. % Si for Fe7oAl5Ga2Pi2.65-.^C5.75B4.6Six and 
^2 at. % Si for the Fe 77 Al 2 .i 4 Gao, 86 Pii--;cG 5 B 4 Sijj.. The first 
and second peaks are due to the crystallization of a-Fe and 
Fe 3 B and of Fe 3 P, Fe 2 B and Fe 3 C for both alloy series. 

Figures 2(a) and 2(b) plot the and r^ax as a function 
of Si content. The AT^ increases with increasing Si content 
up to 3 at. % for Fe 70 Al 5 Ga 2 P 12 . 65 -jcG 5 . 75 B 4 6 Si^ and up to 2.6 
at. % for Fe 77 Al 2 .i 4 Gao. 86 Pii-jcG 5 B 4 Si;,, then decreases rap¬ 
idly. There is a clear tendency for to increase with in¬ 
creasing 

Figure 3 shows the relation between the ratio of to 
ATj^ atx = 0 at. % (Ar;^/Ar^(Si =0 at. %)) and the ratio of 
Si content to total Si and P content (Si/(Si+P)). The 
Ar^/A7;,(Si=0 at. %) increases with increasing Si/(Si+P), 
and reaches the maximum value at Si/(Si+P) = 24%, then 
decreases with increasing (Si/(Si+P)) for both alloy series. 
This fact indicates that the replacement of P by Si as 
Si/(Si+P) = 24% causes the greatest increase in AT^ and 
for Fe-Ga-Al-P-C-B-Si glassy alloys. 

It is important to achieve high thermal stability of the 
supercooled liquid for increase in the glass forming ability. 
That is, the necessity of long-range rearrangements of the 
constituent elements causes the retardation of the crystalliza¬ 
tion reaction, leading to the high stability of the supercooled 
liquid region and the large glass forming ability. It is there¬ 
fore presumed that the atomic rearrangements are most dif¬ 
ficult in case of Si/(Si+P)= 24% for these alloys. The atomic 
sizes of the metalloids change in the order Si>P>B>C. The 
increase in the variety of atomic sizes also implies that the 
atomic rearrangement for the precipitation reaction becomes 
difficult. Furthermore, the similarity of the atomic sizes and 
the large negative heats of mixing^^ between P and Si allow 
us to presume that Si is preferentially dissolved into Fe 3 P 
and the precipitation of the Fe 3 (P, Si) phase becomes more 



FIG. 2. The changes of (a) the AT^. and (b) the the 

F^70^l5G^2Pl2.65-JcQ.75^4.6Sb ^^77^^.146^30.86^1)-j»:QB4Si^ alloy 

sheets with a thickness of about 30 /tm as a function of Si content. 

difficult as a results of the need for the rearrangements of 
two kinds of metalloid atoms. This mechanism is thought to 
cause the most effective extension of the supercooled liquid 
region when the P element in these glassy alloys is replaced 
by Si such that Si/(Si+P) = 24%. 

Figures 4(a), 4(b), and 4(c) show the dependence of , 
juL^ and X, on Si content for Fe 7 oAl 5 Ga 2 Pi 2 . 65 -jcG 5 . 75 B 4 . 6 Si.r 
and Fe 77 Al 2 .i 4 Gao. 86 Pii-jcG 5 B 4 Si^ glassy alloys for a sample 
thickness of 30 ^tm. The of these glassy alloys are below 
3 A/m up to 3 at. % Si for Fe 7 oAl 5 Ga 2 Pi 2 . 65 -.rG 5 . 75 B 4 , 6 Si;,. 
and up to 2.6 at. % Si for Fe 77 Al 2 .i 4 Gao. 86 Pii-jcG 5 B 4 Si^. On 
the other hand, the drastically increases beyond 3 at. % Si 
and 2.6 at. % Si, respectively, for the two systems. The jul^ 
increases with increasing Si content up to 3 at. % Si for 
Fe 7 oAl 5 Ga 2 Pi 2 . 65 -;i:G 5 . 75 B 4 6Si^ and up to 2.6 at. % Si for 
Fe 77 Al 2 .i 4 Gao.g 6 Pii-;cG 5 B 4 Si;t, then decreases for higher Si 
contents. The influence of Si addition on and is not 
reflected in the data for X^, and may be related to the glass 
forming ability. It is, therefore, speculated that the alloys of 
higher glass forming ability have a more homogeneous struc¬ 
ture thus giving superior soft magnetic properties. A detailed 
investigation of the microstructure is expected to shed some 
light on the reason for the effect of Si addition on the soft 
magnetic properties. 



FIG. 3. The relation between the ratio of AT^ to ATj^ at Si free 
(AT;(/Arj.(Si=0 at. %)) and the ratio of Si content total Si and P content 
(Si/(Si+P)). 






J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 



Si content (at*/4) 


FIG. 4. The influence of Si content on (a) , (b) and (c) for the 

Fe7oAl5Ga2Pi2.65-;cC5 75B4 6Si;f and Fe77Al2.i4GaQ86Pji_^C5B4Si^ alloy 
sheets with a thickness of about 30 /i,m. 


Figure 5 shows the changes in core losses at f— 50 Hz 
and 5^=1.0T as a function of sample thickness for 
Fe 77 Al 2 .i 4 Gao. 86 P 8 . 4 C 5 B 4 Si 2.6 gl^ssy alloy and amorphous 
Fe 78 Si 9 Bi 3 alloy. The structure of both samples confirmed by 
x-ray diffractometry are also shown in Fig. 5. The core loss 
for the Fe 77 Al 2 .i 4 Gao 86 ^ 8 . 4 ^ 564812.6 is under 0.3 W/kg at the 
thickness up to 210 yam. However, that for amorphous 
Fe 78 Si 9 Bi 3 alloy is over 0.3 W/kg at the thickness over 70 
yam, and rapidly increase over 100 yam, because of precipi¬ 
tation of 6036 crystalline phase. It is well known that the 
precipitation of crystalline makes the soft magnetic proper- 



0 50 100 Y90 200 250 

ThIcknMs, r/^m 


FIG. 5. Changes in core losses at/=50 Hz and 5,„= 1.0 T as a function of 
sample thickness for Fe 77 Al 2 .i 4 Gao. 86 P 8 . 4 C 5 B 4 Si 2,6 glassy alloy and amor¬ 
phous Fe 78 Si 9 Bj 3 alloy. The structure of both sample confirmed by x-ray 
diffractometry are also shown. 


Mizushima, Makino, and Inoue 6331 



0.1 1 2 


Muimum induction field, B / T 

ID 

FIG. 6. Changes in core losses at 50 Hz for Fe 77 Al 2 ,i 4 Gao. 86 P 8 . 4 C 5 B 4 Si 2.6 
alloy sheet, Fe 78 Si 9 B |3 amorphous ribbon and 6.5% Si-steel with a thickness 
of about 100 yLtm as a function of . 

ties inferior. Therefore, it can be said that the amorphous¬ 
ness of Fe-Al-Ga-P-C-B-Si glassy alloy is much higher 
than that of amorphous Fe-Si-B alloy. 

Figure 6 shows the core losses at 50 Hz for 
Fe 77 Al 2 .i 4 Gao. 86 P 8 . 4 C 5 ^ 4 Si 2.6 g^Assy alloy, amorphous 
Fe 78 Si 9 Bi 3 alloy and for 6.5% silicon steel,having 
in each case a thickness of 100 yam, as a function of maxi¬ 
mum magnetic flux density (B^). The core loss for 
Fe 77 Al 2 .i 4 Gao. 86 P 8 . 4 C 5 B 4 Si 2.6 glassy alloy is much lower than 
those of other magnetic alloys for the whole range of . 
Viewed in this light, Fe-Al-Ga-P-C-B glassy alloys con¬ 
taining Si can be regarded as having good potential as bulk 
soft magnetic materials. 

^T. Mizoguchi, K. Yamauchi, and H. Kiyajima, Amorphous Magnetism 
(Plenum, New York, 1973), p. 325. 

^H. Fujimori, T. Masumoto, Y. Obi, and M. Kikuchi, Jpn. J. Appl. Phys. 
13, 1889 (1974). 

^M. Hagiwara, A. Inoue, and T. Masumoto, Sci. Rep. Res, Inst. Tohoku 
Univ. A 29, 351 (1981). 

'^A. Inoue, K. Ohtera, K. Kita, and T. Masumoto, Jpn. J. Appl. Phys., Part 
2 30, L2248 (1988). 

^ A. Inoue, M. Kohinata, A. P. Tsai, and T. Masumoto, Mater. Trans., JIM 

30, 378 (1989). 

^ A. Inoue, T. Zhang, and T. Masumoto, Mater. Trans., JIM 30, 965 (1989). 
^ A. Inoue, H. Yamaguchi, T. Zhang, and T. Masumoto, Mater. Trans., JIM 

31, 104 (1990). 

^ A. Inoue, T. Zhang, and T. Masumoto, Mater. Trans., JIM 31, 177 (1990). 
^T. Zhang, A. Inoue, and T. Masumoto, Mater. Trans., JIM 32, 1005 
(1991). 

A. Peker and W. L. Johnson, Appl. Phys. Lett. 63, 2342 (1993). 

^‘T. Zhang, A. Inoue, and T. Masumoto, Mater. Trans., JIM 32, 1005 
(1991). 

^^A. Inoue, N. Nishiyama, and T. Matsuda, Mater. Trans., JIM 37, 181 
(1996). 

^^A. Inoue, Mater. Sci. Forum 179-181, 691 (1995). 

^"^A. Inoue, Mater. Trans., JIM 36, 691 (1995). 

^^A. Inoue, Sci. Rep. Res. Inst. Tohoku Univ. A 42, 1 (1996). 

^^T. Mizushima, A. Makino, and A. Inoue, IEEE Trans. Mag. (in press). 
^^T. Mizushima, A. Makino, and A. Inoue, Sci. Rep. Res. Inst. Tohoku 
Univ. A 43, 123 (1997). 

^^F. R. de Boer, R. Boom, W. C. M. Mattens, A. R. Miedema, and A. K. 

Niessen, Cohesion in Metals (Elsevier Science, Amsterdam, 1988), p. 236. 
^^H, N. Ok and Morrish, J. Appl. Phys. 52, 1835 (1981). 

^®Y. Takada, M. Abe, S. Masuda, and J. Inagaki, J. Appl. Phys. 64, 5367 
(1988). 






JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Application of nanocrystalline soft magnetic Fe-M-B (M=Zr, Nb) alloys 
to choke coils 

Y. Naitoh, T. Bitoh, T. Hatanai, and A. Makino 

Central Res. Lab., Alps Electric Co., Ltd., Nagaoka 940, Japan 

A. Inoue 

Institute for Materials Research, Tohoku University, Sendai 980-77, Japan 

We have developed a choke coil made of new nanocrystalline soft magnetic Fe-M-B (M=Zr, Nb) 
alloys (“NANOPERM'T^ ” material) which exhibit high saturation magnetic induction {Bf}, above 

1.5 T, excellent soft magnetic properties and zero magnetostriction. A choke coil made of 
NANOPERM^m material exhibits good dc bias characteristics of inductance because of the high . 

Furthermore, the choke coil made from NANOPERM^^ material showed l/3rd the temperature rise 
shown by a core made from Fe-Si-B amorphous alloy. The low core loss and high B^ of 
NANOPERM™ material allow the reduction of the core size. It is concluded that NANOPERM'^^ 
is suitable as a core material for choke coils. © 1998 American Institute of Physics. 
[80021-8979(98)36611-6] 


I. INTRODUCTION 

In increasing instances the reactors of phase modifying 
equipment are disabled by line current which contains higher 
harmonic distortion generated by switching regulators, etc. 
Line current correction to sinusoidal wave by using active 
filters is a useful method to prevent distortion in the reactors. 
High saturation magnetic induction (B^) and low core loss 
are required for the core material of choke coils as active 
filters because high frequency current with large amplitude 
superimposed on direct current flows into the choke coil. It 
has been reported by us that new nanocrystalline soft mag¬ 
netic Fe-M-B (M=Zr, Nb) alloys (“NANOPERM™ ” ma¬ 
terial) show high B, above 1.5 T, excellent soft magnetic 
properties, low core losses and sufficiently small 
magnetostriction.^"'^ Figure 1 shows the relation between B^ 
and permeability at 1 kHz for NANOPERM^^ material 
and other soft magnetic materials. NANOPERM^^^ material 
is found to be situated in the top right corner of the figure. 
NANOPERM'^^ material is therefore expected to be used as 
core material for choke coils as active filters. In this article, 
we report the characteristics of the choke coil made of 
NANOPERM™ material. 

II. EXPERIMENTAL PROCEDURE 

The Fe 84 Zr 3 5 Nb 3 5 B 8 CU 1 alloy was selected an example 
of NANOPERM''^^ material in this study. The 
NANOPERM^M ribbon with 20 /am in thickness was pro¬ 
duced by using a single-roller melt-spinning method in an Ar 
atmosphere. In order to compare the magnetic properties, a 
commercial Fe 78 Si 9 Bj 3 amorphous alloy (METGLAS® alloy 
2605 S-2) ribbon with the same thickness as the 
NANOPERM™ material was prepared. Table I shows typi¬ 
cal magnetic properties for the alloys.^’^ 

Toroidal samples were prepared as follows. A mixture of 
MgO powders and sodium silica solution (water glass) was 
applied to both sides of the ribbons to prevent electrical con¬ 
tact between the ribbons. The ribbons were wound into tor¬ 


oidal cores with 38 mm in outer diameter, 23 mm in inner 
diameter and 15 mm in height. The annealing treatment of 
the cores was carried out in vacuum by keeping the cores at 
953 K for 600 s (NANOPERM^m) or at 643 K for 7.2 ks 
(Fe-Si-B amorphous alloy). The annealed cores were en¬ 
capsulation in an epoxy resin. Then the cores were processed 
by cutting a 2 mm air gap and inserting an insulating mate¬ 
rial in the gap. 

Measurements of core losses were carried out using an 
ac B-H analyzer after annealing, after encapsulation, and 
after introducing an air gap. dc bias characteristics were mea¬ 
sured after introducing an air gap. 

III. RESULTS AND DISCUSSION 

Table II shows the size, the lamination factor and the 
effective cross section of the cores. The size of the cores is 
almost the same. Figure 2 shows the change in core loss of 
the cores after annealing, encapsulation, and introducing an 



FIG. 1. Relationship between and at 1 kHz for NANOPERM'^’^, the 
nanocrystalline Fe-Si-B-Nb-Cu alloys (Ref. 5) and conventional soft 
magnetic materials. 


0021 -8979/98/83(11 )/6332/3/$15.00 


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© 1998 American Institute of Physics 




J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Naitoh et at. 


6333 


TABLE L Typical example of the saturation induction (B^), permeability (/x), core loss (IV), and saturation 
magnetostriction (\J for the alloys (Refs. 3 and 6). 





1/^1 


W (W/kg) 


Alloys 

Bs{T) 

1 kHz 

100 kHz 

1 kHz, 

IT 100 kHz, 0.1 T 

X,(10-«) 

nanoperm™ 

1.53 

100 000 

18 000 

1.1 

15 

~0 

Fe-Si-B amorphous alloy 

1.56 

10 000 

5 000 

4.0 

48 

+ 27 


TABLE II. Outer diameter (OD), inner diameter (ID), height (H), lamina¬ 
tion factor {K), and effective cross section (5). 


Alloys 

OD 

(mm) 

ID 

(mm) 

H 

(mm) 

K 

(%) 

S 

(mm2) 

NANOPERM™ 

37.1 

23.2 

15.5 

11.\ 

79.0 

Fe-Si-B amorphous 

36.9 

22.9 

15.5 

65.8 

71.4 

alloy 








the air gap 


Process 


FIG. 2. Change in the core loss of the cores with annealing, encapsulation, 
and processing the air gap. 



FIG. 3. Change of inductance as a function of dc bias current (7^^) times 
number of turns {N) for choke coils made of NANOPERM"^^ and Fe-Si-B 
alloy. 


air gap. The core loss of NANOPERM'^^ core after anneah 
ing is about l/3rd as large as that of the Fe-Si-B core. After 
encapsulation in the epoxy resin, the core loss of the Fe- 
Si-B core showed a large increase due to stress from the 
resin. Since the magnetostriction of the Fe-Si-B amorphous 
alloy is large, the soft magnetic properties are inferior in the 
stressed state. On the other hand, the NANOPERM^m core 
exhibits almost the same low core loss value as that of the 
core before encapsulation because of its zero magnetostric¬ 
tion. The encapsulation treatment is necessary to cut an air 
gap. It can be said that the zero magnetostriction is necessary 
for the toroidal core with a gap to exhibit a low core loss. 
After introducing an air gap, the core loss increase in both 
NANOPERM™ and Fe-Si-B alloys. However, the 
NANOPERM™ core exhibits smaller core loss which is only 
l/5th that of the Fe-Si-B core. 

Figure 3 shows dc bias characteristics of the gapped 
cores with 25 turn coil. The inductance of the 
NANOPERM™ and the Fe-Si-B cores show a decrease 
around AX7=700 AT because the saturation magnetic in¬ 
ductions of both the core materials are almost equal. When 
leakage flux from the air gap can be neglected, inductance 
(L) of the gapped core can be written as 

L = N'^S j I 

where is gap length, / is length of magnetic path, fx is 
permeability of material, and fXQ is permeability of vacuum. 
When fji is much larger than , a term of (/ - lg)lfx can be 
neglected. Therefore, the inductance of the gapped core is 
independ of fx. However, although the NANOPERM™ and 
the Fe-Si-B cores have the same size and the same gap 
length, the inductance of the NANOPERM^m core is 10% 
larger than that of the Fe-Si-B core at a dc bias current of 
zero. The difference in inductances is caused by the differ¬ 
ence in effective cross sections of the cores. As shown in 
Table II, the effective cross section of the NANOPERM^m 
core is 14% larger than that of the Fe-Si-B core, which is in 
good agreement with the difference in inductances. 

Next, we have examined the relation between the choke 
coil loss and temperature rise (AT) of the choke cores. The 
miniaturization of the core is limited by and by the core 
loss of the core material. If the core loss is large, the core 
volume should be increased because maximum magnetic in¬ 
duction should be decreased to reduce AT. Figure 4 
shows the B^ dependence of the choke coil loss which con¬ 
sists of the core loss and the copper loss. The operating fre¬ 
quency is 50 kHz and 5^ is changed from 0.01 to 0.1 T. The 
choke coil loss is 4.2 W for Fe-Si-B alloy, and is 1.3 W for 


/“o/’ 


( 1 ) 



6334 


J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Naitoh et al 



FIG. 4. B,n dependence of the choke coil los.s, which consists of the core 
loss and the copper loss. 


NANOPERM™ material at B„=QA T. Figure 5 shows AT 
of the choke coils as a function of When 5„, = 0.1 T, 
A 7 is 34 K for the Fe-Si-B choke coil and 11 K for the 
NANOPERM'^^ choke coil, respectively. The AT of the 
NANOPERM™ choke coil is only 32% that of the Fe-Si-B 
one. In order to achieve a small AT of 11 K for Fe-Si-B 
core, it is necessary to reduce the value to 0.05 T. This 
means that core volume should be doubled for the Fe-Si-B 
choke coil. 

NANOPERM™ shows a high which is comparable to 
that of Fe-Si-B amorphous alloys, and its choke coil loss is 
only l/3rd that of Fe-Si-B amorphous alloys. The very low 
loss allows a reduction in core size. It is concluded that the 



FIG. 5. AT of the choke coils as a function of . 


size of the choke coils can be significantly reduced by re¬ 
placing the core material from Fe-Si-B amorphous alloys to 
NANOPERMTM. Therefore, NANOPERM^m material is suit¬ 
able as core material for the choke coils of active filters. 

^ K. Suzuki, N, Kataoka, A. Inoue, A. Makino, and T. Masumoto, Mater. 
Trans,, JIM 31, 743 (1990). 

^A. Makino, K. Suzuki, A. Inoue and T. Masumoto, Mater. Trans., JIM 32, 
551 (1991). 

^A. Makino, A. Inoue, and T. Masumoto, Mater. Trans., JIM 36, 924 
(1995). 

'‘a. Makino, T. Hatanai, A. Inoue, and T. Masumoto, Mater. Sci. Eng., A 
226-228, 594 (1997). 

^Y. Yoshizawa, S. Oguma, A. Hiraki and K. Yamauchi, Hitachi Metals 
Tech. Rev. 5, 13 (1989). 

^R. Hasegawa, J. Non-Cryst. Solids 61-62, 725 (1984). 




JOURNAL OF APPLIED PHYSICS VOLUME 83, NUMBER 11 lJUNE 1998 

Soft magnetic properties and structures of nanocrystalline 
Fe-AI-SI-B-Cu-Nb alloy ribbons 

B. J. Tate, B. S. Parmar, I. Todd, and H. A. Davies®* 

Department of Engineering Materials, University of Sheffield, Mappin Street, 

Sheffield SI 3JD, United Kingdom 

M. R. J. Gibbs 

Department of Physics, University of Sheffield, Hounsfield Road, Sheffield S3 7RH, United Kingdom 

R. V. Major 

Telcon Limited, Napier Way, Crawley, West Sussex RHIO 2RB, United Kingdom 

The effects of A1 on the magnetic properties of nanocrystalline Fe 73 5 _;fAlxSii 3 5 B 9 Cu 2 Nb 3 alloy 
ribbons, where 0 10, are reported for the first time. The evolution of the structure and magnetic 

properties of the ribbons, which were initially cast into the amorphous state in an inert gas 
environment at subatmospheric pressure, were studied as a function of annealing temperature Tann • 

The minimum dc coercivity developed during annealing, , was found to decrease significantly 
with increasing A1 content from 0.5 A/m at X=0 to 0.3 A/m at Z=2 and to remain at 
approximately this level over the range 2<X^8 before rising to 0.4 A/m at X= 10. The saturation 
polarization, 7^, was, however, found to decrease linearly over this range from 7^=1.5 T at Z 
= 0 to 75 = 0.9 T at Z= 10 for samples exhibiting 7/™". As there was little significant reduction in 
the mean crystallite size, dg , at 7/™" with increasing Z, this decrease in coercivity was considered 
to result from a reduction of the magnetocrystalline anisotropy, , of the crystallites as a result of 
the incorporation of Al. © 1998 American Institute of Physics. [80021-8979(98)49811-6] 


I. INTRODUCTION 

Nearly a decade ago Yoshizawa et aO of Hitachi Re¬ 
search Laboratories showed that small additions of Nb and 
Cu to a base FeBSi glass forming composition induce the 
initially amorphous as-spun ribbon to devitrify, on controlled 
annealing, to a nanocomposite structure of FeSi crystallites, 
of mean diameter 10-15 nm in a glassy matrix which is 
enriched in Nb and B. The Cu and Nb act, respectively, to 
maximize the number density of crystal nuclei and to retard 
grain growth, thus promoting the formation of an ultrafine 
grain structure. Contrary to classical behavior of pinning of 
domains at grain boundaries, for grain diameters (dg) 
^50 nm the coercivity diminishes with decreasing dg 
down to ^^0.5 Am”^ at ~ 10 nm while, correspondingly, the 
initial permeability /X/ increases to a peak value of — 10 ^. 
These properties are better than for amorphous Fe-based al¬ 
loys and are comparable with those of Co-based metallic 
glasses which has significant technoeconomic significance. 
Thus, this so-called Finemet© alloy has stimulated the curi¬ 
osity of a large body of magneticians and materials scien¬ 
tists. 

A number of workers have investigated the effects on 
the soft magnetic properties of the substitution of additional 
alloying elements for Fe in the Fe 73 5 Sii 3 5 B 9 CuiNb 3 alloy 
composition to further improve the properties [e.g., Co,^ Ap] 
as well as the substitution of Cr, V, Ta, etc., for Nb."^ No 
significant improvements in soft magnetic properties were 
reported over those of the base composition with the excep¬ 
tion of the study of Lim et al? which found that substitution 


^^Electronic mail: h.a,davis@shelfield.ac.uk 


of Al for Fe in Fe 73 5 _xAl;^Sii 3 5 B 9 CuiNb 3 in the range 0 
^Z^l improved the dc coercivity {Hf) but caused other 
soft magnetic properties, i.e., relative ac permeability (/x) 
and saturation magnetostriction (X^) to deteriorate. In this 
article we present initial data from an extensive study of 
F® 73 . 5 -xAlxSii 3 . 5 B 9 CuiNb 3 with O^Z^IO. The rationale 
behind this work is that ternary FeSiAl crystals exhibit lower 
Zj than those of the binary FeSi system and that the satura¬ 
tion magnetostriction X^ of the nanocrystallites can be 
readily controlled^ thus leading to the possibility of the de¬ 
velopment of alloys with lower X^ than Finemet®. 

II. EXPERIMENT 

A series of Fe 73 5 _jj^Al;fSii 3 5 B 9 Cu 2 Nb 3 alloy ingots with 
compositions in the range 0 ^Z=^i 0 were prepared by rf 
melting of high purity elements in a flowing Ar atmosphere. 
Ribbons of cross section typically 20 /xmX2.0 mm and sur¬ 
face roughness less than 1.5 /xm were prepared by melt spin¬ 
ning these ingots in helium at 1/3 atm ambient pressure. The 
resultant ribbons were cut into 100 mm lengths and thermal 
treatments were performed in an inert Ar atmosphere in a 
conventional furnace for 1 h after which the samples were 
allowed to air cool. The structure of the alloys, both in the 
as-cast state and after subsequent heat treatment, was con¬ 
firmed by x-ray diffraction using Co Ka radiation, and the 
mean crystallite size {dg) for the Fe-Si phase estimated 
from the half peak breadth of the ( 110 ) x-ray diffraction peak 
via the Scherrer equation. TEM was also employed for se¬ 
lective studies of the nanostructure and grain size. The satu¬ 
ration polarization (7^), , and X^ were measured using a 

vibrating sample magnetometer (VSM) hysteresis loop 


0021-8979/98/83(11)/6335/3/$15.00 


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© 1998 American Institute of Physics 




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J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Tate et ai 



Al content X (at.%) 



01234S6769 10 


Al content X (at.%) 



Al content X (at.%) 


FIG. 1. Variation in (a) the minimum coercivity (b) saturation po¬ 

larization (Jg), and (c) crystallite diameter {d^) for optimally annealed 
samples as a function of Al content X. 

tracer^ and the small angle magnetisation rotation (SAMR) 
method/ respectively. The loop tracer has been specifically 
designed for reliable and reproducible measurements of high 
IJi lovy He materials. 

III. RESULTS AND DISCUSSION 

The results presented in this section are for samples heat 
treated at an optimum annealing temperature (T^n) 
velop the minimum dc coercivity for each of the com¬ 
positions investigated. This was found to be 540 °C for X 
= 0 and 520 °C for all of the Al-containing compositions. 
Figure 1(a) shows the dependence of minimum coercivity 
as a function of Al substitution X, Following a substan¬ 
tial (40%) initial decrease, from 0.5 A/m at X=0 to 0.3 A/m 
for X = 2 remains approximately constant at 0.3 A/m up 
to X = 8 at. %; it then increases to 0.4 A/m at X= 10 at. %. 
The effect of substituting Fe for Al on the magnitude of 
can be seen in Fig. 1(b). The linear decrease in , from 1.5 



0123456789 10 

Al content X (at.%) 

FIG. 2. Variation in the effective anisotropy (K), derived from Eq. (2), as a 
function of the aluminum content X of the alloys. 


T for the base composition to 0.9 T at X=10 (a rate of 
-0.06 T/at. % Al) is as might be expected for replacement 
of Fe by a nonferromagnetic component. Figure 1(c) shows 
that the aluminium content does not influence significantly 
the mean crystallite diameter for alloys in their optimum 
condition, i.e., dg remains constant at 10± 1 nm. This was 
also confirmed by direct observation of the alloy nanostruc¬ 
ture by TEM. This observation contrasts with that of Lim 
et al? who reported dg to decrease upon the addition of 0.1 
at. % Al and to remain constant thereafter although the mag¬ 
nitude of this decrease was not disclosed. 

These values of and allow the variation in effec¬ 
tive magnetocrystalline anisotropy (K) to be estimated as a 
function of X. By using the random anisotropy model 
(RAM) developed by Alben et al? for amorphous ferromag- 
nets Herzer^ showed that, for dg less than the exchange 
length Lex ('^40 nm), (X) could be approximated by 

{K)^K\dllA^ (1) 

and that and {K) were related thus 

= ( 2 ) 

'' S 


which leads to the following relationship between coercivity 
and grain diameter: 






(3) 


where is a constant and A is the exchange stiffness inside 
the crystal with all other symbols as previously defined. 
Assuming^ that the composition of the crystallites is 
Fe-20at. % Si and A= 1 X 10“^^ Jm"^ and Xi = 8 
X 10^ J m“^ and using the measured values of , 7^ and 
dg for the X = 0 alloy in Eq. (3) yields a value of 0.19 for the 
constant . Assuming that this value is applicable for the 
range of aluminium contents studied we can use the experi¬ 
mentally determined values of and to estimate {K) 
from Eq. (2). The variation in {K) with respect to X, derived 
in this way, is shown in Fig. 2. 

Equation (1) shows {K) to be strongly dependent upon 
both dg and Xj and, as such, both of these factors must be 








J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Tate et al. 


6337 


12 

(PPfll) 

8 


4 


0 


FIG. 3. Variation in the saturation magnetostriction (X^) as a function of 
alloy aluminium content, X. 


considered as possible reasons for the observed decrease. 
(K) varies as a so that a 1 nm decrease in dg could 
account for the change in (A^) shown in Fig. 2. As ± 1 mm is 
estimated to be the precision of the x-ray line broadening 
determination of dg it cannot be stated, on this basis, that it is 
the principal contribution to the decrease in (K). However, 
although it is difficult to establish the absolute value of dg to 
better than ± 1 nm by TEM owing to crystallite overlapping 
effects in the thin foil image, the observations indicated that 
no change occurred over the range of X studied and thus it is 
considered that the observed decrease in result prima¬ 
rily from a decrease in the magnetocrystalline anisotropy 
K,, 

The measured magnetostriction of the Al-alloys exhibit¬ 
ing minimum dc coercivity (Fig. 3) is significantly greater 
than that of the Al-free alloy, measured at optimum 
rising to a maximum of lOX 10“^ at X=2 from 3 X 10“^ at 
X=0 and falling as X increases further to a value of = 6 
X 10“^ in the range of 10 and are in good agreement 

with the results of Lim et al? for O^X^l. Figure 4 com¬ 
pares the dependence on annealing temperature of for the 
X~2 alloy of the present work and those of Yoshizawa 
et al? for the Finemet® composition. Clearly X^ is very sen¬ 
sitive to Tann in both alloys. In the case of the alloy contain¬ 
ing 2 at. % Al, for example, X^ falls to approximately zero 
after annealing at 550 °C for 1 h which is significantly 
smaller than the minimum value of 2.1 X 10“^ developed by 
the Al-free composition.^ An advantage of the Al containing 
alloys is that an ultralow coercivity is developed over a 
wider range of annealing temperatures than is the case for the 
Al-free composition, meaning that, if the X=2 alloy is opti¬ 
mized with respect to magnetostriction, for example, the co¬ 
ercivity exhibited in this condition is comparable with that of 
Finemet, i.e., Hc=0.5 A/m. 



0123456789 10 


Al content X (at.%) 



440 490 540 590 


T 


ann 


(”C) 


FIG. 4. Comparison of the response of saturation magnetostriction (\ J to 
annealing temperature forX=0 (Ref. 1) andX=2 (present work). 


IV. CONCLUSIONS 

The soft magnetic properties of nanocrystalline 
F^ 73 . 5 -xAlxSii 3 . 5 B 9 CuiNb 3 have been investigated in the 
range of O^X^ 10. It was found that the minimum dc coer¬ 
civity developed on annealing of the initially amorphous as- 
spun ribbons showed an initial decrease from 0.5 A/m at X 
= 0 to 0.3 A/m at X=2 after which shows little varia¬ 
tion up to X= 8 beyond which it increases to 0.4 A/m at X 
= 10. Over this same range of X the saturation polarization 
decreases linearly while dg was determined by x-ray meth¬ 
ods to remain at a constant 10 ± 1 nm and TEM confirmed 
that there was no change in the structure with increasing 
aluminium substitution. The saturation magnetostriction 
shows a marked increase over this range of X compared with 
the base alloy composition. The improvement in the dc co¬ 
ercivity has been attributed to a decrease in the effective 
anisotropy (K) of the alloy and this decrease has been as¬ 
cribed, on the basis of available evidence, to a decrease in 
the magnetocrystalline anisotropy of the nanocrystallites. We 
have also established that, by the optimization of the heat 
treatment temperature for the X=2 material a zero magne- 
tostrictive alloy with a dc coercivity comparable with that of 
Finemet is achieved. 

^Y. Yoshizawa, S. Oguma, and K. Yamauchi, J. Appl. Phys. 64, 6044 
(1988). 

^S. C. Yu, K. S. Kim, Y. S. Cho, and T. K. Kim, IEEE Trans. Magn. 28, 
2421 (1992). 

^S. H. Urn, W. K. Pi, T. H. Noh, H. J. Kim, and I. K. Kang, J. Appl. Phys. 
73,6591 (1993). 

"^Y. Yoshizawa and K. Yamauchi, Mater. Sci. Eng. A 133, 176 (1991). 
^M. Takahashi, S. Nishimaki, and T. Wakiyama, J. Magn. Magn. Mater. 
66, 55 (1987). 

^P. T. Squire, S. M. Sheard, C. H. Carter, and M. R. J. Gibbs, J. Phys. E 21, 
1167 (1988). 

^K. Narita, J. Yamasaki, and H. Fukunaga, IEEE Trans. Magn. MAG-16, 
435 (1980). 

®R. Alben, J. J. Becker, and M. C. Chi, J. Appl. Phys. 49, 1653 (1978). 
^G. Herzer, IEEE Trans. Magn. MAG-26, 1397 (1990). 





JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER II 


1 JUNE 1998 


Compositional dependence of the effective magnetic anisotropy 
in nanocrystalline Fe-Zr-B-(Cu) alloys 

P. Garcia Tello and J. M. Blanco 

Departamento Fisica Aplicada /, UPV/EHU, 20011, San Sebastian, Spain 

N. Murillo, J. Gonzalez, and R. Zuberek 

Departamento Fisica de Materiales, Facultad de Qmmicas, UPV/EHU, 20009, San Sebastian, Spain 

A. Slawska-Waniewska 

Institute of Physics, Polish Academy of Sciences, Warsaw, Poland 

J. M. Gonzalez 

Instituto de Ciencia de Materiales de Madrid, CSIC, Cantoblanco, 28049, Madrid, Spain 

Results are presented on the evolution with the thermal treatment parameters of the effective 
anisotropy and dispersion fields and of the saturation magnetostriction of samples having nominal 
compositions given by Fe 93 _;^Zr 7 Bj^Cu^ (jc = 6-8 and y = 0-2). From these data we conclude that 
the enhancement of the soft magnetic character of the samples induced by the anneals carried out in 
the temperature range 480-600 °C could be linked both to the decrease of the anisotropy field and 
to the reduced magnetostriction values resulting from the thermal treatments. © 1998 American 
Institute of Physics, [80021-8979(98)36711-0] 


I. INTRODUCTION 

FeZrB(Cu) crystalline alloys with ultrafine microstruc¬ 
tures show excellent soft magnetic properties and are re¬ 
garded as promising candidates for practical uses. These al¬ 
loys are prepared by partial crystallization of melt spun 
precursors resulting in the precipitation, from the amorphous 
matrix, of bcc Fe grains having a typical diameter of 10 nm.^ 

The basic mechanism responsible for the outstanding mag¬ 
netic properties of these nanocrystalline alloys is the averag¬ 
ing (over regions containing a large number of grains) of the 
easy directions of the local magnetocrystalline anisotropy.^ 

From a study of the effective anisotropy in FINEMET-type 
nanocrystalline alloys,^ it was possible to deduce that this 
averaging was based on the occurrence of intergranular cou¬ 
pling. It was also possible to evaluate the typical dimensions 
of the coupled units. Nevertheless, and since the reduction of 
the magnetic anisotropy from the value obtained in the amor¬ 
phous precursor down to that obtained in the nanocrystalline 
alloy was not sufficient to account for the reduction of the 
coercive force accompanying the nanocrystallization, the en¬ 
hancement of the magnetic softness was proposed to be also 
linked to the decrease of the microstructure-magnetization 
interactions.^ On the basis of these interactions there is the 
magnetoelastic coupling, and therefore, a reduced magneto¬ 
striction value is considered to be a crucial property to 
achieve extremely soft magnetic behavior. 

In the present work, we report on the dependence of the 
effective magnetic anisotropy on the annealing temperature 
for nanocrystalline FeZrB(Cu) alloys. Our results will be 
correlated with the evolution of the saturation magnetostric¬ 
tion, ks , during heat treatment. 

II. PREPARATION OF SAMPLES AND EXPERIMENTAL 
TECHNIQUES 

Amorphous alloys of nominal compositions PJQ 1 (a) Temperature dependence of the anisotropy field of the samples. 

Fe 93 _;^Zr 7 B^CUy (x=6-8 and y = 0-2) were prepared by (b) Temperature dependence of the dispersion field of the samples. 


the single-roller melt-spinning method and were annealed 
under on Ar atmosphere for 1 h at temperatures ranging from 
480 up to 650 ®C. 

The anisotropy field, , associated with the effective 
anisotropy, the dispersion field, associated 

with the inhomogeneities of the magnetization distribution, 
were determined, both in the as-quenched and the treated 
samples, from measurements of the transverse biased initial 



0 500 550 600 650 


(a) T,„„(C) 



0 500 550 600 650 


(b) T.„„(C) 


0021 -8979/98/83(11 )/6338/3/$15.00 


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© 1998 American Institute of Physics 




J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Garcia Tello et ai 6339 



FIG. 2. (a) Temperature dependence of the parameter, (b) Temperature 

dependence of the parameter in the studied samples. 

susceptibility, that purpose the original ribbons (3 

mm wide, 20 mm thick) were cut by acid etching into disks 
having diameter 3 mm. 

The transverse biased initial susceptibility, Xt > was mea¬ 
sured by applying simultaneously a saturating dc field, , 
along the directions of the easy and hard axes of the effective 
anisotropy and a small ac field, H 2 , directed perpendicular to 
Hi . We measured the magnetization component parallel to 
H 2 . The transverse biased initial susceptibility can be writ¬ 
ten as 

l/X, = //eff/M,, (1) 

where is the saturation magnetization and is given 
by 

+ + ( 2 ) 

In (2) the plus (minus) signs stand for the cases in which the 
saturating field is applied along the easy (hard) axes. In order 
to identify the macroscopic easy (hard) axis of our samples, 
the transverse biased initial susceptibility was measured in 
all of them by applying the saturating field along different 
in-plane directions. The saturation magnetostriction was 
measured, at room temperature, by means of the strain 
modulated ferromagnetic resonance (SMFMR) method with 
the magnetic field parallel to the ribbon plane. 

III. RESULTS 

Figures 1(a) and 1(b) show the treatment temperature, 
Tann» dependence of and , respectively, corresponding 
to all the samples studied. From our results it is apparent that 
the anisotropy field exhibited a minimum value (occurring at 



(a) T,„„(C) 



FIG. 3. (a) and (b) Temperature dependence of the anisotropy field and the 
saturation magnetostriction of the Cu-containing samples. 

temperatures coinciding with those of the onset of the crys¬ 
tallization process). The minima measured in the Cu- 
containing samples coincide at 570 °C whereas that corre¬ 
sponding to the Cu-free sample is observed at 500 °C. 
Regarding the results, it is important to remark that this 
parameter shows minima at temperatures coinciding with 
those observed in the //^(Tann) curves. The very small 
value obtained in the Cu-containing samples could result 
from strong intergranular exchange coupling promoted by a 
high degree of homogeneity of the grain size distribution. 

The micromagnetic analysis of the transverse biased ini¬ 
tial susceptibility results, allows a further quantification of 
the coupling between the microstructure and the magnetiza¬ 
tion, According to Hoffmann,"^ the minor, major, 

» semiaxis of the elliptical regions in which the magne¬ 
tization is coupled, resulting in a reduction of the effective 
anisotropy, can be expressed as 

R,,=[AH,/K,dHi + i-)H,)] (3) 

and 

+ (- )H,)l (4) 

where A is the exchange constant. Hi is the saturating field 
(our data were evaluated for an Hi value corresponding to 
30//jt), and d is the thickness of the samples. In Figs. 2(a) 
and 2(b) we present the annealing temperature dependence of 
Rqc ^mc measured in the heat treated samples. Our re¬ 
sults are almost independent of the annealing parameters and 
composition, except for the fact that the R^^ values obtained 
in the Cu-containing samples are two orders of magnitude 
larger than those measured in the Cu-free sample. This result 
clearly shows that the intergranular exchange coupling, that 





6340 J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 

induces anisotropy averaging, is not the only source of the 
magnetic softening for these samples. In order to check the 
influence of the magnetoelastic coupling, v^e present in Figs, 
3(a) and 3(b) the evolution of the saturation magnetostriction 
constant with heat treatment temperature and, for the sake of 
comparison, that of the anisotropy field. As can be seen in 
these figures, the saturation magnetostriction decreases down 
to a minimum value coinciding with the minimum of the 
anisotropy field. Since these decreases take place simulta¬ 
neously with the bcc Fe precipitation, the soft magnetic char¬ 
acter should be related to the two-phase nature of the partly 
crystallized samples. 

IV. CONCLUSIONS 

The enhancement of the soft magnetic properties in the 
FeZrB(Cu) alloys occurs due to the combination of two fac¬ 
tors both of them associated with the onset of the nanocrys- 


Garcia Tello et ai 

tallization process: the low values of the effective anisotropy 
field and the decrease of the saturation magnetostriction. The 
intergranular coupling leading to the anisotropy reduction is 
clearly favored by the Cu addition, presumably due to the 
larger number of bcc Fe grains involved in the coupled units, 
compared with those present in the Cu-free sample. Opti¬ 
mum heat treatment conditions (540 ®C, 1 h) result, in the 
case of the Cu-containing samples, in a large degree of in¬ 
tergranular coupling as evidenced [Figs. 3(a) and 3(b)] by 
the minimum value of the magnetization inhomogeneities 
related to the dispersion field. 

*K. Suzuki, A. Makino, A. Inoue, and T. Masumoto, J. Appl. Phys. 70, 
6232 (1991). 

^G. Herzer, IEEE Trans. Magn. 26, 1397 (1990). 

^J. M. Gonzalez, N. Murillo, J. Gonzalez, J, M. Blanco, and J. Echeberria, 
J. Mater. Res. 11, 512 (1996). 

^H. Hoffmann, IEEE Trans. Magn. 4, 32 (1968). 




JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER II 


I JUNE 1998 


Approach to the magnetic saturation in nanocrystailine ferromagnets 
in the random anisotropy model 

G. R. Aranda and J. Gonzalez®' 

Departamento de Fisica de Materiales, Facultad de Qmmicas, Universidad del Pais Vasco, 

20009 San Sebastian, Spain 

K. Kulakowski 

Faculty of Physics and Nuclear Techniques, University of Mining and Metallurgy, 30059 Cracow, Poland 

Recent experimental data on the magnetization curve M{H) of magnetically soft nanocrystalline 
Fe 73 5 CuiNb 3 Sii 3 5 B 9 sample are analyzed in terms of the random anisotropy model. Numerical 
calculations of magnetization are supplemented by a high-field expansion. Near the saturation we 
get M{H)IMs= 1 where {K) is the averaged anisotropy of crystalline grains, 

contained in large magnetic domains. Section I is an introduction. In Sec. II, reference data on the 
model parameters of the nanocrystalline system Fe 73 5 CuiNb 3 Sii 3 5 B 9 are collected in order to justify 
the model approximations and to prepare the comparison with experimental results. In the two 
subsequent sections, the results of the calculations are described and discussed, © 1998 American 


Institute of Physics. [S0021-8979(98)28211-9] 


I. INTRODUCTION 

Nanocrystailine Fe-based materials are interesting for 
their superior magnetic softness.^ A prominent example of 
these materials is Fe 73 5 CuiNb 3 Sii 3 5 B 9 and their magnetic 
behavior can be explained by the random anisotropy model.^ 
Their low coercive field (^1 A/m) and high initial perme¬ 
ability (^10^) are related to a new magnetic phase. More¬ 
over, new relations can be deduced^’^ between the magnetic 
properties of the system and its micromagnetic structure. 

The shape of the magnetization curve in 
Fe 73 5 CuiNb 3 Sii 3 5 B 9 was investigated experimentally"^ both 
for amorphous and nanocrystailine state. The relevant pro¬ 
cess of magnetization was the reversible rotation of magnetic 
moments. The results were fitted to the law 

M{H) = IH^) + (1) 

The last term in Eq. (1) was responsible for a change of 
Ms and it was expected to be relevant in very high magnetic 
fields. The term ailH was adscribed to macroscopic inho¬ 
mogeneities and it was expected to appear for fields below 2 
kOe. The constant a 2 is known^ to describe the curvature of 
energy of local magnetic moments at the equilibrium direc¬ 
tion. In Ref. 4, a 2 was interpreted as due to magnetoelastic 
anisotropies of internal stresses. Thus ^2 was expected to be 
proportional to the squared magnetostriction constant 
This interpretation was based on the theory of stress fields of 
dislocation dipoles in amorphous systems.^’^ 

We will demonstrate, that the term is a direct con¬ 
sequence of the random anisotropy model.^’^ 

II. PARAMETERS OF THE NANOCRYSTALLINE 
SYSTEM 

In Ref. 3, the size Lex of magnetic domains in soft mag¬ 
netic phase of Fe 73 5 CuiNb 3 Sii 3 5 B 9 is of the order of 


“^Electronic mail: wabroarg@scoxol.sc.ehu.es 


10 “^ m, and the density of the magnetic anisotropy energy 

of a magnetic domain is about 2 J/m^. So the energy of 
a virtual thermal excitation of a domain of the order of {K) 
xlL 12 eV, almost three orders of magnitude larger than 
the thermal energy at room temperature. 

For large domains, magnetic coupling between them is 
limited to domain surfaces and neglectable. The energy of a 
domain in its ground state is 

VE{e,(!>)--{K)V ^in^{0-(t>)~HMsV cos (2) 

where {K) is the same as above, 6 the angle between a local 
easy axis of a magnetic domain and the applied magnetic 
field H, (p is the angle between the magnetic moment of the 
domain and the applied field, and V is the domain volume. 
Minimizing the energy L as a function of we get the 
ground state value (jy^ as a function of 9. Macroscopic mag¬ 
netic moment is the average (cos ^ 0 ) over all directions of 
the local easy axis. To avoid hysteresis and limit our consid¬ 
erations to reversible rotations of local magnetic moments, 
only positive contribution to magnetization is taken into ac¬ 
count. 

As we see, at r= 0 the only relevant parameter of the 
model is x-MsHI{K). 

After Ref. 3 we take to be 1.2 T. For fields H 
kOe we get the Zeeman energy of the order of 10^ J/m^. 
Note that in Ref. 4, measurements were performed for fields 
up to 60 kOe. As noted above, the local anisotropy energy 
for nanocrystailine grains is of the order of 2 J/m^. So x for 
the soft nanocrystailine phase is of the order of 10 ^. 

For amorphous as-quenched state, internal stresses 
around 40 MPa^ combined with the magnetostriction 
= 20 X 10 “^ produce anisotropy energy of the order of 
800 J/m^. Finally, for uncorrelated crystalline grains above 
the Curie temperature of the amorphous matrix, the local 
anisotropy energy of the grains is known^ to be about 
8000 J/m^. In all three cases, we obtain x above ten. 


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6341 


© 1998 American Institute of Physics 



6342 J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Aranda, Gonzalez, and Kulakowski 


Does the argument on the ground state of the beginning 
of this section hold for the as-quenched amorphous state? In 
this case, the exchange length can be evaluated as 

L,^={2AI{^\a)y'\ (3) 

where A is the exchange stiffness of the order of 10“ " J/m^. 
Keeping the above-noted value of 40 MPa for annealed 
samples, we get Lam'^lOOnm, and the temperature neces¬ 
sary for thermal excitations of amorphous system of the or¬ 
der of 10^ K. Obviously, this is much 

more than the Curie temperature for grains (about 880 K^). 

For the turning field Hi where the law starts to be 
relevant was found to be 1 to 2 kOe nanocrystalline systems. 
For amorphous ribbons is known to be 0.3 kOe. 


III. CALCULATIONS AND RESULTS 

After Eq. (2), with e=\lx the condition of the minimum 
of energy is sin (f>Q= € sm[2{0~^o)]. For high magnetic 
fields, when x^lO, small 6, the angle between the magnetic 
moment of a domain and the applied magnetic field in the 
equilibrium, > is small and can be developed in 6 powers 

(l>o=e sin(2^) —6^ sin(2^)cos(2^). (4) 

For r>0, the magnetization M{H) can be written as 

flTfl flTT 

MiH)/Ms^l/{27r) sin OdO 
Jo Jo 

(5) 

where 

fTT/l flTT 

(m(^,^,r))= 1/Z sinc^d^j dijj cos (f) 

Jo Jo 

X exp[ - j3VE( (9, (/>, ^)], (6) 

the angles ^ and f denote the direction of a local easy axis, ^ 
and i// denote the direction of a local magnetic moment, and 
Z is the partition function. For 7=0, 

exp[ -j8VF( <9, (f>o) Si if/- ^), (7) 

r7r/2 flir 

MiH)fMs^ 1/(277) sin Odd dC cos (8) 

Jo Jo 

Expanding cos (/>o^ 1 ~and substituting <pQ = e s\n26 
[see Eq, (4)], we get 

MiH)IMs= 1 “46^/15= 1 -4{i^)V(15M^H2) (9) 

which is the law, derived for high field and 7=0. 

A low-temperature approximation is also justifiable for 
soft nanocrystalline phase. For 79^ 0 but very small (Sec. II), 
the deviations from the ground state are much smaller than 
the ground state angle <^o • Thus 

M{H)IMs= 1 - 4(/f)2/( -3KbTI{2VMsH). 

( 10 ) 

Equation (10) is valid if VM sH>V<K>>KqT. As 
was justified in Sec. IL On the contrary, in the limit e-^O, 
^6=const we get M(//)/M^= 1-r6+(f£)^. How¬ 
ever, this limit is not appropriate for our system. 



FIG. 1 . The coefficient a, (points) and its numerical error (dotted line), as 
dependent on the parameter x = M^Hl(K). 

Numerical calculations on the curve MiH) for zero tem¬ 
perature show that the term arises as soon as the value 
of the parameter x = M^HI{K) exceeds 2.0. 

This result can be shown in several different ways. In 
Fig. 1 we show the value of the exponent a, as defined in 
MiH) = Msil-a/H^). In our numerical calculations, 

= 1. The numerical error A a of a is due to the error AM of 
M, and we calculate it from Aaf= A(M/My)/{[ 1 
"(M/M^)]ln(/////o)}, where Hq is a field unit. This result is 
included in Fig. 1. AM is determined numerically by varying 
the step of integration, and it is found to be 3 X 10“^, As can 
be seen in Fig. 1, the value a = 2.0 is the asymptotic one for 
large values of x. Simultaneously, the numerical error A a 
exceeds lO”"^ atx^200. 

Numerical calculations for 7>0 contain triple integra¬ 
tion, and the accuracy for M(T,H) is near 10“"^. Also, the 
exponential Gibbs factors in Eq. (6) disable the low tempera¬ 
ture range to be investigated numerically. Still, we have 
made an attempt to evaluate aj and a 2 of Eq. (1) as depen¬ 
dent on X for various temperatures. For 7=0, the coefficient 
a I is found to be maximal near jc = 1, and above x = 3 its 
absolute value is less than 2X 10“^. The coefficient a 2 in¬ 
creases with X from zero to a maximum value near x = 2,0, 
and then it decreases to about 0.27. Analytical calculations 
give the asymptotic value (22 = 4/15 = 0.266(5) for large x 
[Eq. (10)]. For 7>0 the plots of ai(x) and a 2 ix) are 
smoother. The results are given in Figs. 2(a) and 2(b). 
Clearly in Fig. 2(b), the coefficient ^2 is close to a constant. 
Numerical calculations for (checked from t=0.03 to 
0.066, t being KbTI{K)V), yield ai = KBTIVM,H. In Eq. 
(10), ai = 3K^7/2VMy//. It is possible that this change of 
the coefficient occurs in the range of lower temperatures, 
which cannot be captured numerically. 

In Fig. 3, numerical plots are shown of y = x\l 
—Mix)] for different temperatures. As we see, the values of 
y below jc^2 and the value of x, where the law starts 
to be valid, do not depend on temperature. 

IV. DISCUSSION 

In the nanocrystalline state, the magnetostriction is 
known^ to be reduced by at least a factor of 4, if compared 




J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Aranda, Gonzalez, and Kulakowski 


6343 


0.35 
0.3 
0.25 
0.2 
0.15 
O.I 
0.05 
0 

-0.05 

-2 0 2 4 6 8 10 



FIG. 2. The coefficients (a) a^, (b) ^2 dependent on a:, calculated nu¬ 
merically for various temperatures. Temperature is expressed as t 
= ksTf(K)V. The plots are: (•) r = 0, (-1-) r=0.028, (O) f = 0.33, (♦) t 
= 0.04, (X) r = 0.05, and (V) r = 0,066. Guide-eye solid line is drawn 
through the points for r = 0. Note that for (AT) = 2.7 J/m^ and V= 10"^^ m^ 
the value r= 0.028 means that r=5400 K. 


with that for the amorphous matrix. It was pointed out in 
Ref. 4, that if the coefficient a 2 from Eq. (1) is proportional 
to the second power of the magnetostriction, it should be 
much smaller for the nanocrystalline state. Experimental data 
show that this coefficient is only twice smaller than that for 
the as-quenched amorphous sample. 

We think a 2 for amorphous and nanocrystalline samples 
are of different origin. In amorphous systems, the fluctua¬ 
tions of local magnetic anisotropy are due to local stresses 
and the magnetoelastic coupling. On the contrary, in soft 
nanocrystalline phase the local magnetic anisotropy is due to 
crystalline grains of bcc-FeSi, and it is partially averaged out 
within magnetic domains.^ The experimental value of ^2 is 
about 2X 10“^ Oe^.^ With this result and Eq. (10), we get 
{K)^2J J/rG?, close to the value 2J/m^, accepted for the 
soft nanocrystalline phase.^ 



FIG. 3. The quantity x\ I -M{x)] as dependent on jc for various tempera¬ 
tures t^ksTf{K)V. The plots are: (•) f=0, (+) r = 0.028, (O) r=0.33, 
(♦) f=0.04, (X) r = 0.05, and (V) f = 0.066. Guide-eye solid line is drawn 
through the points for t — 0. 

On the contrary, if we apply Eq. (10) to an amorphous 
as-quenched system, we get the local anisotropy 3/2 \((j) 
near 4 J/m^. Keeping X = 20X 10“^, we get the average am¬ 
plitude of stress to be about 0.1 MPa, which is more than two 
orders of magnitude smaller than the values in Ref. 9. 

The experimentally observed value of the coefficient <21 
for the soft nanocrystalline phase was 4 to 5X10“^ Oe. As 
it was pointed out in Ref. 3, the origin of the MH term is due 
to macroscopic inhomogeneities. Substituting V=l\^ into 
Eq. (10), we get the coefficient Ui much smaller than the 
experimental value. The MH term of Eq. (10), if observed 
experimentally for nanocrystalline phase, should be only a 
small correction to the contributions of other effects. 

In conclusion, the law of approach to the magnetic 
saturation, which was observed in the soft nanocrystalline 
phase of Fe 73 5 CuiNb 3 Sii 3 5 B 9 , can be entirely assigned to 
the FeSi crystalline grains. The coefficient a 2 is found to be 
temperature independent, as it was shown experimentally. 

ACKNOWLEDGMENTS 

The authors are grateful to the Spanish MEC (project 
PB96-0899-C02-02) and to the Polish Scientific Committee 
for financial support. 

^Y. Yoshizawa, S. Oguma, and K. Yamauchi, J. Appl. Phys. 64, 6044 
(1988). 

^G. Herzer, IEEE Trans. Magn. 26, 1397 (1990). 

^G. Herzer, Scr. Metall. Mater. 33, 1741 (1995). 

^ J. Gonzalez, M. Vazquez, E. du Tremolet de Lacheisserie, and G. Herzer, 
in Ordering and Disordering in Alloys, edited by A. R. Yavari (Elsevier 
Applied Science, London, 1992), p. 473. 

^S. Chikazumi, Physics of Magnetism (Krieger, Malabar, 1964). 

^H. Grimm and H. Kronmuller, Phys. Status Solidi B 117, 663 (1983). 

^M. Vazquez, W. Fernengel, and H. Kronmuller, Phys. Status Solidi A 115, 
547 (1989). 

*R. Alben, J. J. Becker, and M. C. Chi, J. Appl. Phys. 49, 1653 (1978). 

^ J. Gonzalez, M. Vazquez, and J. M. Barandiaran, Phys. Status Solidi A 93, 
K165 (1986). 





JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Numerical Methods 


I. A. Tsukerman, Chairman 


Multigrid methods for computation of magnetostatic fields in magnetic 
recording probiems 

Igor Tsukerman and Alexander Plaks 

Electrical Engineering Department, The University of Akron, Akron, Ohio 44325-3904 

H. Neal Bertram 

Center for Magnetic Recording Research, University of California, San Diego, La Jolla, 

California 92093-0401 

Calculation of magnetostatic fields is usually the most time-consuming stage of micromagnetic 
simulations. In this article, the Bramble-Pasciak-Xu multilevel preconditioners (MP) are applied to 
the computation of magnetostatic fields in media such as magnetic tapes or thin films. The 
asymptotic number of arithmetic operations is optimal and proportional to the number of nodes in 
the finite element mesh. Unlike the fast Fourier transform, MP are applicable to irregular meshes. 

Local (adaptive) mesh refinement can be implemented by switching to the hierarchical basis. 

© 1998 American Institute of Physics. [80021-8979(98)38311-5] 


L INTRODUCTION 

Magnetization of media in micromagnetic problems is 
usually simulated by minimizing the sum of the magneto¬ 
static energy, the exchange energy, the anisotropy energy, 
etc. Calculation of the magnetostatic field is the crucial stage 
of the overall numerical process of energy minimization. The 
objective of this study is to develop efficient magnetostatic 
field algorithms for micromagnetic simulations. The focus is 
on media such as magnetic tapes or thin films where the 
nonuniform arrangement of the magnetic particles or grains 
is of particular interest. 

Various linear system solvers are currently in use in 
magnetostatic finite element (FE) analysis.’^ The incomplete 
Cholesky conjugate gradient (ICCG) method^ is probably the 
most popular among iterative methods. Direct methods, such 
as nested dissection^ (ND) or quotient minimum degree,^ for 
two-dimensional (2D) problems are usually faster^ ^ and 
more robust than ICCG. Linear 2D magnetostatic problems 
of moderate size (say, up to 10 000 unknowns) can be solved 
easily using either of the methods mentioned. 

However, performance of these methods deteriorates, es¬ 
pecially in three-dimension (3D), when finite element 
meshes are refined and thus the number n of unknowns in the 
system increases. The number of arithmetic operations for 
ICCG and ND grows as n^^^ in 2D and as n"^^^ and 
respectively, in 3D. 

Multigrid methods are asymptotically much faster. Typi¬ 
cally for these methods, the number of arithmetic operations 
per unknown is independent or almost independent of the 
size of the linear system being solved. This behavior is on a 
par with the fast Fourier transform (FFT) and the Greengard- 
Rokhlin multipole method.^ FFT, however, is applicable 
only to regular FE meshes (or a spatially uniform particle 
a^angement),^^ while multigrid methods can be applied to 


arbitrary tetrahedral meshes. Comparison with the multipole 
method is interesting and is planned for future work. 

II. THE MAGNETOSTATIC MULTIPARTICLE PROBLEM 

The magnetic scalar potential w of a system of magne¬ 
tized particles satisfies the Poisson equation 

Am = V-M, (1 ) 

where M is the magnetization vector. For the purpose of 
computing the magnetostatic field, the magnetization of each 
of the particles is assumed to be known. Particles may have 
arbitrary orientation in space and, in principle, arbitrary 
shapes, although practical restrictions may be imposed by the 
capabilities of an FE mesh generator. The direction of mag¬ 
netization may also be arbitrary. 

In the weak (variational) form Eq. (1) can be written as 

^z(m,w') = (Vm,Vm') = (M,Vw'), (2 ) 

where the angle brackets denote an L 2 “type inner product of 
two vector functions in a given computational domain fi, 
and u' is an arbitrary trial function from the appropriate 
Sobolev space. Different types of boundary conditions can 
be considered with Eqs. (1) or (2); for unbounded problems, 
the potential is assumed to be zero at infinity. 

The FE method has already been successfully applied to 
multiparticle problems by Koehler, Yang, and Fredkin,^’^’^ 
but multigrid solvers have not been tried. 

III. MULTILEVEL PRECONDITIONERS 

The Bramble-Pasciak-Xu (BPX) multilevel precondi¬ 
tioners are among the least restrictive and the 

most efficient multigrid methods. The method is applicable 
to 2D and 3D magnetostatic problems (and to linear elliptic 
problems in general) and is suitable for highly irregular 


0021 -8979/98/83(11 )/6344/3/$15.00 


6344 


© 1998 American Institute of Physics 



J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Tsukerman, Plaks, and Bertram 6345 



meshes and inhomogeneous materials. For the magnetostatic 
multiparticle problem on a mesh with n nodes, the 
asymptotic number of arithmetic operations for BPX-MP is^^ 
0{n). In addition, the BPX preconditioner is a double sum 
which can be computed in parallel, 

A few levels of nested tetrahedral meshes are generated. 
In the simplest case of global refinement, each of the tetra¬ 
hedral elements is subdivided into eight tetrahedra, thus ob¬ 
taining the next level of triangulation. Associated with each 
level k ... ,m) is a set of FE basis functions {i 

— where is the number of nodes at level k, and 

a finite dimensional space Pj, (of dimension spanned by 
these basis functions. Then • 

One of the simplest versions of the BPX preconditioner 
can be written as follows: 

m nj^ 

J, reP„. (3) 

k=l 




FIG. 3. Exact and multigrid solutions for one particle. (Tetrahedral mesh 
with over 600 000 elements.) 


For the Poisson equation, the conjugate gradient method with 
the preconditioner B requires only 0(1) iterations to con¬ 
verge and Oin) arithmetic operations. For inhomogeneous 
problems and/or highly irregular grids the preconditioner B 
in Eq. (3) needs to be modified, as proposed by Yserentant^^ 
and further explained by Bomemann et al? 


Pr=Ao V 








(4) 


where the operator Aq corresponds to the FE representation 
of the bilinear form a(u,u') on the coarsest mesh. 

Adaptive refinement of the FE mesh may be needed to 
achieve the desirable accuracy of the numerical solution. 
Two main problems arise in connection with such refine¬ 
ment. First, if one of two elements having a common bound¬ 
ary is refined, the FE basis becomes nonconforming and the 
continuity of the solution must be explicitly imposed. Sec¬ 
ond, effective error estimates are needed in order to deter¬ 
mine where the local refinement is needed. 

Both of these problems can be solved simultaneously by 
using hierarchical FE bases, as proposed by Mitchell^^ and 
Riide.^^ By setting the hierarchical basis value of an FE 
function at nonconforming (“slave”) nodes to zero, the con¬ 
tinuity of the function can be assured. At the same time, the 
hierarchical basis representation provides means of error es¬ 
timation and control. The method is known as “fully adap- 
live multigrid” (FAM) 


TABLE I. Number of iterations and solution time for the problem with one 
particle. 


Level of 

refinement 

Number 

of elements 

Number of 
iterations^ 

Solution time 
(seconds)*’ 

0 

162 

7 

<1 

1 

1296 

25 

<1 

2 

10 368 

40 

<1 

3 

82 944 

56 

8 

4 

663 552 

78 

88 


^The norm of the residual was reduced by a factor of 10-5. 

*The computations were performed on a personal computer with a Pentium 
11 300 MHz processor and 64 M RAM. 










6346 J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Tsukerman, Plaks, and Bertram 



FIG. 4. The scalar magnetic potential for a model problem with three mag¬ 
netized particles. 

Our implementation of the multigrid algorithm is based 
on the BPX preconditioner transformed to the hierarchical 
basis. This approach combines the high convergence rate of 
BPX with the flexibility of local refinement provided by 
FAM. Representation of the magnetic scalar potential in the 
hierarchical basis ensures the continuity of the potential over 
nonconforming tetrahedral elements. In order to combine the 
hierarchical basis representation essential for FAM with 
BPX-MP, all vector variables and the BPX preconditioner 
are converted into the hierarchical basis. 

IV. TESTING THE METHOD 

Several test problems with magnetized particles were 
solved. To simplify mesh generation, the particles were con¬ 
sidered to be parallelepipeds oriented parallel to the xy plane. 
The mesh initially consists of a set of prisms which are then 
subdivided into tetrahedra (Fig. 1). 

The problem is solved on the finest mesh; the auxiliary 
coarser levels are needed only to construct the precondi¬ 
tioner. Since the domain properties are homogeneous (the 
Poisson equation is being solved), coarser meshes need not 
represent the exact geometry of the particles; rather, finer 
levels can be adaptively adjusted to the shape of the par¬ 
ticles. (However, our current mesh generator exactly repre¬ 
sents the geometry starting from the coarse mesh level.) Re¬ 
sults for two of the model problems are presented below. 

Problem 1. The main purpose of this test example was to 
compare the FE-multigrid solution with the analytical one. A 
cubic particle in free space is magnetized along the x axis. 
The analytical solution for the magnetic scalar potential is 
M(r) = (l/47r)/5(Af• J57 |r-r'|). In FE analysis, the do¬ 
main was bounded and homogeneous Dirichlet conditions 
were imposed on the boundary. The lines of equal magnetic 
potential are shown in Fig. 2. The magnetic potential distri¬ 
bution along the central line of the domain is shown in Fig. 
3. The computational statistics are shown in Table I. 

Problem 2. Three particles are magnetized along their 
axes (Fig. 4). Homogeneous Dirichlet boundary conditions 
are imposed on the external boundary. Computational statis¬ 
tics are shown in Table IL 


TABLE II. Number of iterations and solution time for the problem with 
three particles. 


Level of 
refinement 

Number of 
elements 

Number of 
iterations^ 

Solution time 
(seconds)’’ 

0 

1296 

8 

1 

1 

10 368 

25 

1 

2 

82 944 

38 

6 

3 

663 552 

50 

62 


^The norm of the residual was reduced by a factor of 10-5. 

‘’The computations were performed on a personal computer with a Pentium 
II 300 MHz processor and 64 M RAM. 


V. FUTURE WORK 

The multigrid solver is to be incorporated into the over¬ 
all micromagnetic simulation process. A straightforward ap¬ 
proach would be to use the BPX preconditioner within the 
usual iterative procedure of minimizing the free energy. 
Whether or not energy minimization can be more fully inte¬ 
grated in the multigrid method remains an open question. 

For open boundary problems, the modification of the 
multigrid method proposed by Hsiao and Zhang^ is promis¬ 
ing. The asymptotic number of arithmetic operations remains 
the same as in a bounded problem. Comparison with the 
Greengard-Rokhlin fast multipole method, which has similar 
asymptotic characteristics, would be interesting. 

It is anticipated that a posteriori error estimates will be 
implemented and used in the mesh refinement process. 

VI. CONCLUSIONS 

Magnetostatic fields in micromagnetic simulations are 
efficiently computed using multilevel preconditioners. A fi¬ 
nite element problem with half a million elements can be 
solved in about a minute on a modem personal computer. 

ACKNOWLEDGMENTS 

The work of I. Tsukerman and A. Plaks was supported in 
part by the National Science Foundation. 

‘B. Yang, Ph.D. thesis, University of California, San Diego, 1997. 

^B. Yang and D. R. Fredkin, J. Appl. Phys. 79, 5755 (1996). 

^F. Bornemann, B. Erdmann, and R. Komhuber, Int. J. Numer. Methods 
Eng. 36, 3187-3203 (1993). 

'‘j. H. Bramble, J. E. Pasciak, and J. Xu, Math. Comput. 55, 1 (1990). 

^ A. George and G. Liu, Computer Solution of Large Sparse Positive Defi¬ 
nite Systems (Prentice-Hall, Englewood Cliffs, NJ, 1981). 

^L. Greengard and V. Rokhlin, J. Comput. Phys. 73, 325 (1987). 

^G. C. Hsiao and S. Zhang, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 
31, 680 (1994). 

^T. R. Koehler and D. R. Fredkin, IEEE Trans. Magn. 28, 1239 (1992). 
^J. A. Meijerink and H. A. van der Vorst, Math. Comput. 31, 148 (1977). 
‘‘^W. F. Mitchell, SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 13, 
146 (1992). 

“U. Riide, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 30, 230 (1993). 
‘^I. Tsukerman, IEEE Trans. Magn. 29, 2365 (1993). 

‘^I. A. Tsukerman, A. Konrad, G. Bedrosian, and M. V. K, Chari, IEEE 
Trans. Magn. 29, 1711 (1993). 

‘"‘j. Xu, Ph.D. thesis, Cornell University, 1989. 

‘^J. Xu, SIAM (Soc. Ind. Appl. Math.) Rev. 34, 581 (1992). 

'^S. W. Yuan and H. N. Bertram, IEEE Trans. Magn. 28, 2031 (1992). 
'^H. Yserentant, Numer. Math. 49, 379 (1986). 

‘^H. Yserentant, Numer. Math. 58, 163 (1990). 







JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Modified scalar potential solution for three-dimensional magnetostatic 
probiems 

K. Sivasubramaniam S. Salon, and M. V. K. Chari 

Department of Electric Power Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180-3590 

I. D. Mayergoyz 

Department of Electrical Engineering, University of Maryland, Maryland 20742 

A novel three-dimensional magnetostatic solution based on a modified scalar potential method has 
been developed. This method has significant advantages over the traditional total scalar, reduced 
scalar, or vector potential methods. The new method was successfully applied to a 
three-dimensional geometry of an iron core inductor and a permanent magnet motor. The results 
obtained are in close agreement with those obtained from traditional methods. © 1998 American 
Institute of Physics. [80021-8979(98)38411-X] 


L INTRODUCTION 

Solutions for two-dimensional magnetostatic field prob¬ 
lems using a vector potential have been extensively reported 
in the literature.^ However, there is a need for a computa¬ 
tionally robust method particularly for three-dimensional 
field problems. Total scalar and reduced scalar^’^ potential 
solutions, and to a lesser extent three-dimensional vector 
potential"^ solutions, or a combination of scalar and vector 
methods,^ have been presented by researchers. The scalar 
potential solutions do not suffer from the uniqueness prob¬ 
lem that are encountered in the vector potential methods, 
although elaborate vector potential schemes of overcoming 
this difficulty have been described in the literature. The re¬ 
duced scalar potential method allows current sources to be 
accurately represented and has, thus, found a wider applica¬ 
tion than the total scalar method because of the limitations of 
current sheet representation of sources and the need for 
branch cuts in the latter. However, even in the traditional 
reduced scalar potential method, the forcing function is 
evaluated over the entire solution domain and the zero diver¬ 
gence of the magnetic field due to current sources in free 
space is needlessly implemented resulting in numerical er¬ 
rors. 

In this article, a three-dimensional modified scalar poten¬ 
tial solution is described which minimizes numerical inaccu¬ 
racies. In the new method, the forcing function is evaluated 
only in the iron region, and the zero divergence of the source 
magnetic field is eliminated from the computation. 

II. THEORY 

The fundamental theory behind the new method has 
been presented in an earlier paper,^ but is summarized here 
for completeness. 

Since magnetic induction is divergence-free, the follow¬ 
ing equation may be writen in terms of a reduced scalar 
potential formulation 

V.[/i(ff,-V<D)] = 0, (1) 


where is the magnetic field due to current sources (i.e., 
the rotational part of H), O is the scalar potential, fi is the 
permeability, and (jl^ is the free space permeability. 

Since He is divergence-free in free space, 

V.(moHc)=0. (2) 

Subtracting Eq. (2) from eq. (1), 

V.[(/i-/ro)Hc]-V.(/iV<3E>) = 0. (3) 

Applying the Galerkin weighted residual process to Eq. 
(3) using shape functions ^k(k = l,2,...,n), 

f f ^*V.(/xV<l>)rfu = 0. (4) 

J V j V 

This equation can be solved using the traditional finite 
element formulation for three-dimensional problems. 

III. THREE-DIMENSIONAL APPLICATION TO AN 
IRON-CORE INDUCTOR 

Figure 1 shows an octant of an iron core inductor excited 
by a current source (not shown in the figure) surrounding the 
central limb. The field due to this current source is evalu¬ 
ated by Biot-Savart law separately. Equation (5) was solved 



“^Electronic mail: sivask@rpi.edu 


FIG. 1. Iron core inductor. 


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© 1998 American Institute of Physics 






6348 


J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Sivasubramaniam et al. 



FIG. 2. Flux density variation along X-X. 


using a nonlinear finite element procedure with second-order 
isoparametric bricks. The field in the iron core was then 
computed as the sum of and the negative gradient of the 
solution <I>. The flux density variation along X-X, obtained 
by this procedure is illustrated in Fig. 2. 


IV. PERMANENT MAGNET FORMULATION 

The flux density, B, the magnetizing force H and the 
intrinsic magnetization, M, of a permanent magnet material 
are related by 

B=iiH+fiQMo. (5) 

Since Eq. (5) can be written as 

B = + ( 6 ) 

Taking the divergence on both sides of Eq. (6), and set¬ 
ting it to zero yields 

V.^ = 0 = V.yLt(^^-Va)) + V«(/xoMo). (7) 

Also, 

V.(/xo^,) = 0. (8) 

Substituting Eq. (8) into Eq. (7), as before, gives 

V.[(/4-;Uo)^J-V.(;aV<I>) + V.(MoMo) = 0. (9) 

The weighted Galerkin formula yields 



FIG. 3. Permanent magnet motor under no-load condition. 




[ [ MV.fiV^)dv 

J V J V 

+ f ik'^.{iioMo)dv = 0. (10) 

J V 

Equation (10) is then solved by the three-dimensional 
finite element method in the traditional manner. 

V. THREE-DIMENSIONAL PERMANENT MAGNET 
APPLICATIONS 

Figure 3 shows a three-dimensional section of a six-pole 
permanent magnet motor. The rotor poles are of linear per¬ 
manent magnet pieces, and the stator is of conventional de¬ 
sign with one conductor per slot. The flux path is shown in 


FIG. 5. —Flux due to current sources without effect of iron. 












































J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Sivasubramaniam et al. 6349 



FIG. 7. Airgap flux density under load (directly demagnetizing case). 


the figure by arrows representing the magnetic field intensity 
vectors. The flux density profile in the airgap is illustrated in 
Fig. 4 for the open circuit condition. 

The short circuit condition with stator currents directly 
demagnetizing the rotor field is illustrated by the flux pattern 
in a cross section as shown in Figs. 5 and 6. The correspond¬ 
ing flux density variation in the airgap is given in Fig. 7. 


The potentials obtained from these solutions are then 
used to compute eigineering quantities like forces and induc¬ 
tances. 

VI. CONCLUSIONS 

An economical and efficient method for solving three- 
dimensional magnetostatic problems has been developed. 
The method has been applied to solve various three- 
dimensional problems including permanent magnet applica¬ 
tions. The new method minimizes numerical inaccuracies by 
implementing the zero divergence of only in the iron 
parts. It also reduces the amount of computation necessary to 
solve the problem. 

^P. P. Silvester, Finite Elements for Electrical Engineers (Cambridge Uni¬ 
versity Press, Cambridge, 1983). 

^J. Simkin and C. W. Trowbridge, lEE Proc., vol. 1.27, part B, No. 6, pp. 
238-347, 1980. 

^O. C. Zienkiewicz, J. Lynnes, and D. J. R. Owen, IEEE Trans. Magn. 13, 
1649 (1977). 

V, K. Chari, Z. J. Cendes, P. P. Silvester, A. Konrad, and M. A. Palmo, 
IEEE Trans. Power Appar. Syst. 100, 40 007 (1981). 

^R. Wang and N. A. Demerdash, IEEE Trans. Magn. 27, 3971 (1991). 

^M. V. K. Chari, S. Salon, G. Bedrosian, and J. Joseph, IEEE Trans. Magn. 
31, 1468 (1995). 












JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Numerical simulation of the magnetization structures in thin polycrystalline 
films with the random anisotropy and intergrain exchange 

D. V. Berkov®* and N. L. Gorn 

INNOVENT e, V,, Gbschwitzer Str. 22, D-07745, Jena, Germany, and Institute of Physical High 
Technologies, Helmholtzweg 4, D-07743, Jena, Germany 

We have developed a new algorithm which enables a fast and exact evaluation of the dipolar 
interaction field for lattice systems of magnetic moments when periodic boundary conditions should 
be applied. The method uses the combination of (i) the fast Fourier transformation technique for the 
dipolar field evaluation and (ii) the modified version of the Ewald method known from the 
calculations of the Coulomb lattice sums. The algorithm enabled us to perform large-scale numerical 
simulations of the remagnetization processes in polycrystalline thin magnetic films with the random 
single-grain anisotropy and the intergrain exchange. The well known ripple-like structures forming 
during the remagnetization process were observed. The dependence of the ripple correlation lengths 
and the hysteresis loop parameters on the intergrain exchange coupling and the film thickness was 
studied. © 1998 American Institute of Physics. [80021-8979(98)23411-6] 


I. INTRODUCTION 

The most time-consuming part of any micromagnetic al¬ 
gorithm for the simulation of the equilibrium magnetization 
structures — including simulations of the quasistatic remag¬ 
netization processes — is the calculation of the dipolar inter¬ 
action field (also called the demagnetizing or stray field) due 
to its long-range character. For finite samples or aperiodic 
magnetization structures with fixed boundary conditions, the 
application of the convolution theorem allows the usage of 
the fast Fourier transformation (FFT) technique with zero 
padding resulting in the operation count '^N log N (where 
N is the total number of lattice sites or discretization cells), 
which is only slightly worse than for systems with the short- 
range interaction. However, in lattice systems with periodic 
boundary conditions direct application of the convolution 
theorem is not possible due to the already mentioned long- 
range character of the dipolar field. Various methods were 
suggested to overcome these difficultybut all of them 
encounter serious problems: (i) cut-off of the dipolar inter¬ 
action at some prescribed distance^’^ can be applied only to 
2D models and introduces small but significant errors which 
can strongly influence the result especially in low external 
fields (see below); (ii) the so called hierarchical model"^ suf¬ 
fers from the same drawback and, in addition, its implemen¬ 
tation is quite complicated; (iii) direct solution of the Poisson 
equation for “magnetic charges”^’^ enables to calculate the 
Fourier components of the dipolar field analytically, but the 
cut-off of the corresponding Fourier spectrum — even at 
arbitrary large frequency — introduces strong artificial oscil¬ 
lations into the calculated dipolar field, because Fourier com¬ 
ponents of, e.g., the stray field of the point dipole do not tend 
to zero for large wave vectors. 

In this contribution we propose a method which com¬ 
bines advantages of the FFT technique for the computation 
of the long-range interaction field (~VlogV operation 


“^Electronic mail; DBerkov@t-online.de 


count) and of the Ewald method normally used for the cal¬ 
culation of the lattice sums for the Coulomb potential (the 
error by the field evaluation may be reduced to a vanishingly 
small value with only a minor — of order — computa¬ 
tional effort). Thus we obtain an algorithm which allows fast 
and exact evaluation of the dipolar interaction field in lattice 
systems with periodic boundary conditions. 


II. METHOD FOR THE DIPOLAR FIELD EVALUATION 


We are going to calculate the stray field created by the 
lattice of point-like dipoles. Following the basic idea of the 
Ewald method,we add and subtract at each lattice node 
(which carries the dipole moment fiij) an artificial 
“Gaussian dipole” with total moment — l^ij and “magnetic 
charge” density given by 




Puir) 


S{z) 




[ {x - +(y - y 




Xexp 


(r-r,/ 


2a^ 


( 1 ) 


where the choice of the “dipole width” a will be discussed 
elsewhere. The charge density of the system can then be 
written as the sum p(r) = p^(r) + p^(r), where the first part 


N ,N . N .,N 

pA(r)= E [A7-^<5(r-ro)]+ 2 Py(r) 

/J=l ij=\ 


( 2 ) 


is the sum of the point dipoles [p(r) of the initial system] 
and the contribution of the “negative” Gaussian dipoles (1). 
The second part 


PB(r)=- X Puir) 


<j=i 


( 3 ) 


represents the density of the “positive” Gaussian dipoles 
which should cancel the second sum in Eq. (2). 


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© 1998 American Institute of Physics 



J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


D. V. Berkov and N. L. Gorn 6351 


The advantage of this transformation is the following. 
For the first part, PaW the total moment attached to each 
lattice site is zero, because the total moment of the negative 
Gaussian dipole —fiij exactly compensates the moment of 
the corresponding point dipole of the initial system 
Hence the field created by magnetic charges of this first part 
p^(r) associated with each lattice site tends to zero faster 
than exponentially [to be more precise, as exp(-r^/2a^)] and 
may be treated as a short-range interaction field, so it can be 
evaluated in operations for the whole lattice. On the 
other hand, the second part p^Cr) of the charge density is 
smooth, because it is given not by the point dipoles, but by 
the smooth Gaussian distribution at each lattice site. This 
means that the field created by ps(r) can be safely calculated 
using the solution of the corresponding Poisson equation and 
the FFT technique (see Introduction). Further details of the 
method will be reported elsewhere. 


III. NUMERICAL SIMULATIONS 


We consider a thin magnetic film consisting of single¬ 
domain grains (crystallites) with saturation magnetization 
forming a 2D hexagonal lattice. The magnetization M,- 
inside each grain (cell) is assumed to be homogeneous, and 
hence is completely described by the unit vector 
mi=Mi/Ms. To calculate the equilibrium magnetization 
structure for the given external field we minimize a total 
system energy E taking into account, as usual, four energy 
contributions: (i) energy in the external field, (ii) energy due 
to the exchange between the neighboring crystallites, (iii) 
single-crystallite magnetic anisotropy energy and (iv) stray 
field energy: 


E 


2 m/ho' 


exch 

-r— 2 j m,in 

IM^VoUj) 


--^2 (m,n,)^-y2 m,hf"’, (4) 

i ^ i 

where Vo is the cell volume, reduced fields are defined as 
, K is the anisotropy constant. The constant Cexch 
which characterizes the strength of the exchange interaction 
can be evaluated from the exchange stiffness of the bulk 
material A, the hexagonal cell side b, the intergrain separa¬ 
tion S, the film thickness J, and the exchange weakening k 
on the grain boundaries using the method described, e.g., in 
Ref. 11: 'AbdIS; in the exchange term the sum is 

taken over the nearest neighbors (ij) only. Random space 
orientation of the crystallite anisotropy axes and periodic 
boundary conditions are assumed. To minimize the energy 
(4) we have used the simplest version of the relaxation 
method described in Ref. 2. 

Numerical simulations which results are presented below 
were performed for a system with magnetic parameters cor¬ 
responding to Co films (A = 10”^ erg/cm, 1400 emu/cc, 
^=4X10^ erg/cm^), film thickness d=l0 nm (when not 
stated otherwise), hexagonal cell side b = 5 nm, intergrain 
boundary thickness I nm. The magnetic structures shown 
in Fig. 1 and Fig. 4 are A^^XA^^=64X 128 cuts out of a 
lattice with 128X256 cells actually simulated (physical sys- 


JC = 0 K = 0.05 K = 0,1 K = 0.2 



X 


FIG. 1. Magnetization configuration (m^-gray-scale maps) of the thin film 
near the coercivity for various exchange weakening degrees k as indicated 
in the figure. 


tern size ^ 1.1 X 1.9 /xm). All simulations were performed on 
the IBM Pentium PC 133 MHz. A typical run for a complete 
hysteresis loop (—40 values of the external field, — 2X 10^ 
iterations totally) took about 10 hours. 


IV. RESULTS AND DISCUSSION 

Due to the limited paper length we present here in some 
detail only the dependence of the system behavior on the 
exchange coupling strength Cgxch • Figure 1 demonstrates the 
magnetization structures at the coercivity point obtained by 
the simulation of the hysteresis loops for thin films with 
various values of the exchange weakening on the grain 
boundaries k as indicated in the figure {k = 0 means ex¬ 
change decoupled grains, whereby, e.g., k'=0.1 means that 
the exchange through a grain boundary is 10 times weaker 
than in the bulk). Initial direction of the external field was 
chosen parallel to the y direction in Fig. 1). The gray-scale 
map is used to present the x projection of the magnetization 
vectors — 1 <mx< 1, so Fig. 1 is supposed to simulate a stan¬ 
dard Kerr-microscopy image. As expected, the average scale 
of the observed ripple structure (with stripes mostly perpen¬ 
dicular to the initial field direction) increases strongly with 
the exchange coupling at grain boundaries. 



FIG. 2. Dependencies of the average ripple wavelength X and the transverse 
correlation length L, on the exchange weakening k (statistical errors, where 
not shown, are smaller than the symbol size.) 



6352 J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


D. V. Berkov and N. L. Gorn 



FIG. 3. Dependencies of the reduced remanent magnetization and the 
coercivity on the exchange weakening k. 


To investigate this dependence qualitatively, we have 
studied the average ripple wavelength X and the transverse 
correlation length of the m^^-component L, (defined as the 
decay distance of the spatial -correlation function in the 
direction perpendicular to the external field) as functions of 
K. Corresponding dependencies are shown in Fig. 2. The 
growth of both correlation lengths with the exchange cou¬ 
pling is evidently faster than a linear one predicted by the 
linear and even by the nonlinear ripple theories (see, e.g., 
Ref. 12). 

The exchange dependence of the most important hyster¬ 
esis loop parameters — reduced remanent magnetization 
= and reduced coercivity hc = HclM^ — is 

presented in Fig. 3. First of all, we point out that the rema- 
nence for low exchange coupling differs significantly 
from that obtained using the cut-off method^’^ and the hier¬ 
archical model."^ This discrepancy is probably due to the 
small errors introduced by these both latter methods. Indeed, 
performing special test runs we have found that adding ran¬ 
dom errors with the relative magnitude ~ 0.01-0.02 to the 
exact stray field values evaluated by our method leads to a 
significant increase of the remanence especially in the case 
of small exchange coupling where the dipolar interaction is 
of a major importance. The second difference with the 
known results^"^ is the stronger decrease of the coercivity for 
large values of the exchange coupling obtained in our simu- 


d-lnm d = 4nm d = 10nm d = 20nm 


It#. 

A**' ^ ^ 




X 


FIG. 4. Remanent magnetization states shown as m^-gray-scale maps for 
various film thicknesses d as indicated in the figure. 

lations which may be due to the much larger system size 
used by us. Namely, large correlation lengths occuring for 
strong exchange couplings (see Fig. 2) may lead to substan¬ 
tial finite-size effects for smaller system sizes. 

We have also studied the dependence of the parameters 
discussed above on the film thickness d. Remanent magne¬ 
tization states obtained for various film thicknesses are 
shown in Fig. 4. Here we would like only to point out that 
for a very thin film (where the intergrain interaction is almost 
negligible) the almost random magnetization pattern is 
formed (see image for d=l nm) whereby for the thicker 
films the ripple structure became more and more pro¬ 
nounced. Detailed results of these studies, discussion of their 
relation to the available experimental data and of the appli¬ 
cability of our method to numerical simulations by finite 
temperatures will be presented elsewhere.*® 

ACKNOWLEDGMENTS 

The authors are very grateful to Professor W. Andra and 
Dr. R. Mattheis for helpful discussions. 

’ S. W. Yuan and H. N. Bertram, IEEE Trans. Magn. MAG-28, 2031 
(1992). 

^D. V. Berkov, K. Ramstoeck, and A. Hubert, Phys. Status Solid! A 137, 
207 (1993). 

^M. Mansuripur and R. Giles, IEEE Trans. Magn. AG-24, 2326 (1989). 

J. Miles and B. K. Middleton, J. Magn. Magn. Mater. 95, 99 (1991). 
^J.-G. Zhu and H. N. Bertram, J. Appl. Phys. 63, 3248 (1988). 

^J. J. Miles and B. K. Middleton, IEEE Trans. Magn. MAG-26, 2137 
(1990). 

^M. Mansuripur and R. C. Giles, Comput. Phys. 4, 291 (1990). 

*C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1953). 
^J. C. Slater, Insulators, Semiconductors and Metals (McGraw-Hill, New 
York, 1967). 

V. Berkov, Phys. Rev. B (submitted). 

’’C. Kittel, Rev. Mod. Phys. 21, 541 (1949). 

‘^K. J. Harte, J. Appl. Phys. 37, 1295 (1966). 







JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Finite eiement anaiysis of the influence of a fatigue crack on magnetic 
properties of steel 

Y. Shi and D. C. Jiles 

Center for Nondestructive Evaluation, Iowa State University, Ames, Iowa 50011 

Fatigue can affect the magnetic properties of materials due to microstructural changes. Previous 
investigations have shown that several structure sensitive magnetic properties, such as coercivity 
and remanence 5^, changed systematically as a result of fatigue. When approaching failure the 
accumulated changes in microstructure resulted in the occurrence of fatigue cracks and the magnetic 
properties showed dramatic changes which mainly resulted from the geometrical changes in samples 
due to the cracks. It was found that the remanence followed the changes in stress, while the 
coercivity sometimes showed different trends. In this article the influence of the size and the 
position of a fatigue crack on magnetic field and magnetic induction were studied using finite 
element modeling. Models were constructed to simulate the geometry of the test sample and sensor. 

It was found that, for a given coil current in the exciting coil, the magnetic induction was mainly 
determined by the geometry of the crack, while the magnetic field was influenced by both the size 
and the position of the crack. © 1998 American Institute of Physics. [80021-8979(98)50711-6] 


I. INTRODUCTION 

In recent years there has been increased interest in cor¬ 
relating magnetic properties of ferromagnetic materials with 
their mechanical properties.The evolution of the magnetic 
properties during fatigue is of particular interest because of 
the relation between the fatigue and magnetic properties of 
materials.^"^ It has been shown that the measured magnetic 
properties change systematically throughout the fatigue life¬ 
time. When approaching failure, the cumulative stress results 
in the occurrence of cracks, which normally start from the 
outer surface. After cracks appeared there was little overall 
change in the microstructure of the materials because most 
stresses then concentrated at the tip of the crack and the main 
change subsequently was the growth of the crack. During 
this period, the corresponding changes of magnetic proper¬ 
ties mainly resulted from geometrical changes in the samples 
because of crack growth. It was found during this period that 
the remanence still depended primarily on the crack ge¬ 
ometry although the coercivity sometimes showed differ¬ 
ent trends. 

To explain the above observations magnetic finite ele¬ 
ment modeling (FEM) work was conducted to establish the 
relation between the fatigue crack geometry and the sur¬ 
rounding magnetic field distribution. Finite element analysis 
techniques, although yielding only approximate solutions to 
the classical partial differential equations of the electromag¬ 
netic field, are particularly attractive for the study of field 
distribution within magnetic structures having complex 
boundary configurations. This property makes the method 
very suitable for the analysis of the interaction between the 
magnetic field and defects within materials, and thus it has 
been applied to magnetic leakage field inspection^"^ and 
creep damage detection.^ In this article, it is shown that the 
method can be extended to fatigue analysis. 


II. FINITE ELEMENT MODELING 

The general geometry of the FEM solid model is shown 
in Fig. 1. The shape of the fatigue sample on which experi¬ 
mental measurements were made was a cylindrical rod which 
was subjected to a uniaxial cyclic stress. An inductive mag¬ 
netic sensor consisting of a search coil wound on a magnetic 
C core was used to measure the magnetic properties of the 
sample during the fatigue lifetime. The magnetic field was 
measured using a Hall probe which was located at the center 
of the C core and on the surface of the sample. Magnetic 
induction was measured using a detection coil which was 
wound on the core of the sensor. To simplify the modeling 
two-dimensional representations were constructed to simu¬ 
late the geometry of the sample and sensor. The magnetic 
field values were calculated at the location of the Hall probe 
and the magnetic induction values were calculated from the 
throughout the volume of the detection coil. 

The amplitude of the excitation current was small 
enough that the sensor operated in the low field hysteresis 



0021-8979/98/83(11 )/6353/3/$15.00 


6353 


© 1998 American Institute of Physics 












6354 J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Y. Shi and D. C. Jiles 



FIG. 2. Calculated magnetic field H vs crack depth in the position with the 
crack on the side of the specimen facing the C core and positioned at the 
center of the sensor. 


region which can be considered as approximately linear. So 
the magnetic properties of the sensor material were assumed 
linear to simplify the problem. However, nonlinear B-H 
data, which were measured experimentally, were used for the 
sample material, because different regions would have dif¬ 
ferent magnetic states during fatigue after the crack gener¬ 
ated. 

The vector potential formulation was employed to con¬ 
duct calculations.^^ With this method it is possible to calcu¬ 
late the flux passing through a predefined line contour. At 
first calculations were conducted to determine the magnetic 
field distribution of the whole system for different crack 
sizes and positions under a fixed excitation current. Then the 
magnetic field value at the Hall probe (location 1 in Fig. 1) 
and the magnetic induction at the detection coil (location 2 in 
Fig. 2) were calculated. 

111. RESULTS AND DISCUSSION 

The magnetic field in the specimen was influenced by 
both the crack size and its position as shown in Figs. 2-4. 
This is because the magnetic field distribution in the space 
between the sample and the C core was mainly determined 
by two factors: the leakage field of the corners and tips of the 
crack and the demagnetizing effect generated by the crack 
surfaces. The leakage field increased as the crack grew, 
which resulted in a larger field amplitude. However growth 
of the crack also increased its surface area which led to an 
increase in the demagnetizing effect and hence reduction of 
the magnetic field. When the crack was located below the C 
core at the center of the sample, the leakage field dominated. 
The resultant field increased with the crack size as shown in 
Fig. 2. When the crack did not occur at the midpoint, the 
demagnetizing effect of crack surfaces altered the magnetic 
field. Therefore, as the crack was initiated, the magnetic field 
at first decreased because of the demagnetizing field from the 
crack surface. Later it increased because of the leakage field 
introduced by the corners of the crack as shown in Fig. 3. As 
the distance between the probe and the crack increased, the 



FIG. 3. Calculated magnetic field H vs crack depth in the position with the 
crack on the side of the specimen facing the C core and positioned away 
from the center of the sensor. 


influence of the demagnetizing effect on the resultant ampli¬ 
tude of the magnetic field became greater, and the influence 
of the leakage field became less. 

A similar explanation can be applied to the case when 
the crack is on the side of the specimen opposite from the C 
core. The only difference is that the leakage field generated 
by the tip of the crack dominated in most cases. The demag¬ 
netizing effect hardly influenced the magnetic field in the 
immediate vicinity of the crack. Only when the crack was 
farther away from the center of the sample did the influence 
of demagnetizing effect on the magnetic field become appar¬ 
ent as shown in Fig. 4. 

Compared with the magnetic field //, the resultant mag¬ 
netic induction B exhibited much smaller changes with the 
crack geometry as shown in Fig. 5. This result can be ex¬ 
plained because the detection coil measured the flux change 
in the sensor, which was distant from the crack region. 
Therefore, the measured magnetic induction was an average 



0 1 2 3 4 5 9 

Crack 

FIG, 4. Calculated magnetic field H vs crack depth in the position with the 
crack on the opposite side of the specimen from the C core and away from 
the center of the sensor. 







J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Y. Shi and D. C. Jiles 6355 



FIG. 5. Calculated magnetic induction B vs crack depth in the position with 
the crack on the opposite side of the specimen from the C core and away 
from the center of the sensor. 



Cmckdvfrth (mm) 


FIG. 6. Calculated magnetic field H and magnetic induction B vs crack 
width and depth with the crack on the side of the specimen facing the C core 
and located at the center of the sensor. 


which was much less influenced by the two effects than was 
the highly localized magnetic field. The main factor influenc¬ 
ing the resultant magnetic induction was the size of the air 
gap which was introduced by the crack into the magnetic 
circuit. This increased the magnetic reluctance around the 
flux path and resulted in a decrease in magnetic induction 
with crack size under the same magnetomotive force as 
shown in Figs. 5 and 6. 

IV, CONCLUSIONS 

The interactions of the magnetic field and the fatigue 
crack were modeled using finite element techniques. It was 
found that the detected magnetic field was determined prin¬ 
cipally by two factors: the leakage field of the comers and 
tips of the crack and the demagnetizing effect of the crack 
surfaces. These two factors had opposite effects on the de¬ 
tected magnetic field amplitudes. On the other hand, the cal¬ 
culated magnetic induction appeared to be only determined 
by the crack geometry. 


ACKNOWLEDGMENT 

This research was supported by the National Science 
Foundation, Division of Civil and Mechanical Structures, un¬ 
der Grant No. CMS-9532056. 


^D. C. Jiles, NDT & E Int. 21, 311 (1988). 

^M. K. Devine, D. C. Jiles, D. A. Kaminski, and D. Chandler, Rev. Prog. 
Quantitative NDE 11, 1771 (1992). 

^M. S. C. Bose, NDT & E Int. 19, 83 (1986). 

K. Devine, D. A. Kaminski, L. B. Sipahi, and D. C. Jiles, J. Eng, 
Performance 1, 249 (1992). 

^Y. Bi, M. R. Govindaraju, and D. C. Jiles, International Magnetics Con¬ 
ference, New Orleans, 1-4 April 1997 (unpublished). 

^F. Forster, NDT & E Int. 19, 3 (1986). 

^J. H. Hwang and W. Lord, ASTM J. Testing Evaluation 21 (1975). 

*W. Lord, J. M. Bridges, W. Yen, and R. Palanisamy, Mater. Eval. 47 
(1978). 

^M. J. Sablik, S. W. Rubin, D. C. Jiles, D. Kaminski, and Y. Bi, IEEE 
Trans. Magn. Int. 32, 4290 (1996). 

^^Electromagnetic field analysis guide, ANSYS Inc., Release 5.3, 1996. 





JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Magnetohydrodynamic calculation for free surfaces 

Keisuke Fujisaki and Takatsugu Ueyama 

Process Research Tech Labs. Nippon Steel Corp., 20-1 Shintomi, Futtsu-city, Chiba 293-8511, Japan 

A magnetohydrodynamic calculation for free surface is used in the design and evaluation of a 
cold-crucible or initial solidification such as stirring phenomena commonly found in the metal 
processing industry, A direct calculation of both the electromagnetic field and the fluid dynamics 
field for the surface of a molten metal that changes with time requires significant computing times, 
especially for three-dimensional models. An approximate calculation method, the shadow method, 
is one which uses a fixed mesh. Results obtained by the shadow method show that the shape of 
molten metal does not collapse under gravity as observed experimentally. © 1998 American 
Institute of Physics. [80021-8979(98)33011-X] 


I. INTRODUCTION 

A magnetohydrodynamic calculation for free surface is 
used in the design and evaluation of cold-crucible or initial 
solidification such as stirring phenomena commonly found in 
the metal processing industry.The magnetohydrodynamic 
calculation is necessary for an electromagnetic field calcula¬ 
tion based on Maxwell equations and a flow dynamics cal¬ 
culation based on the Navier-Stokes equations. A direct cal¬ 
culation method that allows for the surface of the molten 
metal to change with time requires significant computing 
times, especially for three-dimensional models. Hence an ap¬ 
proximate scheme of calculation is desirable. 

In a free surface calculation, the shape of molten metal 
changes with time and the numerical solutions are iterated to 
within a certain error. Since the shape of the molten metal 
changes, a moving mesh calculation method is used."^ How¬ 
ever, using a moving mesh requires extra calculations needed 
to solve for the mesh positions. Moreover, the influence of 
the flow dynamics on the free surface shape is ignored. Only 
the balance of electromagnetic and gravitational forces is 
considered. Here, we propose a shadow method on a fixed 
mesh. 

II. CALCULATION METHOD 
A. Direct method 

Figure 1 shows the results of a magnetohydrodynamic 
calculation using the direct method. Through an electromag¬ 
netic analysis, the electromagnetic force is calculated, and 
the fluid dynamics is analyzed using the condition that the 
electromagnetic force is the driving force for the fluid dy¬ 
namics, During the fluid dynamic analysis, the velocity and 
the mesh shape are calculated, and the electromagnetic 
forces are analyzed using the condition that the velocity 
makes the electromotive force, and the mesh shape provides 
the new boundary condition. 

Here, the eddy current field and the quasistationary field 
are assumed in the electromagnetic analysis.^ Turbulent flow 
in the fluid dynamic analysis is assumed, because the Rey¬ 
nolds number is as large as 10^-10^. The direct method has 
been used for a two-dimensional model using a static 
condition.^’^ However, calculations of the electromagnetic 


fields and fluid dynamics in the case of a three-dimensional 
model or one with transient dynamics requires alot of com¬ 
putation. Hence an approximate shadow method is described 
and tested in this article. 

B. Shadow method 

Figure 2 shows the results of a magnetohydrodynamic 
calculation using the shadow method proposed here. The 
shadow method is used to model the electromagnetic fields 
in a flow dynamic calculation. The problem to be solved is 
how to calculate the new electromagnetic forces when the 
shape of molten metal changes as a result of the old electro¬ 
magnetic forces. Usually, the new electromagnetic forces are 
different from the old electromagnetic forces whenever the 
shape of molten metal changes. In the shadow method, it is 
assumed that the electromagnetic field is the same when the 
clearance between the coil and the molten metal is the same. 

In the shadow method, we consider one line in the mol¬ 
ten metal to be solved. The line could be selected to be along 
a direction in which the molten metal shape changes. Along 
this line, we can make any point of the molten metal which 
does not change shape corresponds to a certain point of the 
molten metal which changes under the influence of the old 
electromagnetic force distribution. Then the new electromag¬ 
netic force in the molten metal can be obtained from this one 
to one correspondence. 

The flow dynamics calculation for a free surface uses a 
fixed mesh. The mesh in free surface is expressed as the 
occupation rate of the molten metal. The curve of the free 
surface is made smooth on the mesh, where the pressure is 
equal. ^ 


Electromagnetic force 



Velocity 

Free surface shape 


FIG. 1. Magnetohydrodynamic calculation by direct method. 


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J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


K. Fujisaki and T. Ueyama 6357 


Electromagnetic force 




- 1 

Electromagnetic Analysis 

Eddy current field 

Quasi stationary field 

< - 

Fluid Dynamic Analysis 

Turbulent flow 

Free surface (VOF method) 



Velocity Electromagnetic force 

Free surface shape I i- 


Free surface mesh 


Shadow method 


FIG. 2. Magnetohydrodynamic calculation by shadow method. 


The shadow method is based on a modeling method 
called MORDY, which stands for moving reference frame 
model for multibodyThe MORDY approach is used in dy¬ 
namic calculations such as in electromagnetic levitated 
vehicles.^® 

III. CALCULATION RESULTS 
A. Calculation method 



1 OOnim 

Specification of molten metal 
Mass density : 9500 kg/m*^ 

Kinematic viscosity : 6.3 * 10'^ mVs 

FIG. 3. Calculation model (cylindrical 2D model). 


Figure 3 shows the calculation model here. To test the 
validity of the shadow method, we use a cylindrical two- 
dimensional non-static model. The z direction is the line that 
is selected. Along this line, the electromagnetic force is shad¬ 
owed from the old molten metal to the new molten metal. 
This model is used in the initial solidification in continuous 
casting.^ 

The electromagnetic forces are calculated using a gen¬ 
eral solver of electromagnetic fields called FLEDY.^^ The 


electromagnetic force is applied to the molten metal for the 
first 0.1 s. The calculation time of fluid dynamics is 2.0 s. 


B. Calculation results 

Figure 4 shows the calculated results without the shadow 
method. For z> 0.0557 m, no electromagnetic forces are ap¬ 
plied to the molten metal as shown in (2-1) of Fig. 4 (the 






FIG. 4. Calculation results by no shadow method, (a) Velocity distribution, (b) Electromagnetic force distribution. 












6358 J. Appl. Phys., Vo!. 83, No. 11, 1 June 1998 



(1-1). 1 sec. later. 



K. Fujisaki and T. Ueyama 



(2-1). 1 sec. later. 



FIG. 5. Calculation results by shadow method, (a) Velocity distribution, (b) Electromagnetic force distribution. 


electromagnetic force distribution after 1.0 s). The molten 
metal near the center line rises, and then falls down because 
there is no electromagnetic force to support it, as shown in 
(1-2) of Fig. 4 (the velocity after 2.0 s). This contradicts 
experimental observations during initial solidification,^ 
in which collapse of the metal does not occur. The electro¬ 
magnetic force only supports the molten metal in the first 
few seconds. 

On the other hand, Fig. 5 shows the calculated results 
with the shadow method. In contrast to the direct calculation, 
for z> 0.0557 m electromagnetic forces are applied to the 
molten metal as shown in the corresponding panel (2-1) of 
Fig. 5, The molten metal near the center lie also rises up. 
However, the molten metal does not fall down because the 
electromagnetic forces support the molten metal, as shown in 
(1-2) of Fig. 5. 


IV. CONCLUSION 

A shadow method is proposed here as the modeling 
method for free surface magnetohydrodynamic calculations. 


The results obtained by the shadow method show that the 
shape of molten metal does not collapse under gravity in 
accordance with experimental observations. 

*K. Fujisaki, J. Nakagawa, and H. Misumi, IEEE Trans. Magn. 30, 4764 
(1994). 

^S. Sato, Proceedings of Japan Industry Applications Society Conference, 
International Sessions of 7-th Annual Conference, S.11-5, August 1993, 
pp. 240-243. 

^A. J. Mestel, Proceedings of the International Union of Theoretical and 
Applied Mechanics, 1982, pp. 197-204. 

^Y. Kawase, Y. Murai, and N. Hayashi, Trans. Inst. Electron. Inf. Com¬ 
mon. Eng. Dll, J72 271 (1989). 

^K. Fujisaki, T. Ueyama, and K. Okazawa, IEEE Trans. Magn. 33, 1642 
(1996). 

^T. Toh, E. Takeuchi, J. Sakane, M. Hojo, H. Takeuchi, H, Kawai, and S. 
Matsumura, International Symposium on Electromagnetic, Processing of 
Materials, October 1994, pp. 254-259. 

’H. Ohsaki, Proceedings of Japan Industry Applications Society Confer¬ 
ence, International Sessions of 7-th Annual Conference, J.93-A-6, August 
1993, pp. 117-122. 

^C. W. Hirt and B. D. Nichols, J. Comput. Phys. 39, 201 (1981). 

^K. Fujisaki and E. Masada, Simulation (Japanese) 3, 88 (1984). 

‘^E. Masada and K. Fujisaki, “Untersuchung am dynamischen Verhalten 
des electromagnetischen Schwebefahzeugs durch die Simulation,” VDI- 
Berichte, Nr.510, S.223, March 1984. 

^^T. Ueyama, K. Shinkura, and R. Ueda, IEEE Trans. Magn. 25, 4153 
(1989). 










JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Differential Preisach model for the description of dynamic 
magnetization processes 

P. Andrei, Al. Stancu,®’ and O. Caltun 

‘ 'AL /. Cuza '' University, Faculty of Physics, Iasi, 6600, Romania 

A differential dynamic Preisach model developed by us and introduced as an idea suggested by 
Bertotti is generalized. The starting point of this model is that the instantaneous excess field due to 
the moving and dynamic processes can be approximated as a function of M and it’s variation rate 
dMfdt\ F{M,dMldt). Thus, we determine a differential equation for the magnetic susceptibility. 
The model’s parameters are found by an original identification method. As an application we 
simulate a simple electrical circuit and compare the results with the experimental data. A very good 
agreement between the measured and simulated data is observed. © 1998 American Institute of 
Physics. [80021-8979(98)33111-4] 


1. INTRODUCTION 

Generally, the actual phenomenological models for the 
magnetic hysteresis are given by a differential equation 
for the magnetization (or induction) and they try to fit theo¬ 
retical curves to experimental data. Usually, this differential 
equation (the model equation) is of the first order and one 
can determine the susceptibility x (or permeability) as a 
function of the magnetization M, of the applied field H, and 
of their variation rate {M and H). If x depends on all these 
variables then the model is called a dynamic model and if x 
is only a function of M and H, the model is a static one. 
Integrating one obtains the magnetization M 

as a function of time. There have also been a few attempts^’"^ 
to present some dynamic Preisach models in a mathematical 
form but none of them gives a differential equation. This 
makes it very difficult to use the Preisach model in many 
applications where the dynamic effects must be taken into 
account such as: simulation of electrical circuits that contain 
a coil with a nonlinear core or prediction of some magneti¬ 
zation processes where H is given by a differential equation. 

In this article we have generalized a dynamic Preisach 
model (DPM) recently developed by us.^ It is known^ that 
the dynamic effects in a magnetic core (such as the effects 
produced by eddy currents) can be taken into account by 
supposing that the effective magnetic field is the sum be¬ 
tween the applied field and an excess instantaneous field 
which depends on the variation rate of M. To consider a 
classical moving term depending on M as well, we suppose 
that the effective field is the sum of the applied field, H, and 
a general moving term, F(M,M), depending on M and M: 

7/eff=^ + W,M). (1) 

Due to the symmetry of the major loop the general moving 
function F must satisfy the condition F{M,M)^ -F(-M, 
-M). 


II. DYNAMIC PREISACH MODEL 


by us previously.^ We consider the generalized moving Prei¬ 
sach model with the effective field given by (1). The Prei¬ 
sach distribution function is assumed to be the product of a 
Gaussian distribution in the interaction field and a log¬ 
normal distribution in the coercive field: 


P{H,,Hp) = P^Pi\ 


VI I 



v 5 r 


with (Pq is a normalization factor): 


SM,Ho 


P,(/!)=exp| 



( 2 ) 


(3) 


1 

^c(^)=^exp 




where ^ttd are distribution standard deviations, Hq is 
the center of the distribution after coercivities and is the 
saturation value of the magnetization. The factor S represents 
the weight of the irreversible part in the total magnetization 
of the sample. The reversible component of the model is 
given by: 




(l-S)Ms I 




(4) 


where is a fit parameter. 

In order to find the susceptibility in DPM, we differen¬ 
tiate the total magnetization of the generalized moving Prei¬ 
sach model with respect to the magnetic field. Using the 
same method presented earlier^ one finds the differential 
equation: 


dx _ 1 

dt F'„{M,M) 


In order to find an analytical expression for the magnetic 
susceptibility in DPM we will employ a method developed 




^^Electronic mail: alstancu@uaic.ro 


where we have introduced the notations: 


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© 1998 American Institute of Physics 



6360 J. AppL Phys., Vol. 83, No. 11, 1 June 1998 


Andrei, Stancu, and Caltun 




i=< 


f%e 

JH 


6>^eff 

if H is increasing; 

dE{HQ^^,Hf^ eff) 


P{h,H,^^)dK 


= 2 P{H,^^,h)dK 

^ eff 


( 6 ) 


dH^ff 

if H is decreasing; 


is the value of the effective field, //^eff is the last 
extreme value of the effective field in the Preisach plane), 
and 




(7) 


The functions F'^{MM) and represent the par¬ 

tial derivatives of F with respect to M and M, respectively. 
The function F is the Everett integral defined as: 


E{H,,Hy) = 

J-H„ 


m 


erf 




H„ 



Hy + Hq + h 


P,{h + Ho)dh, 


( 8 ) 


where erf is the error function.^ The functions I and J rep¬ 
resent the irreversible and the reversible part of the suscep¬ 
tibility in the generalized Preisach model, respectively. 

The choice of the function F is a quite intricate problem. 
Bertotti^ has shown that the average excess field in a half 
hysteresis loop depe nds on the average magnetization rate as 
P sgn(M)(Vl + y|M| — 1), where fd and y are two 
parameters that depend on the material. In this article we 
suppose that at each point of the hysteresis loop the instan¬ 
taneous excess field is given by the same equation where M 
is the instantaneous magnetization rate. Thus, the generalized 
moving function is: 


F{M,M) = aM-p sgn(M)(Vl + rl^|-l). (9) 

where a is the moving parameter.^ The existence of the ex¬ 
cess magnetic field //gxc that adds to the applied magnetic 
field implies an important variation of the coercive field of 
the major hysteresis loop with the frequency of the applied 
field. Thus one can determine the parameters (3 and y by 
measuring the coercive field for different M. 


III. IDENTIFICATION METHOD 

There are some identification methods for the Preisach 
distribution but all of them are quite intricate and need many 
experimental data (e.g., Mayergoyz^). In this section we pro¬ 
pose a robust identification method for the Preisach distribu¬ 
tion’s parameters (M^, Hq, and 5) and for the 

moving parameter a from the experimental major hysteresis 
loop and the experimental remanent major loop, respectively. 

In order to determine the distribution’s parameters we 
have used the following method. First, one determines from 
the static hysteresis loop: the coercive field , the remanent 
magnetization the magnetization at the upper branch of 
the loop for the coercive field , and the energy lost per 
cycle (the surface of the loop) w, the closure field (the field 
where the upper branch of the major loop touches the lower 


branch) , the saturation field and the susceptibility at 
//cl and Hs [;^(//ci) and respectively]. Then, one de¬ 

termines the parameters (as the saturation value of the 
major loop) and //^ from the equation: 

(the susceptibility for field greater than is given by the 
reversible part of the susceptibility). Finally, one follows the 
iteration: 


( 1 ) 

( 2 ) 


(3) 


One starts from two “first guess” values of the param¬ 
eters Hq and (in our simulation we have always 
started from Hq = Hc and //^=//c). 

One determines S from the condition that the surface of 
the major loop is w: 


4MMf) 


/■ 


P,{V2h)hdh 


( 11 ) 


The parameter is determined from the remanent 
magnetization by solving the next transcendental 
equation: 


SM,Hq h\ 

M= " P,{Vlh)tTf\ — ]dh, (12) 

Vtt//^ Jo Went 

(4) The Hq parameter is determined from the coercive field 
by solving the transcendental equation: 


SM,Hq 




(v^/i)erf 


iH-h 

\ 


dh + 2 


r 


R{h)dh = 0. 

(13) 


(5) One repeats steps 2, 3 and 4 until the convergence is 
attained (in our simulations we imposed that the actual 
values of the 5, //^, and Hq differ from the old ones 
with a relative error of 10“*^). 

(6) One determines the actual value of from the upper 
branch of the major loop (we denote this value by M^): 


SM,Hq 

Mc=-^ - 


I 


^ P,(vlh)erfl^—jdh + 2 


r 


R{h)dh. 

(14) 


(7) If \M[ — Mc\<€ (where 6 is a small parameter that en¬ 
sures the convergence; we considered e- then 

one stops the iteration; else one pass to the next step. 

(8) One determines the new value of //^^ by adding to the 

old value of H^ the term — Mc), where ^ is an 

appropriate relaxation factor. This constant has to be suf¬ 
ficiently great in order to increase the convergence rate 
of the algorithm but not so large that it causes the algo¬ 
rithm to diverge (in our simulations we considered 1/ 
MJ. Then one passes to step 2 and one repeats the al¬ 
gorithm. 


In order to determine the moving parameter a we used 
the following algorithm. One starts with a “first guess” 
value for the moving parameter a (in our simulations we 
have started with a= 0) and transforms the experimental ma¬ 
jor loop in the operational plane (the operational plane is the 
plane (M,//+aM)). One determines the distribution’s pa¬ 
rameters using the method presented above and then the new 
value of the moving parameter by adding to the old value, 
the quantity:^ 



J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Andrei, Stancu, and Caltun 6361 



FIG. 1. Static hysteresis loops: experimental (points) and simulated (con¬ 
tinuous line). 

f (rem)_^(rem) 

where and are the coercive fields of the experi¬ 

mental and the simulated remanent major hysteresis loops, 
respectively, and is the simulated magnetization 

corresponding to One continues the iteration 

until Aa is negligible. 

IV. RESULTS AND DISCUSSIONS 

The experimental setup consists of a RL circuit in series 
with an ac generator. The inductance L is a MnZn soft mag¬ 
netic torus (A-41) having the inner radius ri = 23mm, the 
outer radius r 2 = 35 mm, and the high /z = 20mm. The ex¬ 
perimental magnetic hysteresis loop is determined using a 
digital storage oscilloscope.^ 

Using the identification method presented above we 
have obtained the next set of parameters: 3.2X10”^ 

A/m, 5=0.23, H^=21.5 A/m, H^=67A A/m, H^=in.O 
A/m, Hq=14A A/m, and a=1.13X10“l The experimental 
and the simulated static hysteresis loops are shown in Fig. 1. 
In Fig. 2 is shown the dc demagnetization (witch is used in 
the identification of a) and the isothermal remanent magne¬ 
tization curves. The identification method ensures that the 
coercive field , the magnetizations and and the 

looses (the area) in one major hysteresis loop are the same as 
the experimental ones. The dynamic parameters (B and y are 



FIG. 2. Experimental (points) and simulated (continuous line) remanent 
magneti-zation curves: IRM for positive fields and DCD for negative fields. 



FIG. 3. Dynamic hysteresis loops for v=\ kHz: experimental (points) and 
simulated (continuous line). 

calculated from least-squares criteria applied to the simulated 
and experimental wave form magnetization in the dynamic 
loop. We present in Fig. 3 the dynamic hysteresis loop, ob¬ 
tained for the frequency of the applied field v -1 kHz. One 
observes a substantial increase of the coercive field (approxi¬ 
mately five times) that is characteristic to the soft ferrites. 

V. CONCLUSIONS 

Various magnetization processes were simulated with a 
differential Preisach model. The dynamic processes were 
taken into account using a simple phenomenological assump¬ 
tion: the effective field in the Preisach plane is the sum of the 
applied field and a generalized moving field depending on 
the instantaneous magnetization and its variation rate. The 
same method can be applied to all the phenomenological 
models of hysteresis (e.g., the files-Atherton model and 
Hodgdon model). We have deduced a differential equation 
for the magnetic susceptibility, analogous to that previously 
presented. 

In order to determine the model’s parameters we have 
developed a robust identification method that needs the ex¬ 
perimental major hysteresis loop (for the distribution param¬ 
eters) and the experimental dc demagnetization curve (for the 
moving parameter). A very good agreement is observed be¬ 
tween the simulated and experimental curves. 

ACKNOWLEDGMENTS 

Petru Andrei extends his gratitude to Prince Dimitrie 
Sturdza for financial support. The authors also wish to ac¬ 
knowledge IEEE Magnetics Society and “Al. I. Cuza” Uni¬ 
versity for financial support. 

*D. C. files and D. L. Atherton, J. Appl. Phys. 55, 2115 (1984). 

^C. D. Boley and M. L. Hodgdon, IEEE Trans. Magn. MAG-25, 3922 
(1989). 

^I. D. Mayergoyz, Mathematical Models of Hysteresis (Springer, New 
York, 1991). 

"^G. Bertotti, F. Fiorillo, and M. Pasquale, IEEE Trans. Magn. 29, 3496 
(1993). 

^P. Andrei, O. Caltan, and Al. Stancu, IEEE Trans. Magn. 34, 231 (1998). 
^G. Bertotti, J. Appl. Phys. 57, 2118 (1985). 

^M. Abramovitz and I. A. Stegun, Handbook of Mathematical Functions 
(National Bureau of Stand. Appl. Math. Series) (NBS, Washington, DC, 
1964), Vol. 55. 

^J. Oti, F. Fajda, and E. Della Torre, J. Appl. Phys. 69, 4826 (1991). 

^N. Schmidt and H. Giildner, IEEE Trans. Magn. 32, 489 (1996). 



JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Influence of the permanent magnet overhang on the performance 
of the brushless dc motor 

J. P. Wang and D. K. Lieu 

University of California, Berkeley, California 94720 

W. L. Lorimer and A. Hartman 

Quantum Corporation, Milpitas, California 95035 

Axial overhang of the permanent magnets has been used to enhance the performance of radial flux 
brushless dc motors, but its precise contribution to performance is not well known. This article aims 
at the investigation of the overhang effects by finite element and lumped parameter modeling. An 
empirical formula which allows two-dimensional analysis to account for overhang effects is 
proposed. A three-dimensional equivalent magnetic circuit model is developed and its ability to 
accurately predict overhang effects is assessed. Results of finite element and lumped parameter 
models are compared and a design methodology is forwarded. © 1998 American Institute of 
Physics. [80021-8979(98)46911-1] 


I. INTRODUCTION 

High performance and low power brushless dc motors 
continue to be the trend in the hard disk drive (HDD) indus¬ 
try. Axial oyerhang of the permanent magnets has been used 
to enhance the performance of radial flux brushless dc mo¬ 
tors, but its precise contribution to performance is not well 
known. Besides adding cost, there are three other reasons 
why it is not wise to use overhang without knowing its 
proper length. First, not all the extra magnetic flux produced 
by magnet overhang produces useful torque. Second, the 
originally preferred trapezoidal back EMF shape will be dis¬ 
torted if the flux increment is not uniform at all rotor posi¬ 
tions. Third, magnet overhang is not effective in improving 
performance unless the stator has been sized to accommodate 
the additional flux. The purpose of this paper is to investigate 
the overhang effects by three-dimensional (3D) finite ele¬ 
ment (FEM) and lumped parameter modeling (LPM). The 
former is favored for its high accuracy in handling highly 
nonlinear magnetic field in electrical machines. The latter is 
popular for its fair accuracy but quick repetition of compu¬ 
tation. 

To account for magnet overhang and end leakage ef¬ 
fects, which can be significant in low-profile motors, a 3D 
model is required. The data storage space and CPU time 
required for a 3D finite element model, however, may be 
prohibitive. 

Lumped parameter modeling, an alternative to FEM, has 
a good capability in predicting magnetic flux and back EMF 
in 2D problems.^ The model is extended to 3D by adding 
permeances representing extra flux and leakage paths to the 
original magnetic circuit built for 2D problem. 

A typical 8-pole 12-slot spindle motor used in the HDD 
is used in this analysis. To illustrate three-dimensional ef¬ 
fects, magnetic flux and back EMF are computed for differ¬ 
ent overhang lengths as a function of rotor position. Differ¬ 
ent permanent magnet strength (remanence) is applied to 
achieve different saturation levels. Overhang effects pre¬ 
dicted by FEM and LPM are compared, and recommenda¬ 


tions for accurately predicting optimum magnet overhang 
without a full 3D finite element analysis are forwarded. 

II. 3D MODEL DESCRIPTION 
A. Finite element model 

The top view of a typical 8-pole 12-slot spindle dc 
spindle motor and a description of the finite element mesh is 
shown in Fig. 1 (and Table I, respectively). The aspect ratio 
(airgap diameter divided by stator height) for this motor is a 
moderate 2.5, but ratios as high as 10 are common in HDD 
motors. Permanent magnets are modeled with radial magne¬ 
tization, materials are assumed isotropic and hysteresis ef¬ 
fects are ignored. The size of analyzed domain can be re¬ 
duced to one octant by taking advantage of the symmetry 
and imposing the proper boundary conditions. The angular 
size of the elements in the airgap are chosen to be the same 
as that of rotor step angle in order to maintain mesh unifor¬ 
mity and in turn improve accuracy. In selecting axial mesh 
density, models of increasing coarseness are solved. The 
coarsest mesh to produce the converged (fine mesh) solution 
is chosen for speed considerations. Solution time for a single 
rotor position ranges from 2 hours to 8 hours in the nonlinear 
cases. 



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© 1998 American Institute of Physics 



J. Appl. Phys,, Vol. 83, No. 11, 1 June 1998 


Wang et al. 6363 



FIG. 2. 3D lumped parameter model permeances. 



FIG. 3. The effect of the size of magnet deadzone on the flux increment, 
15% overhang. 



angle (degree) 



FIG. 4. The effect of the size of slot opening on the flux increment, 15% 
overhang. 



FIG. 6. Flux increments for motors with various aspect ratios and overhang 
lengths in linear cases. 


B. Lumped parameter model 

Three-dimensional LPM is developed by modifying 2D 
model described in Ref. 1. Permeances modeling extra flux 
and leakage paths are added and properly connected to the 
2D model. Figure 2 shows part of the modification. Instead 
of a single path in 2D model, one additional path is added to 
lead flux originating from the overhang part to the stator 
tooth through its top. Three permeances, P2, P3, and P4 are 
added to account for this axial flux. As in the 2D case, per¬ 
manent magnets are modeled as constant potential sources 
and their permeances are determined by a periodic function 
of theta.^ In the 3D model, the 2D magnet permeance used to 
represent the internal resistance of one magnet is split into 
two, PI and P2. P2 has the same angular distribution as PI 
(original 2D magnet permeance) and is computed by (1). 

P2 = Pl*(rotor height-stator height)/stator height. (1) 

Conventional straight-line and circular-arc technique is used 
for modeling permeances P3 and P4. P3 models the flux 
linking to the tooth foot from its top, P4 models the flux 
going directly to the tooth stem and equals to zero for a short 
overhang. 

Unlike FEM, where there is a significant computational 
cost associated with 3D solutions, the addition of 3D per¬ 
meances in LPM has a much smaller impact. End-to-end 
leakage permeances can be numerically superposed to exist¬ 
ing 2D permeances according to electrical circuit theory. The 
additional 3D permeances are all linear, and consequently 




FIG. 5. The effect of the saturation level and overhang on the flux incre¬ 
ment, Br=0.71 in nonlinear cases. FIG. 7. The effect of the overhang length on the back EMF, Br=0.5. 


























6364 


J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Wang et al. 



angle (degree) 


FIG. 8. Flux increment of different overhang lengths predicted by LPM. 


have a minimal impact on computation time. Computation 
time consumed in 2D and 3D LPM simulation are of the 
same order. 

III. RESULTS AND DISCUSSION 

Figures 3-8 show results over one-half pole pitch, start¬ 
ing from the zero flux (peak back EMF) position. Flux incre¬ 
ment is defined as the difference between effective tooth flux 
predicted by 3D and 2D models divided by that of the 2D 
model. With this definition, flux increment at 0° is unde¬ 
fined. Magnet overhang is defined as the difference between 
magnet height and stator height divided by stator height. 

Intuitively, several factors such as the size of the slot 
opening and magnet dead zone, as well as the overhang 
length, rotor position, and saturation level of stator teeth may 
influence the overhang effects. The first two factors are ex¬ 
amined first. Figure 3 and Fig. 4, respectively, illustrate the 
influence of the magnet deadzone and slot opening on the 
flux increment. Both linear and nonlinear cases are investi¬ 
gated. It is seen that the sizes of magnet dead zone and slot 
opening have no (slight) influence on the flux increment in 
the linear (highly saturated) cases. 

Figure 5 shows how the flux increment changes with 
magnet overhang. In the linear cases, the flux increment is 
positive and uniform through the cycle, but it is not propor¬ 
tional to the overhang length. Being independent of the rotor 
position, the flux increment can be simply related to the 
overhang length. As shown in Fig. 6, motors with lower 
aspect ratio require higher order polynomial functions of 
overhang length to approximate the flux increment. The back 
EMF (the derivative of flux) is also magnified proportionally. 
Thus, in the linear case, only magnet overhang and motor 
aspect ratio influence the flux increment. 

Magnetic saturation complicates the flux increment be¬ 
havior. The nonlinear results shown in Fig. 5 are for a se¬ 
verely saturated design (Br=0.71 T). The flux increment as¬ 
sociated with the position where the magnet transition is 
aligned with a tooth edge is comparable to the linear case, 
i.e., flux is increased by the introduction of magnet overhang. 


TABLE I. Motor dimensions and mesh details. 


Gap diameter 

19.5 mm 

Stator z-height 

7.66 mm 

Gap 

0.25 mm 

Element type 

8-node brick 

Mesh size 

1° angular 

Gap elements 

4 radial 

No. nodes 

30 000-64 000 


As the rotor moves away from this position, however, the 
flux increment decreases, and near the peak back EMF posi¬ 
tion (0°), the flux is actually lower than in the 2D case. 
Figure 7 shows that the detrimental effect of excess overhang 
occurs even under conditions of moderate saturation (Br 
=0.5 T). Some overhang (up to 15%) is beneficial to the 
back EMF its magnitude is increased and shape is preserved. 
As overhang is increased, the back EMF dip becomes evi¬ 
dent. This tendency is more pronounced in highly saturated 
designs and in configurations with pole pitch longer than slot 
pitch. The complicated behavior exhibited in the nonlinear 
case encourages the construction of 3D LPM rather than the 
simple correction factor applicable to linear cases. 

To test the capability of the 3D LPM, flux increments 
due to different overhang lengths are computed and com¬ 
pared with FEM results. It is observed by comparing Fig. 5 
and Fig. 8, the 3D LPM successfully predicts the trends, but 
tends to overpredict the flux decrement in the vicinity of 0°. 
This discrepancy may be tolerable for design if the impact on 
rms back EMF is small. The reason for the discrepancy be¬ 
tween LPM and FEM is the subject of current research, and 
an improved LPM is expected. 

IV. CONCLUSION 

A typical 8-pole 12-slot spindle motor used in the HDD 
is used to investigate overhang effects. In the case of mild 
saturation, magnet overhang always enhances motor perfor¬ 
mance, increasing back EMF without changing its shape. A 
series of polynomial functions of overhang length approxi¬ 
mate the flux increment of motors with various stator heights 
and can be used together with 2D FEM in lieu of a full 3D 
model. Under saturating conditions, however, the simple re¬ 
lationship does not hold. Furthermore, excessive overhang is 
shown to be detrimental to back EMF. To properly design 
for magnet overhang, a 3D lumped parameter model using 
straight-line and circular-arc technique to model axial flux is 
proposed. Although there is some discrepancy in the magni¬ 
tude of flux increment at certain rotor positions under severe 
saturation, the 3D LPM well predicts the trend of flux incre¬ 
ment, and seems a better tool for the searching of optimal 
overhang length in terms of the accuracy and CPU time. 

U. P. Wang and D. K. Lieu, IEEE Trans. Magn. 33, 4092 (1997). 

^Z. Q. Zhu and D. Howe, IEEE Trans. Magn. 29, 124 (1993). 




JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Optimization of coils for detecting initial rotor position in permanent 
magnet synchronous motor 

S. Wakao T. Onuki, K. Tatematsu, and T. Iraha 

Department of Electrical, Electronics and Computer Engineering, Waseda University, 3-4-1 Ohkubo 
Shinjuku-ku, Tokyo 169-8555, Japan 

This article describes the shape optimization of detective coils for initial rotor position estimation in 
the drive system of permanent magnet synchronous motors. The characteristics of magnetic circuits 
in rotating machinery are very complicated. The magnetic flux distribution in the air gap is 
nonsinusoidal due to the influence of slots, magnets, and magnetic saturation, etc. By utilizing the 
slot ripple influence and taking the effects of both magnetic saturation and permanent magnets into 
consideration, an optimization of the detective coil by means of a genetic algorithm combined with 
a hybrid finite element and boundary element method is reported. This produces a global optimal 
solution in a shorter time. © 1998 American Institute of Physics. [S0021“8979(98)50811-0] 


I. INTRODUCTION 

There is a growing interest in permanent magnet syn¬ 
chronous motors (PMSMs) owing to their high power den¬ 
sity and efficiency. Recent efforts are directed toward devel¬ 
oping the sensorless drive system for PMSM applications, 
and various algorithms of rotor-position estimation have 
been proposed. However, these algorithms, which are gener¬ 
ally based on the measurement of terminal voltages and cur¬ 
rents of the motor, have some difficulties to detect the rotor 
position at standstill because the terminal quantities cannot 
be measured. This results in unstable starting with counter 
rotation. 

To overcome these difficulties in PMSM sensorless 
drives at standstill, the authors propose to attach additional 
coils to the motor for detecting the initial rotor position. The 
proposed detection scheme is based on the voltage induced 
in the additional coil owing to the small displacement of the 
rotor with permanent magnets. Applying an impulse input to 
the armature results in the small displacement of the rotor, 
and the displacement is transformed into induced voltages. 
Thus, we can estimate the initial rotor position, and hence 
sensorless operation follows by using the detected position. 
It is desirable that the wave form of the induced voltage be a 
square wave that is suitable for digital processing. This re¬ 
sults in both a decrease of the dead zone and an increase in 
accuracy of the initial rotor-position estimation. This article 
is aimed at designing the additional coil to obtain the desir¬ 
able wave form of the induced voltage. Taking the charac¬ 
teristics of magnetic circuits in rotating machinery, e.g., 
magnetic saturation, into consideration, the authors perform 
an optimization procedure by means of the genetic algorithm 
(GA) combined with the hybrid finite element and boundary 
element (FE-BE) method. 

Finally, the numerical example of a concrete model (a 
four-pole PMSM) is presented to indicate the validity of the 
proposed optimization procedure. 


®^Electronic mail: wakao@mn.waseda.ac.jp 


II. INVESTIGATED SYSTEM 

The configuration of the investigated model is shown in 
Fig. 1. The stator is made of isotropic silicon steel, and the 
rotor of carbon steel (S45C). Figure 2 represents iht B-H 
curves of the steel. Rare-earth magnets of Sm-Co type are 
attached to the rotor, and their remahence Bj. and coercive 
force He are 0.9 T and 7.0X 10^ A/m, respectively. 

The additional coils are thin and placed in the air gap 
along the stator surface. The voltage induced in the addi¬ 
tional coil is amplified and transformed into the rotor posi¬ 
tion data by a signal processing circuit. A signal processing 
circuit is usually composed of some logic-integrated circuits 
of complementary metal-oxide semiconductor type that have 
two logic states, i.e., //-level and L-level. The boundary be¬ 
tween //-level and L-level is called the threshold voltage. 
The variation of output voltage in the detective coil is illus¬ 
trated in Fig, 3. If the induced voltage rises slowly, the 
L-level region becomes larger than that of the fast rise case 
as in Fig. 3. The dead zone of detective coil increases with 
the L-level region, which causes the detection capability of 
the proposed scheme to decrease. Hence it is desirable that 
the wave form of the induced voltage changes in the rectan¬ 
gular form with rotation. This article describes a shape opti- 


permanent magnet 




FIG. 1. Four-pole permanent magnet synchronous motor. 


0021-8979/98/83(11 )/6365/3/$15.00 


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© 1998 American Institute of Physics 




6366 J, Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Wakao et al. 



Magnetic field intensity H (A/m) 
(a) stator 



Magnetic field intensity H (A/m) 
(b) rotor 


FIG. X B-H curve of steel. 


L-region H-region V„,: Threshold Voltage 



desirable waveform 
(wide H-region) 


undesirable waveform 
(narrow H-region) 

Mechanical degree 


L-region H-region 
FIG. 3. Wave form of induced voltage. 



FIG. 4. Magnetic flux distribution. 


mization procedure to give the detective coil with the above- 
mentioned characteristics. 


Hi. OPTIMIZATION PROCEDURE 

The finite element method (FEM) and the boundary ele¬ 
ment method (BEM), which have entirely different features 
from each other, are very useful for numerical analysis of the 
physical phenomena described by partial differential equa¬ 
tions. Both methods seem to be complementary partners and 
not opponents. Therefore, taking into account of the advan¬ 
tages in these methods, the authors adopt the hybrid FE-BE 
method as a field calculation tool in this article. By apply¬ 
ing the FEM to the rotor and stator regions and the BEM to 
the air-gap region, a two-dimensional analysis of magnetic 
field with moving boundaries is naturally implemented with¬ 
out remeshing. This also allows easy consideration of mate¬ 
rial nonlinearlity by the FEM, and enables the precise esti¬ 
mation of air-gap field by the BEM. 

The fundamental equation of the magnetic field in terms 
of the magnetic vector potential A can be obtained as 
follows: 

Vx(vVXA) = yo + ^^ (1) 

where v is the reluctivity, J is the current density, and M is 
the magnetization density. The demagnetization characteris¬ 
tic of the permanent magnet is approximated by a straight 
line, and M is described as 

M = B-/XoH = B-MB-Br){H,IB,), (2) 

where /m is the permeability. The reluctivity is not constant 
but dependent on the applied magnetic field. Therefore, the 
distribution of the magnetic field is calculated by the itera¬ 
tion method including a nonlinear analysis. In this article, the 



FIG. 5. Reluctance torque characteristic. 



FIG. 6. Coding for string structure. 


















J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Wakao et al. 6367 



FIG. 7. Optimized configuration of additional coil. 

Newton-Raphson method^ is used in considering the nonlin¬ 
ear characteristics as in Fig. 2. The magnetic field distribu¬ 
tion and the reluctance torque characteristic of the investi¬ 
gated model are shown in Figs. 4 and 5, respectively. On the 
whole, the calculated values of the reluctance torque agree 
with the experimental data. Finally, regarding the flux distri¬ 
bution in the shaft direction as uniform, we estimate the 
magnetic flux interlinkage of the detective coil and derive the 
wave form of the induced voltage by inner field calculation 
of the BEM. 

As regards to a search algorithm, the genetic algorithm 
(GA) is adopted.*^’^ The GA is a powerful search method 
based on probabilistic evolution through generations, which 
consists of three fundamental operators upon the string struc¬ 
tures; reproduction, crossover, and mutation. These string 
structures called chromosomes represent different design pa¬ 
rameters, respectively, (see Fig. 6). Calculating the objective 
function value, i.e., the length of L-level region, by the hy¬ 
brid FE-BE method, the GA estimates the fitness of each 
string structure and creates a new generation from the previ¬ 
ous one by the three above-mentioned operators. This results 
in the survival of the strings that better suit the environment, 
i.e., the decrease of L-level region, along the future 
generations. 


TABLE I. Optimization results. 


Design 

variable 

Result 

(Xpole pitch) 

Design 

variable 

Result 

(xpole pitch) 

Wa 

0.021 

Wh 

0.000 

Wb 

0.021 

Wi 

0.056 

Wc 

0.104 

Ha 

0.144 

Wd 

0.083 

Hb 

0.544 

We 

0.049 

He 

0.611 

Wf 

0.056 

Hd 

0.428 

Wg 

0.021 

He 

0.628 



FIG. 8. Voltage induced in additional coil. 


IV. NUMERICAL RESULTS 

An optimization procedure using a GA combined with a 
hybrid FE-BE method is reported. The initial population of 
the search has 40 members. The members of the initial popu¬ 
lation are created by randomly placing the binary code of 
{0, 1} into the bit positions of the chromosomes. Each of the 
14 design variables is coded into a four- or five-bit string 
segment as shown in Fig. 6. Both the roulette wheel and elite 
technique are implemented for the reproduction operator. 
The uniform crossover, where each bit in the string has a 
probability of 0.6 to be swapped, is adopted for the crossover 
operator. The occurrence probability for mutation is 0.05. 
The decision on the convergence of solutions is based on the 
fitness, i.e., the objective function value, of the population. 
The search is terminated in 937 generations in this example. 
The whole CPU time required for the optimization procedure 
is about two days under typical workstation-implementing 
conditions. The optimization results are shown in Fig. 7 and 
Table I. Figure 8 indicates the computational results of the 
normalized voltage wave form induced in the shape- 
optimized coil. For a comparison, the wave forms of the 
rectangle-shaped coils with lengths W of one or half pole 
pitch are also computed and shown in Fig. 8. In this ex¬ 
ample, setting the threshold voltage of 0.2, we can find the 
L-level region, i.e., the dead-zone, of the shape-optimized 
coil is reduced to about 20% of that of the rectangle-shaped 
coils. 


^T. Onuki, IEEE Trans. Magn. 26, 582 (1990). 

^S. Wakao and T. Onuki, IEEE Trans. Magn. 29, 1487 (1993). 

^T. Onuki, S. Wakao, and T. Hattori, IEEE Trans. Magn. 30, 2908 (1994). 
'^T. Onuki, S. Wakao, and T. Yoshizawa, IEEE Trans. Magn. 31, 1436 
(1995). 

^T. Nakata, N. Takahashi, K. Fujiwara, N. Okamoto, and K. Muramatsu, 
IEEE Trans. Magn. 28, 1048 (1992). 

^D. E. Goldberg, Genetic Algorithm in Search, Optimization and Machine 
Learning (Addison-Wesley, 1989). 

’F. G. Uler, 0. A. Mohamed, and C. S. Koh, IEEE Trans. Magn. 30, 4296 
(1994). 














JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER II 


1 JUNE 1998 


Temperature analysis of induction motors using a hybrid thermal model 
with distributed heat sources 

S. C. Mukhopadhyay®^ and S. K. Pal 

Department of Electrical Engineering, Jadavpur University, Calcutta 700032, India 

The article presents a hybrid thermal model for the accurate estimation of temperature distribution 
of induction motors. The developed model is a combination of lumped and distributed thermal 
parameters which are obtained from motor dimensions and other constants such as material density, 
specific heats, thermal conductivity, etc. The model is especially suited for the derating of induction 
motors operating under distorted and unbalanced supply condition. The model have been applied to 
a small (2hp, 415 V, 3-phase) cage rotor induction motor. The performance of the model is 
confirmed by experimental temperature data from the body and the conductor inside the slots of the 
motor. © 1998 American Institute of Physics. [80021-8979(98)23511-0] 


I. INTRODUCTION 

Prediction of temperature distribution of induction mo¬ 
tors is very important to the design engineers as well as 
motor manufacturers. To have a good knowledge of tempera¬ 
ture rise, studies on thermal model of induction motors 
started quite a long time back. Thermal circuit have been 
used in the past for electric machinery analysis. An equiva¬ 
lent thermal circuit for non-ventilated induction motors was 
reported by Kotnik.^ The different parts of the machine had 
been considered as lumped parameters interconnected with 
each other. This just gives some ideas of average temperature 
rise of motors which was sufficient during that time. Many 
papers have dealt with the temperature estimation method of 
the induction motor by using finite element (FE) analysis. In 
FE analysis usually only a part of stator core and rotor core is 
considered in the model.^ It is difficult to know the tempera¬ 
ture distinction along the motor lamination unless a whole 
model is taken into consideration, particularly under unbal¬ 
anced voltage operation. This article has described the devel¬ 
opment of a hybrid thermal model for the analysis of motor 
temperature distribution. The model can be used during the 
unbalanced and distorted supply operation of the motors. 


II. THERMAL MODEL FORMULATION 

The nonsteady conduction equation of heat flow in two 
dimensions is known to be 


dh 




dh 


dy^ dt 


dT 

+ q* = pCp—, 


( 1 ) 


where and Ky are the thermal conductivities along X and 
Y direction, respectively, is the internal generated heat 
per unit volume, p is the density, and Cp is the specific heat. 
Equation (1) can be expanded and the equation for the cen¬ 
tral node, a, in terms of adjacent nodes b, c, d, and e as 
shown in Fig. 1, can be expressed as 




R 


ab 


Rn 


R 


ad 


Rn 


( 2 ) 


where and 7^ represent current and future temperature of 
node “a,” respectively, is the rate of heat addition to 
node a, Ca is the thermal capacitance associated with node 
a\ Rah^ Rqc^ Rad^ Rae represent the thermal resistance 
between nodes a-h, a~c, a-d, and a-e, respectively. 

Based on this idea the nodes are assumed throughout the 
motor cross section, while the thermal capacitances are con¬ 
sidered to be lumped at each node and thermal resistances 
between two consecutive nodes. The thermal model devel¬ 
oped for the determination of temperature condition along 
the motor cross section is shown in Fig. 2. The nodes lying 
extreme outside represent the ambient temperature and the 
next inside ones are lying on the motor surface. Adequate 
number of nodes are assumed to know the detailed tempera¬ 
ture distribution of the motor. 

The thermal resistances are given by 


Rt= 


1 L 


(3) 


where is the thermal conductivity, L is the length of heat 
flow path and A is the area normal to heat flow path. The 
thermal conductivities of different materials are chosen as: 
iron=73, air=0.0241, copper=386, aluminium=202, and 



“^Electronic mail: chandra@magstar.ec.t.kanazawa-u.ac.jp 


FIG. 1. Nodal network representation for two-dimensional heat flow. 


0021 -8979/98/83(11 )/6368/3/$15.00 


6368 


© 1998 American Institute of Physics 



J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


S. C. Mukhopadhyay and S. K. Pal 6369 



9lf SOS 


FIG. 2. Thermal model of induction motor. 


insulation=0.05. Using Eq. (3) the thermal resistances of the 
following sections are calculated: (i) frame, (ii) stator core, 
(iii) stator teeth, (iv) stator slot to stator core, (v) stator slot to 
stator teeth, (vi) rotor slot to rotor teeth, (vii) rotor slot to 
rotor core, (viii) rotor teeth, (x) rotor core, and (x) shaft. The 
following resistances are calculated separately: (i) between 
frame and ambient, (ii) contact resistance between frame to 
stator laminations, and (iii) airgap between stator and rotor. 

The thermal resistance between frame and ambinet (such 
as /?j 5 , etc. are catculated by ^^/^node» where 

A r is the frame temperature rise over ambient and is 
the power dissipated from each node. The approximate value 
of A? is obtained by ts.t~Wl{AK), where W is the total 
power loss of the machine in W, A is the surface area in m^, 
and is a constant chosen as 97.1 W/m^rC. 

Using Eq. (4) the heat dissipated by radiation, is 
obtained, where e is relative emissivity, assumed to be 0.9. 


W,=5n2Ae 


273+r,„b+A?\4 

100 


100 j 


(4) 


The rest power Wc—W—Wj. is dissipated by convection. 
From Eq. (5) A? is obtained, where D is the outer surface 
diameter of the machine in meter. 

W,= 12.02a|^| (5) 


If Af obtained from Eq. (5) does not match to that obtained 
earlier, by slight adjustment At is obtained by repeating (4) 
and (5). 

Due to imperfect contact between stator lamination and 
frame, the thermal resistance is calculated by 
where is thermal contact resistance and depends on the 
metals involved, the surface roughness, the contact pressure, 
the materials occupying void spaces and temperature. The 
value of rjc has been chosen as 0.0005 m^ °CAV in the 
model. 



FIG. 3. Experimental setup. 


The thermal resistance of airgap between stator and rotor 
is defined in terms of a dimensionless Nusselt number, 
the airgap length, and is given by Eq. (6). to be 
properly chosen.^ 

4 • (6) 

airbag 

The lumped thermal capacitance at each node is defined as 

Ca-VaPC,, (7) 

where length {dx and 8y being the average 

length between two consecutive nodes along X and Y direc¬ 
tion, respectively), p is the density, and is the specific 
heat of the material on which it lies. 

In order to model accurately, the heat input to each node 
must be allocated properly. The dissipated power are: ohmic 
losses in stator and rotor winding, iron losses in stator core 
and teeth, flux pulsation loss in stator and rotor teeth, and 
frictional windage loss. The ohmic losses are calculated from 
the ohmic resistance and current. Ohmic resistance should be 
properly adjusted to take into account of temperature rise. 

The iron losses are calculated from Eq. (8), 

p = afBl + b{VfBp)\ ( 8 ) 

where p is the power loss per kg, / is frequency, V is the 
thickness of lamination in mm. Bp is the peak value of flux 
density; a and b are two constants and are assumed to be 
0.057 and 0.00282 in the model. 

In machines with slots both on stator and rotor, the flux 
density in the teeth varies as the relative position of the teeth 
varies. The amplitude of the flux fluctuation in the stator 
teeth is 



JjL 


^c2-l 

Kc2 


■B 


tm \ » 


(9) 


where and 7^2 are the slot pitches of stator and rotor, 
respectively. Kc 2 is the Carter factor of the rotor, and is 
the maximum value of flux density in the middle of the 
tooth. 

The frequency is given by where Q 2 

is the number of slots in the rotor. For the rotor teeth the 
indices 1 and 2 should be interchanged. 

The pulsation loss in watts per unit weight of the teeth is 
given by 






6370 J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


S. C. Mukhopadhyay and S. K. Pal 




FIG. 4. Thermal characteristic (a) at continuous running with short time 
load, (b) steady-state temperature with power output. 


P=b{VfBp)\ (10) 

The mechanical loss due to friction of the bearing and wind¬ 
age loss are 

5-4* 10^(rpm)^‘^*P^, (11) 


where Py? is the rated power of the machine in watts. 

After calculating all the thermal resistances and capaci¬ 
tances and allocating the losses to each node, the temperature 
of each node is calculated by 



0 _ 


( 12 ) 


Starting values of all the nodes are taken to be equal to 
ambient temperature. The time step Sr should be critically 
selected so that 


dr^ 


1 


(13) 


The solution is assumed to reach steady-state values when 

(14) 

is satisfied for each and every node, where 6 is a convergence 
criterion. 


III. PERFORMANCE OF THE MODEL AND 
EXPERIMENTAL VERIFICATION 

The model is applied to a small 4 pole motor. The de¬ 
tailed specifications of the motor are: Three-phase cage-rotor 
induction motor; power output=2hp, voltage=415 V, 
current=3.2 A, frequency=50 Hz, speed=1425 rpm, 
insulation=Class B, no of stator slots=36, no of rotor slots 
=44, stator outer diameter =190 mm, rotor outer diameter 
= 114.5 mm, core length=100 mm, stator resistance per 
phase=6.8 fl, rotor resistance referred to stator=6.4 fi. 

The experiments are conducted using the setup as shown 
in Fig. 3, The load on the motor is changed by varying the 
excitation. The surface and slot temperatures are measured 
by temperature sensors. 

Figure 4(a) shows the simulated and experimental ther¬ 
mal characteristic at continuous running with short time load. 
Figure 4(b) shows the variation of steady-state temperature 
of surface and slot with power output. It is seen that the 
difference of the experimental and simulated values are less 
than 2 °C. 


IV. CONCLUSION 

This article has reported the development of a thermal 
model for the temperature analysis of induction motors. The 
model is based on distributed thermal resistances and capaci¬ 
tances with properly allocated heat sources to each node. The 
model can predict both steady state and transient temperature 
rise of motors. Predicted results were compared with mea¬ 
surements showing good agreement, thus proving the valid¬ 
ity of the model. 

‘R. L. Kotnik, AIEE Trans. Feb. 1955, pp. 1604-1608. 

^A. F. Armor and M. V. K. Chari, IEEE Trans, Power Appar. Syst. PAS- 
95, (1976). 

^S. C. Mukhopadhyay, Ph.D. thesis, Jadavpur University, India, 1994. 






JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER II 


1 JUNE 1998 


Bifurcation phenomena and chaotic attractors in a six-dimensionai 
noniinear system 

T. Sutani®* 

Kanazawa Institute of Technology, 7-1 Ogigaoka, Nonoichi, Ishikawa 921-8812, Japan 

T. Czaszejko 

Monash University, 900 Dandenong Road, Caulfield East, Victoria, Australia 3145 

A. Nafalski 

University of South Australia, Warrendi Road, The Levels, Adelaide, South Australia 5095 

Some chaotic properties of a six-dimensional nonlinear dynamic system are investigated. Equations 
describing the system are based on the equivalent circuit of a magnetic frequency tripler. Numerical 
solutions are obtained using the fourth-order Runge-Kutta algorithm. Simulation results reveal the 
presence of Hopf and a period-doubling bifurcations. Phase space projections at points before and 
after bifurcations show the existence of three symmetrical and four asymmetric regions. Poincare 
maps reveal six different chaotic attractors within the asymmetric regions. The correlation 
dimension of the sea horse attractor is found to be 2.37. © 1998 American Institute of Physics, 
[S0021-8979(98)23611-5] 


I. INTRODUCTION 

Studies of bifurcation phenomena in the Van der Pol- 
Duffing oscillator as well as in two coupled Duffing oscilla¬ 
tors were described recently in Refs. 1 and 2. A similar be¬ 
havior can be observed in an electromagnetic circuit of a 
frequency tripler. This circuit can be described as a six¬ 
dimensional nonlinear dynamic system and it can be simu¬ 
lated on a computer using the fourth-order Runge-Kutta al¬ 
gorithm. In the previous attempt to depict bifurcation 
diagrams of the magnetic frequency tripler using voltage of 
the saturable reactor as a parameter, a period-doubling (PD) 
bifurcation and the presence of a chaotic attractor were re¬ 
vealed. These results were presented in Refs. 3 and 4. 

This article describes equations of state for a six¬ 
dimensional nonlinear system based on the equivalent circuit 
of a magnetic frequency tripler. Numerical solution of these 
equations enable further analysis. Characteristic sequences of 
transitions are studied using bifurcation diagram. The phase 
space projections obtained from the numerical solution 
verify existence of chaotic attractors in the regions after bi¬ 
furcations as well as the presence of symmetry in the phase 
space. Then, the correlation dimension of the phase space 
trajectory is performed in the region of sea horse attractor. 


II. EQUATIONS OF STATE 

The six-dimensional nonlinear system described in this 
article is obtained from the equivalent circuit of a magnetic 
frequency tripler with series-connected reactors.^ Figure 1 
shows the six-dimensional nonlinear system for computer 
simulations. This system was presented in detail previously 
in Refs. 3 and 4. Here, we bring only its short description. If 


“^Electronic mail: t-sutani@neptune.kanazawa-it.acjp 


magnetizing characteristics of the saturable reactors are ap¬ 
proximated by third-order polynomials, equations of state for 
this system become 

ii = —/^iXi —sin T, 

X2 = /:3^1 “ “ PliA " ^2i^4 ^ 

i3 = ^4(x2 + X6), 

X4 = k5(X2-X6), 

i5 = ^6^6, 

■^6“ ^20^4“ ^10^3“ ^00^5 “^00^5 “^7*^6? 

where (jcj ,X 2 ,.^.,X 6 ,t) eR^XS\teSK 

These equations are solved numerically using the fourth- 
order Runge-Kutta algorithm with double precision. The 
system is iterated 36 000 times (200 periods, 4007r). A step 
size of 3.4906585X10”^ (27r/180) ensured converged nu¬ 
merical results. 

III. BIFURCATION DIAGRAM 

Bifurcation diagrams are obtained by setting the coeffi¬ 
cient k 4 (voltage across Cin and Co) as a parameter and by 
plotting solutions for ;c 5 obtained at 27r radian intervals. In 
order to exclude initial transient solutions for 0^r<1007r are 
ignored, and then, solutions for 10077=^7^40077 are plotted. 

Figure 2 shows bifurcation diagram obtained by incre¬ 
menting parameter k 4 by 0.002 units. It can be seen from the 



FIG. 1. Six-dimensional nonlinear system for computer simulations. 


0021 -8979/98/83(11 )/6371/3/$15.00 


6371 


© 1998 American Institute of Physics 



6372 


J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Sutani, Czaszejko, and Nafalski 



FIG. 2. Bifurcation diagram with ajo^ ^oo^O, a2/=5.0Xl0 ^ a 20 
= 6.0X10~^ /S,,= 1.5, )0oo=l-8, /3io=l-3, /=12.5, ;t, = 0.05, A:2 = 0.011, 

/:3 = 20.0, ^5 = 0.2, = = a:2o=1<0, X3o=5.0, jc4o=2.0, JC50 

= 3.0, and X6o=4.0. 


diagram that the region k4<0A is chaotic. This chaotic re¬ 
gion is followed by a sequence of period-one, period-two, 
and period-one solutions. The Hopf bifurcation takes place at 
k4=0.3 followed by another band of period-one solutions. 
The PD bifurcation occurs at ^4 = 0.448, followed by another 
chaotic region. Later, for 0.63 </: 4 < 0.79, period-one solu¬ 
tions dominate except for a few chaotic regions appearing 
sporadically. The bifurcation diagram converges finally to 
stable period-one solutions for /: 4 > 0 . 8 . 

IV. PHASE SPACE PORTRAITS 

All period-one solutions of the analyzed system return 
generally identical phase space trajectories if the initial tran¬ 
sients are ignored. Phase space trajectories for chaotic solu¬ 
tions, on the other hand, assume several characteristic 
shapes. Figure 3 shows some examples of the phase space 
diagrams obtained for 1007r<r^ 10277 before and after Hopf 
bifurcation points. 

The orbit shown in Fig. 3(a) is obtained for /:4 = 0.272. 
This orbit is asymmetric. Figure 3(b) shows the orbit for the 
parameter increased to 0.284. The resulting orbit becomes 
symmetrical with respect to origin, i.e.,/( —x)— —f(x). Fig¬ 
ure 3(c) shows an asymmetric orbit at an upper symmetry¬ 
breaking (SB) point which occurs for ^4 = 0.298. The transi¬ 
tion from the upper SB point leads to the onset of the Hopf 
bifurcation. This transition can be identified as Hopf bifurca¬ 
tion following Sparrow’s work on the Lorenz system^ and 
Kozlowski’s work on two-coupled Duffing oscillators. From 
there, it is concluded that Hopf bifurcation is always accom¬ 
panied by SB in the phase space diagram. 

Figure 4 shows examples of orbital trajectories from the 
third and the widest region on the bifurcation diagram in 
which symmetry is maintained. Figure 4(b) shows the orbit 



(a) (b) (c) 

FIG. 3. Phase space projections: (a) k 4 =0.212, (b) ^4 = 0.284, and (c) k 4 
= 0.298. 


at k 4 = 0.360 with its typical shape for this symmetrical re¬ 
gion. In comparison with Fig. 3(b), the orbit has similar in¬ 
verse structure except that this time it has more loops which, 
in turn, indicates the presence of higher harmonics. Further, 
symmetric trajectories become asymmetric at ^4 = 0.390, but 
here the SB point does not precede a PD bifurcation. 

In the analyzed system, there are no further symmetrical 
regions observed for k4^0.390. In such a case, a question 
arises whether phase space portraits at points prior and after 
PD bifurcation present the same asymmetric structure. In or¬ 
der to clarify this question, orbital projections of the phase 
space are investigated around this PD bifurcation point. Fig¬ 
ure 5(a) shows an orbit for r between IOO 77 and 10277 for 
/:4 = 0.4465, i.e., just prior the bifurcation. This orbit is asym¬ 
metric. Figure 5(b) shows an orbit for ^4 = 0.4466. The orbit 
also appears to be asymmetric. However, comparison of the 
shape of orbits prior to bifurcation with that after the bifur¬ 
cation reveals that they are in central symmetry with each 
other with respect to origin. For the first time it is shown that 
a reversal of phase space occurs in order to preserve asym¬ 
metry at the PD bifurcation point. 

V. CHAOTIC ATTRACTORS 

There have been several types of chaotic attractors de¬ 
fined in multidimensional dynamic systems.^ In order to find 
the types of attractors existing in the frequency tripler ana¬ 
lyzed in this paper, Poincare maps are constructed for chaotic 
regions identified previously on the bifurcation diagram. Six 
maps, consisting of 2000 periods (t=400077) each, are 
shown in Figs. 6 (a)- 6 (f). These maps are obtained for k 4 
=0.05, 0.16, 0.30, 0.50, 0.59, and 0,74, respectively. Figures 
6 (a) and 6 (b) show two slightly different Poincare sets but 
both displaying characteristics of hyperchaos.^ Figure 6 (c) 
shows a chaotic attractor obtained at a point after Hopf bi¬ 
furcation. This attractor does not represent a limit cycle and 



(a) (b) 

FIG. 5. Phase space projections: (a) ^4 = 0.4465 and (b) k 4 -0.4466. 



J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


SutanI, Czaszejko, and Nafalski 6373 



FIG. 6. Two hyperchaos: (a) A:4=0.05 and (b) k^=0.l6, and four chaotic attractors: (c) A:4=0.30, (d) ^4 = 0.50, (e) /c4=0.59, and (f) ^4 = 0.74. 


it can be called a string attractor. Figure 6(d) shows a shape 
of the before-presented sea horse attractor. The harp attractor 
is also identified within the region of the PD cascade and it is 
shown in Fig. 6(e). It should be noted that the harp attractor 
is not a part of the sea horse attractor, as it may appear, but 
it is another type of attractor. Figure 6(f) shows a sparrow 
attractor which appears in the narrow chaotic regions after 
the PD cascade. In summary, two hyperchaos and four other 
chaotic attractors are identified in the six-dimensional system 
investigated in this article. 

In order to determine dimensionality of a dynamic sys¬ 
tem the correlation method is used. Following the work of 
Grassberger and Procaccia,^ the correlation dimension 
can be defined as 


Dc= lim[log C(^)log S], (2) 

5->0 


where C(S) is a correlation integral as a function of the 
diameter S, of the phase space volume element in which the 
integral is evaluated. 

Computations of the correlation dimension for the fre¬ 
quency tripler are performed on the phase space trajectory 
assuming the shape of a sea horse attractor on the Poincare 
map. As the result, the value of D^=2.37 is obtained. This 
outcome indicates that our original six-dimensional system 
can be described with a substantially smaller number of vari¬ 
ables, possibly as low as three. 


VL CONCLUSION 

Bifurcation phenomena and chaotic attractors in a six¬ 
dimensional nonlinear system based on the equivalent circuit 
of a magnetic frequency tripler have been analyzed in this 
article. The main results are as follows. 

(1) Phase space projections are asymmetric at regions 
where hyperchaos, period-two solutions, the Hopf bifurca¬ 
tion and the period-doubling bifurcation occur. 

(2) The occurrence of the Hopf bifurcation is accompa¬ 
nied by symmetry breaking of the phase space trajectory. 

(3) The phase space trajectory reverses at the point of 
the period-doubling bifurcation to preserve asymmetry. 

(4) The existence of two hyperchaos and four chaotic 
attractors is found in the system. 

(5) The correlation dimension of the sea horse attractor 
is 2.37. 

Our next subjects are investigation on mechanics of de¬ 
velopment of chaotic attractors and controlling chaos in the 
six-dimensional system. 

^G. P. King and S. T. Gaito, Phys. Rev. A 46, 3092 (1992). 

Kozlowski, U. Parlitz, and W. Lauterbom, Phys. Rev. E 51, 1861 
(1995). 

^T. Sutani and K. Bessho, Trans. lEE Jpn. 115-D, 936 (1995) (in Japanese). 

"^T. Sutani and A Nafalski, Australasian Universities Power Engineering 
Conference, AUPEC’96, 1, 1996, pp. 263-267. 

^T. Sudani and K. Bessho, IEEE Trans. Magn. MAG-23, 1956 (1987). T. 
Sudani changed the expression of his family name to T. Sutani in 1993. 

^C. Sparrow, The Lorenz Equations: Bifurcations, Chaos, and Strange At¬ 
tractors (Springer, New York, 1982), p. 11. 

^M. Franaszek, Phys. Rev. E 49, 3927 (1994). 

^0. E. Rossler, Phys. Lett. A 71, 155 (1979). 

^P. Grassberger and I. Procaccia, Physica D 9, 189 (1983). 



JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Symposium on Layered Manganites 


J. D. Jorgensen, Chairman 


Two-dimensional ferromagnetic correlations above Tq in the naturally 
layered CMR manganite La 2 _ 2 xSri+ 2 xMn 207 (x=0.3-0.4) (invited) 

D. N. Argyriou and T. M. Kelley 

Los Alamos Neutron Science Center, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 

J. F. Mitchell 

Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439 

R. A. Robinson 

Los Alamos Neutron Science Center, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 

R. Osborn and S. Rosenkranz 

Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439 

R. I. Sheldon 

Los Alamos Neutron Science Center, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 

J. D. Jorgensen 

Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439 

Neutron diffuse scattering in the form of rod-like features has been observed in single crystals of the 
layered CMR material La2- 2jcSri + 2xMn207 (jc = 0.4,0.36), consistent with the presence of 2D 
ferromagnetic spin correlations. These diffuse features are observed over a wide temperature region. 
However, their coherence length does not appear to diverge at , although there is evidence of the 
development of three-dimensional correlations around ferromagnetic reflections of the 3D-ordered 
magnetic structure close to 7^' Quasi-elastic neutron scattering on a ceramic sample of x = 0.3 
shows that the lifetime of these ferromagnetic correlations increases at 7—>7^. They exhibit a 
spin-diffusion constant above 7^ of ~5meVA^, much lower than that reported for 
La2/3Cai/3Mn03. We discuss the relationship of these magnetic correlations to models of the 
ferromagnetic transition in CMR compounds. © 1998 American Institute of Physics. 
[80021-8979(98)43211-0] 


The close interplay among charge, spin, and lattice de¬ 
grees of freedom in the colossal magnetoresistive (CMR) 
manganite oxides is widely believed to play an important 
role in the mechanism of transport in these itinerant ferro- 
magnets. Among the current models of transport in the three- 
dimensional perovskite materials is that magnetic polarons— 
mobile lattice distortions carrying spin—are the fundamental 
charge-carrying entity, at least above the Curie temperature 
(7^).^’^ Indeed, localized lattice distortions have been ob¬ 
served above and below 7^,^’"^ in the (La, Ca)Mn03 perov¬ 
skite system. DeTeresa et al have extended this work by 
inferring that these lattice distortions carry spin (magnetic 
polarons) from recent in-field small angle neutron scattering 
(SANS) experiments on the perovskite La2/3Cai/3Mn03.^ 
While current attention is centered on perovskite 
manganites, the discovery of layered compounds 
La2_2jcSrn.2jcMn207 as another class of CMR oxides pro¬ 
vides a rich opportunity to explore structure-property rela¬ 
tionships on varying length and time scales in reduced di¬ 
mensions. The material of interest, is comprised of 
perovskite bi-layers of comer-linked MnO^ octahedra form¬ 
ing infinite sheets. Bi-layers of (La, Sr)Mn03 are separated 


along the c-axis by insulating (La, Sr)0 layers. We have 
shown that although below Tq Mn-spins order ferromagneti- 
cally within the a^-plane^ in a certain compositional range, a 
competition between super- and double-exchange may re¬ 
sults to a canting of Mn-spins between adjacent ferromag¬ 
netic sheets, within the perovskite bi-layer.^ There is evi¬ 
dence to show that this competition may be reflected within 
ferromagnetic correlations above 7^7, as reported recently by 
Osborn et al} Perring et al also report that weak antiferro¬ 
magnetic and ferromagnetic spin fluctuations coexist in these 
layered materials above Clearly, understanding both 
long and short range magnetism—structure and 
dynamics—is an essential ingredient in developing a coher¬ 
ent picture of the physics of this class of transition metal 
oxides. 

In this paper we report neutron scattering results from 
single crystals with jc = 0.4 and 0.36 that demonstrate that 2D 
ferromagnetic correlations exist in these layered CMR mate¬ 
rials, as high as 2.87^. Their size increases as 7^7^ reach¬ 
ing a size of ~ 10 A at 7^. The coherence length of these 
ferromagnetic correlations does not appear to diverge at 7^. 
Quasielastic neutron scattering from a polycrystalline x 


0021 -8979/98/83(11 )/6374/5/$15.00 


6374 


© 1998 American Institute of Physics 




J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Argyriou et al. 6375 


=0.3 sample, reproduce the single crystal results and find a 
spin diffusion constant of 5 meV A^, lower than that re¬ 
cently determined for the 3D perovskite materials. 

Single crystals of were melt-grown 

in flowing 100% O 2 in a floating zone optical image furnace 
(NEC SC-M15HD). The crystals were characterized using 
inductively coupled plasma spectroscopy (ICP), d.c. magne¬ 
tization, and resistivity. Two single crystals were prepared 
and characterized by these methods; ICP measurement of 
their composition was determined to be consistent with a 
doping of x = 0.40(1) (Laj 2 Sri gMn 207 ) and x = 0.36(1) 
(Laj 28 Sri 72Mn207). These samples exhibit transitions from 
a paramagnetic insulator (PI) to a ferromagnetic metal (FM) 
at 133 K for x = 0.36 and 116 K for jc = 0.4. Diffraction data 
were obtained as a function of temperature from these single 
crystals, using the neutron time-of-flight single crystal dif¬ 
fractometer (SCD) located at the Manual Lujan Jr., Neutron 
Scattering Center (MLNSC) at the Los Alamos National 
Laboratory. Quasi-elastic neutron scattering data were mea¬ 
sured as a function of temperature from a polycrystalline 
sample with x=0.3 (La^^Sr^ 6 Mn 207 ) synthesized via stan¬ 
dard ceramic techniques exhibiting coupled PI to FM transi¬ 
tions at 116 K, using the time-of-flight chopper spectrometer 
PHAROS, also located at the MLNSC. Data were recorded 
using an incident energy of 12.1 meV, except for data mea¬ 
sured at 115 K where incident energies of 12.1 and 8.1 meV 
were used to extend the Q range of the measurement. Neu¬ 
tron powder diffraction data were measured as a function of 
temperature from 20-300 K, using the Special Environment 
Powder Diffractometer (SEPD)^^ at the Intense Pulsed Neu¬ 
tron Source at the Argonne National Laboratory. 

Single crystal time-of-flight neutron diffraction is ideally 
suited for the broad survey of reciprocal space for both 
Bragg reflections (long range structure) and also diffuse scat¬ 
tering which reflects structural features on a local scale. For 
both x = 0.36 and x=0.4 single crystals, we observe a diffuse 
rod-like feature along c* centered at (0,1,0) and (1,0,0). An 
example of these rod-like features is shown in Fig. 1, mea¬ 
sured at 120 K from the x = 0.36 crystal. The diffuse scatter¬ 
ing is strongly temperature dependent, becoming more in¬ 
tense as while below it decreases, consistent 

with scattering from magnetic correlations. For the x=0.4 
crystal we do observe rod-like features for higher orders of h 
and k [(/i,00) or (0,A:,0) with /z or A: as high as 7], where the 
magnetic form factor is expected to decrease substantially 
the magnetic scattering. These features have a smaller 
FWHM than the scattering at /i= 1, or A: = 1, suggesting that 
there is an additional nuclear component to the observed 
magnetic scattering. This nuclear scattering may arise from a 
low density of perovskite intergrowths in the crystal as pro¬ 
posed by Potter et al and also observed in high resolution 
electron microscopy. For the x = 0.36 crystal we observed 
no diffuse scattering at higher orders of h and A, suggesting 
a significantly lower concentration of intergrowths than in 
the x = 0.4 crystal. 

Figure 2 shows the variation of the intensity of the mag¬ 
netic rod scattering in both x = 0.36 and x = 0.4 crystals as a 
function of temperature. These values were obtained by fit¬ 
ting data perpendicular to the rod, along the [010] direction. 


1.00 


t 

8 0.00 



t 


8 


FIG. 1. Time-of-flight neutron diffraction data measured from a single crys¬ 
tal of Laj 28 Sri 72Mn207 at 120 K. The observed scattering is shown as a 
section through reciprocal space (a) perpendicular to [100] and (b) perpen¬ 
dicular to [001]. The small peak just below the (011) reflection corresponds 
to a much smaller second crystal in the sample with a relative intensity of 
the main (011) reflection of 1/5000. 


with a Lorentzian function and accounting for the nuclear 
scattering with a narrower Lorentzian with its width fixed at 
a value determined at 20 K. We find that the intensity of the 
magnetic diffuse scattering increases as from above, 

while below Tc its intensity decreases, vanishing for T 
<0.5Tc. That this scattering appears as a diffuse rod along 
c* and with a finite width along [hOO] or [OAO], clearly 
shows that the spin correlations are 2D. We find that these 
modulations are ferromagnetic but do not strictly obey a 
cos^(7r.Az./) dependence (where Az is the difference of the 
fractional z coordinate between neighboring Mn atoms); we 
have proposed a model where these modulations are de¬ 
scribed in terms of spin-canting in these ferromagnetic cor¬ 
relations resulting from a competition between super- and 
double-exchange which is reported elsewhere.^ On Fig. 2 we 
also show the variation of intensity of the (0,1,1) ferromag- 





6376 J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Argyriou et al. 


Ti 


1.0 

.■•■r— 

.T'" 




ju 

1 



1.2 

r Magnetic 


Correlations 



Long Range U 



0.8 

Ordering 

^1 



0.4 

<- 

• 

1 



0.0 


1 

• x=0.4 



J ^ 

1 

ll 

o x=0.36 



_ 

1 

___ 

■> 


1 


# 5 I 0 

_J 


0.0 0.5 1.0 1.5 2.0 2.5 


T/T^ 


FIG. 2. Temperature dependence of diffuse scattering intensity at (0,1,0) 
and the intensity of the ferromagnetic (0,1,1) measured from single crystals 
of jc = 0.4 and 0.36. The intensity of the (0,1,1) reflection has been normal¬ 
ized to its intensity measured at 300 K. 


netic reflection as a function of temperature. This demon¬ 
strates that peak in the intensity of the ferromagnetic 2D 
fluctuations is correlated with the onset of 3D magnetic or¬ 
dering. The observed ferromagnetic reflections below Tc 
were consistent with ordered Mn spins aligned ferromagneti- 
cally within the ab plane as reported previously.^ 

The coherence length of the ferromagnetic correlations 
within the perovskite bilayers, is —4-5 A at 300 K, 
and increases to —10 A at 7^. Surprisingly ^ 2 d does not 
appear to diverge at 7^ (see Fig. 3). It is unclear where the 
critical region for these 2D ferromagnetic correlations lies, 


11 

9 

iU' 

7 


c 

. 


80 100 120 140 160 180 200 

Temperature (K) 


FIG. 3. The planar coherence length ^ 2 d a function of temperature. 


however, from a more detailed study on the same x=0.4 
crystal we find that power law scaling of ^2 d suggests a 
much lower critical temperature for these correlations than 
actually observed; a =98 K is obtained using a mean 
field exponent f= 0.5, or a 7^^=63 K for a 2D-Ising expo¬ 
nent of 1.^ Interestingly, measurement of the critical scat¬ 
tering close to the (004) ferromagnetic reflection suggests 
that there is a buildup of three-dimensional correlations be¬ 
low 120 K resulting in a coherence length that appears to 
diverge at 7^ These data suggest that there may be a cross¬ 
over close to Tc from 2D to 3D critical scaling. However, 
we also note that in the same temperature region we have 
reported significant electron-phonon coupling in these 
materials.^ As discussed below, these localized lattice distor- 



2 
1 

0 

-1 

-2 

2 

1 

0 
-1 
-2 

0.0 0.1 0.2 0.3 0.4 0.5 





Q(A-1) 


Energy Tranfer (meV) 


FIG. 4. Inelastic neutron data in Q,o) space measured at 128 K (a) and 30 K (b) using an incident neutron energy of 12.1 meV. The same data measured at 
128 K (c) and 30 K (d) plotted as a function of energy integrated over the accessible g-range of this measurement. See text for details. 
















J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Argyriou et af. 6377 



FIG. 5. (a) Temperature dependent resistivity and magnetization (deter¬ 
mined from full profile Rietveld refinement of neutron powder data) from 
the polycrystalline sample Laj 4 Sri 6 Mn 207 , (b) integrated intensity of the 
quasi-elastic Lorentzian component, and (c) coherence length as a function 
of reduced temperature T/r^. In (c) the dashed lines are a fit to a power law 
function. Magnetic reflections from the x = 0.3 sample were consistent with 
a ferromagnetic alignment of Mn spins in the plane.® 

tions may contribute to the lack of divergence in the 2D 
coherence length. Theoretical considerations suggest that this 
coupling arises from local Jahn-Teller effects in these mixed 
valent materials. 

To investigate the spin dynamics of these 2D ferromag¬ 
netic correlations we have measured quasi-elastic neutron 
scattering from a large polycrystalline sample of x = 03. 
(The need for a large sample mass to yield sufficient signal- 
to-noise prohibited the use of a single crystal specimen for 
this experiment.) We have deliberately selected a range 
to measure ferromagnetic scattering as I or Q~^0 without 
the measurement being perturbed by spin waves and 3D spin 
correlations at lower Q. Figures 4(a) and 4(b) show data 
measured at 128 and 30 K in space, while panels (c) 
and (d) show the same data, integrated over the accessible Q 
range, as a function of energy. On panels (c) and (d) we 
show a fit to the elastic incoherent peak using a Gaussian 
function with a fixed FWHM that reflects the resolution of 
the spectrometer (dashed line). At 30 K we find no signifi¬ 
cant deviations from the fit, as seen in Fig. 4(d). This con¬ 
trasts with the scattering at higher temperatures, and espe¬ 
cially close to Tc, where we find an additional broad 
Lorentzian component superimposed on the Gaussian elastic 



FIG. 6. The (2-dependence of the Lorentzian quasielastic width (F) at 115 K 
measured from a ceramic sample of La| 4 Sri 6 Mn 207 . The dashed line rep¬ 
resents a fit to r = Aj2^, while the solid line represents the behavior ob¬ 
served in La 2 / 3 Ca|/ 3 Mn 03 reported by Lynn et al}^ 


incoherent peak. This feature is clearly shown in Figs. 4(a) 
and 4(c). The intensity of the Lorentzian component diverges 
as Q—^0, as expected for ferromagnetic correlations. 

Both quantitatively and qualitatively this ceramic x 
”0.3 sample behaves similarly to the single crystals dis¬ 
cussed above. A broad Lorentzian component is observed as 
high as 2,8[Fig. 5(b)], while with decreasing temperature 
and approaching Tq, the intensity of the quasi-elastic scat¬ 
tering increases and reaches a maximum at Below Tq 
the quasi-elastic scattering decreases linearly with tempera¬ 
ture suggesting that it may result from soft c-axis spin wave 
scattering. The peak in the quasi-elastic scattering at Tc 
strongly correlates with a sharp decrease in the resistivity of 
the sample, and the development of three-dimensional order¬ 
ing of Mn spins determined from neutron powder diffraction, 
as shown in Fig. 5(a). These observations resemble those 
reported from inelastic scattering experiments on three- 
dimensional perovskite materials. The spatial extent 
of the ferromagnetic correlations—computed from the Q de¬ 
pendence of the Lorentzian signal—yields an overall | of 
^^5 A (~ 1.30a), increasing to ~ 12 A at Tci^'iAa), simi¬ 
lar to that found for the single crystal samples described 
above [see Fig. 5(c)]. 

The lifetime of these ferromagnetic correlations, ob¬ 
tained from the width of the quasi-elastic scattering inte¬ 
grated over the accessible Q range of the measurement, in¬ 
creases T^Tc, reaching a value of 1.1(1)X 10“^^ s at 7^. 
Interestingly like the correlation length, the lifetime does not 
diverge suggesting that even close to there are 2D fer¬ 
romagnetic spins that are rapidly fluctuating [see Fig. 5(c)]. 
Lynn et al}^ have suggested that the magnetic transition in 
CMR perovskites is unusual as the spin waves stiffness con¬ 
stant D does not collapse close to 7^. Instead they describe 
the magnetic transition in the perovskite La 2 / 3 Cai/ 3 Mn 03 in 
terms of spin-diffusion due to slow polaronic hoping of 
carriers with a spin diffusion constant. A, of 30 meV A^, a 
quantity that is analogous to the spin-stiffness constant for a 
magnetically ordered system. From the Q dependence of the 
Lorentzian width we estimate a spin-diffusion constant A 
~5 meV A^ at 115 K for our sample (see Fig. 6), a value 
substantially lower than the perovskite material 








6378 J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Argyriou et al. 


(30meV A^). Presumably, this reduced A is a consequence 
of the low dimensionality of these naturally layered manga- 
nites. 

The results presented here clearly demonstrate that in 
these naturally layered materials 2D ferromagnetic correla¬ 
tions exist at temperatures as high as ~2.8rc. As T 
Tq , their size and lifetime increases but these quantities 
do not appear to diverge at Clearly there is a need to 
reconcile the behavior of these ferromagnetic correlations 
with the 3D ferromagnetic transition at 7^, where critical 
behavior and a divergent coherence length is observed about 
magnetic reflections. The data support a model where the 3D 
magnetic transition interrupts 2D fluctuations that would oth¬ 
erwise order over a long range at a lower Tc (see also Ref. 
8). That the measured Tc occurs at a higher temperature that 
than the estimate of suggests that at a critical size ^ 2 D » 
Mn spins in adjacent perovskite bilayers may start ordering 
ferromagnetically in three dimensions. This implies a cross¬ 
over to 3D critical scaling close to 7^. Indeed the underly¬ 
ing physics of these 2D ferromagnetic correlations may be 
competing antiferromagnetic super-exchange and ferromag¬ 
netic double-exchange; in a previous paper we have reported 
that this competition may result in a canted Type-A ferro¬ 
magnetic structure in x = 0.4 below 7^.^ As pointed out by 
Osborn et aL these ferromagnetic correlations may arise 
from the same competition above 7^.^ 

Alternatively the observation of nondivergent ferromag¬ 
netic correlations over a wide temperature region, may lend 
support to the small polaron model put forward to explain 
CMR in the manganite perovskites.^’^ Rdder et al} have cal¬ 
culated the magnetic behavior of localized phenomena such 
as Jahn-Teller polarons associated with localized e^ carriers 
and argue that the magnetic transition in the CMR mangan- 
ites is accompanied by a crossover of length scales from a 
quasi-self-trapped small polaron to a large polaronic state 
below Tc . At Tc their calculation predicts a magnetic co¬ 
herence length of ^3-4 Mn sites or ^12-16 A. As mag¬ 
netic polarons have a finite size, their coherence length is not 
necessarily expected to diverge as in a second-order mag¬ 
netic transition. That is, the coherence length of the 2D mag¬ 
netic correlations may be constrained by the lattice degrees 
of freedom (localized Jahn-Teller effects), which are in turn 
influenced by the electronic state. Our values of ^ 2 d 
reasonable agreement with the prediction of Roder et al. and 
the size measurements of magneto-elastic polarons by De- 
Teresa et al in La 2 / 3 Cai/ 3 Mn 03 ,^ while the lower value of A 
observed here may reflect polaronic mobility in reduced di¬ 
mensions compared to the 3D octahedral network of perov¬ 
skite materials. However, since the degree of electron- 
phonon coupling (via the Jahn-Teller effect) and 7^ are 
closely coupled in the CMR materials,the difference 
between the two possible explanations put forward here may 
be subtle. 


In conclusion, we have demonstrated the existence of 2D 
ferromagnetic correlations in layered CMR materials over a 
wide temperature range, with a coherence length ^ 2 D 
lifetime that do not diverge at 7^- These 2D ferromagnetic 
correlations accompany the ferromagnetic transition at 7^-, 
which appears to exhibit critical scattering and a divergent 
coherence length. Quasi-elastic neutron scattering shows 
these ferromagnetic correlations still fluctuate rapidly close 
to Tc y while the spin diffusion constant is much lower than 
the perovskite materials. Importantly, the naturally layered 
manganites provide a unique opportunity to examine in de¬ 
tail the mechanism of this crossover between 2D and 3D 
magnetism. 

This work was supported by the U.S. Department of En¬ 
ergy, Basic Energy Sciences-Materials Sciences under con¬ 
tract W-7405-ENG-36 (D.N.A, T.M.K, R.A.R) and W-31- 
109-ENG-38 (JEM, RO, JDJ, SR). D.N.A also thanks R. 
Heffner, H. Rdder, H. N. Bordallo, and P. G. Radaelli for 
stimulating discussions on this subject, and the Institut Laue 
Langevin for financial support during the preparation of this 
manuscript. 


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JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Chemistry of naturally layered manganites (invited) 

P. D. Battle,®* N. Kasmir, J. E. Millburn, M. J. Rosseinsky, R. T. Patel, L. E. Spring, 
and J. F. Vente 

Inorganic Chemistry Laboratory, Oxford University, South Parks Road, Oxford 0X1 3QR, United Kingdom 

S. J. Blundell, W. Hayes, A. K. Klehe, A. Mihut, and J. Singleton 

Department of Physics, Clarendon Laboratory, Oxford University, Parks Road, Oxford 0X1 3PU, 

United Kingdom 

Experiments on three double-layer (n = 2) Ruddlesden-Popper (RP) systems are reported. Doping 
Srj gLai 2 Mn 207 (r^= 126 K) with Nd to form Srj gLai 2 -A:Nd;^.Mn 207 leads to a reduction in Curie 
temperature for low doping levels {x = 0.2), and to behavior reminiscent of Srj gNdj 2 Mn 207 for 
x^OJ. This suggests that it may be possible to control the temperature of maximum 
magnetoresistance chemically in these phases. The application of pressure (0<P/GPa^l.8) is 
shown to modify the magnetotransport properties of Sr 2 NdMn 207 to resemble those of 
Srj 9 Nd 2 iMn 207 , The changes can be explained by considering the relative strength of 
ferromagnetic and antiferromagnetic interactions within the material. Finally, the need for careful 
phase analysis of n = 2 RP materials is demonstrated by the misleading magnetization data recorded 
for a sample of Srj gSmj 2 Mn 207 containing —2.8% of an n = ^ perovskite phase. © 1998 
American Institute of Physics. [80021-8979(98)20911-X] 


I. INTRODUCTION 

Compounds of manganese have played a central role in 
recent studies of the magnetotransport properties of mixed 
metal oxides. It has been shown that the electrical resistivity 
of oxides containing Mn in a nonintegral oxidation state 
can decrease dramatically in an applied magnetic 
field, an observation that may lead to applications in the area 
of data storage. The effect has been most widely studied^in 
perovskites of the general form Lnj _j^A;,.Mn 03 , where the 
presence of both lanthanide (Ln) and alkaline earth (A) cat¬ 
ions results in the adoption of a mixed-valence state by the 
Mn cation. Perovskite can be regarded as the n = co member 
of the Ruddlesden-Popper (RP)^ family of compounds 
(Ln, A)„+iB„ 03 „+ 1 , with the K 2 NiF 4 structure being at the 
opposite (n = 1) extreme (Fig. 1). RP phases can be consid¬ 
ered to consist of perovskite-like blocks of vertex sharing 
BOg octahedra which extend to infinity in the xy plane and 
have a thickness of n octahedra parallel to the z axis; 
neighboring blocks are separated by a rock-salt layer such 
that the overall composition can be described as 
[(Ln, A)B 03 ]„(Ln, A)0. Following the observation of co¬ 
lossal magnetoresistance (CMR) in n = RP phases, the 
electronic properties of other members of the series have 
been studied. CMR is not observed in samples of the n = 1 
system Sr 2 -;cLa;^Mn 04 which, for x—0.5, show charge or¬ 
dering on the Mn sublattice."^"^ However, CMR has been 
detected around the Curie temperature (126 K)^ of the n 
~2 (Fig. 1) composition Srj gLaj 2 Mn 207 , which does not 
show charge ordering. The majority of the data collected to 
date for n= 1, 2, and oo suggest that CMR is incompatible 
with charge ordering on the Mn sublattice, and that it is 
closely linked to the appearance of a spontaneous magneti¬ 
zation in the sample. There are, however, a number of ex- 


“^Electronic mail: peter.battle@chem.ox.ac.uk 


ceptions to this sweeping generalisation. Sr 2 _jj-Ndi+;^Mn 207 , 
for example, shows^’^^ CMR in the absence of a spontaneous 
magnetization. Studies of this system have demonstrated that 
the nature and behavior of the sample are very sensitive to 
the conditions used in the chemical synthesis.^^ More spe¬ 
cifically, samples with the composition x==0.0 or 0.1 appear 
to contain two n = 2 phases with the same stoichiometry, as 


(a) 


(b) 


(C) 





FIG. 1. Ruddlesden-Popper structures: (a) K 2 NiF 4 (« = 1), (b) Sr 2 LnMn 207 
{n — 1), (c) perovskite (/z = oo). MnOs octahedra are shaded, hollow circles 
represent Sr/Ln atoms. 


0021 -8979/98/83(11 )/6379/6/$15.00 


6379 


© 1998 American Institute of Physics 




6380 J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Battle et aL 


TABLE 1. Unit cell parameters for Sri gLaj 2 -;cNdjtMn 207 . 


X 

% phase 1 


Cl 

% phase 2 

«2 

C 2 

0.2 

40.0(5) 

3.8684(2) 

20.138(2) 

60.0(5) 

3.8698(2) 

20.117(1) 

0.7 

53.2(6) 

3.8532(2) 

20.145(2) 

46,8(6) 

3.8551(2) 

20,124(2) 

1.1 

96.6(7) 

3.84191(1) 

20.149(1) 

3.4(7) 

3,8372(8) 

20.093(7) 


judged by the unit cell volume, but with a different distribu¬ 
tion of Sr^^ and Nd^*^ cations over the available sites, 
whereas Sr^ gNdj 2 Mn 207 can be prepared to contain a single 
n = 2 phase, albeit contaminated by rt = oo perovskite.^^ The 
difference between the Nd- and La-containing n = 2 com¬ 
pounds demonstrates that the electronic properties are very 
sensitive to elemental composition, and diffraction 
experiments^^’^"^’^^ have indicated that the sensitivity can be 
traced to the subtle structural changes which are brought 
about by the variations in composition. We have previously 
shown^^’^^ that the introduction of smaller Ln cations 
(Ho^"^, into the n = 2 structure results in the formation 
of a spin-glass phase at low temperatures, and also in the loss 
of CMR. In this article, we describe the magnetic behavior of 
Sri gLaj 2 -A:Nd;cMn 207 , a system which can be thought of as 
a solid solution between the “conventional” Mn-containing 
CMR compound Sri gLai 2 Mn 207 and the “unconventional” 
Sri gNdi 2 Mn 207 . We also discuss the pressure dependence 
of the CMR in Sr 2 -;<:Ndi+;tMn 207 and show how the appli¬ 
cation of pressure can mimic the effect of changes in chemi¬ 
cal composition. Finally, we discuss the consequences for 
the magnetic and magnetotransport properties of introducing 
the Sm^"^ cation, intermediate in size between Nd^"^ and 
into the n = 2 structure. 

II. EXPERIMENT 

The n = 2 RP system Sri gLai 2 -jcNdj,Mn 207 could not 
be prepared free of perovskite impurity by traditional ce¬ 
ramic techniques, A synthetic strategy which involved the 
use of a 61263 flux^® was more successful. Stoichiometric 
quantities of SrC 03 , Nd 203 , La 203 , and Mn 02 were ground 
together with a small amount of 61263 such that the initial 
cation composition was Sri gLai 2 ^;cNd;cMn 26 io.i. The reac¬ 
tion mixture, contained in an alumina crucible, was heated at 
900 (12 h) and 1200 °C (12 h) before being pelletized and 
heated at 1500 °C for a total of 36 h. X-ray powder diffrac¬ 
tion measurements, carried out on a Siemens D5000 diffrac¬ 
tometer using Cu Kai radiation, showed that the products 
were free of n = and n = l impurity phases. The {0 0 10} 
reflection of all samples in the composition range 0.1 
=^1.1 had a full width at half maximum (FWHM) of A2^ 
'^0.1®. We have previously shown^^’^^ that values less than 
this are characteristic of unstrained, monophasic samples, 
whereas larger values indicate that the sample either has a 
high degree of strain or is actually biphasic, possibly in a 
very subtle way.^^ The quality of the new samples was thus 
uncertain, and structure refinement by Rietveld profile 
analysis^^’^^ was carried out in order to determine their true 
nature. Analysis by ICP emission spectroscopy established 
that the metal content of the samples was in agreement with 


the expected values and iodometric titrations established y 
= 7.00(2) for the oxygen content in Srj gLaj 2 -jcNdj^Mn 26 ^. 
The temperature dependence of the magnetization of three 
selected samples (x = 0.2, 0.7, 1.1) was measured in an ap¬ 
plied field of 1 kG using a Quantum Design MPMS super¬ 
conducting quantum interference device (SQUID) magneto¬ 
meter. 

The synthesis of Sr 2 ~x^^\+x^^ 2 ^i (^ = 0.0, 0.1) has 
been described previously.^ These samples both contain two 
n = 2 RP phases, but no n = 00 perovskite was detectable by 
x-ray or neutron diffraction. The pressure dependence of the 
resistance of Sr 2 _jtNdi+^Mn 267 (x = 0 . 0 , 0 . 1 ) was measured 
using currents 21=^//rtA=^210. No current dependence of the 
resistance was detected. The magnetoresistance was mea¬ 
sured using standard, low-frequency (30 Hz), four-wire ac 
techniques in magnetic fields up to 15 T, with the current 
perpendicular to the magnetic field. Field reversal verified 
that the Hall contribution to the magnetoresistance was neg¬ 
ligible. The measurements were restricted to {P,T,B) re¬ 
gions where the sample resistance was less than 10 ^ 6 . 
They were performed on two different pieces of ceramic 
sample to verify the sample independence of the observed 
signal. All resistance values were normalized to the sample 
resistance at ambient pressure, 275 K and 0 T. A standard 
piston-cylinder cell with petroleum spirit as pressure medium 
was used^^ to apply pressure at room temperature. The pres¬ 
sure inside the cell, which was monitored with a calibrated 
manganin wire,^^ decreased by ^-0.3 GPa during cooling 
from room temperature to 4.2 K; all pressures quoted are 
room temperature values. 

A sample of Sri gSmj 2 Mn 2 G 7 was prepared by firing a 
stoichiometric mixture of SrCG 3 , Sm 2 G 3 , and MnG 2 in air at 
800 (24 h), 1000 (24 h), and 1350 °C (10 days). Initial x-ray 
characterization was carried out using a Siemens D5000 
diffractometer, and the sample was then examined under 
higher resolution using the diffractometer 2.3 at the SRS, 
Daresbury Laboratory (X= 1.3997 A, A 2 ^= 0 . 01 °). The 
zero field cooled (ZFC) and field cooled (FC) magnetic sus¬ 
ceptibility of the sample was measured in a field of 500 G. 
Ambient pressure magnetoresistance measurements on 
Sri gSmi 2 Mn 2 G 7 were accomplished using a four-terminal 
dc technique in fields of up to 14 T. 

ML RESULTS 

Analysis of the x-ray diffraction patterns of the compo¬ 
sitions Sri gLai 2 -jcNd^Mn 267 showed (Table I) that they all 
contain more than one n = 2 RP phase, as do Sr 2 LaMn 267 
and Sr 2 NdMn 267 , The relative proportions of the two 
phases varied in an irregular manner as a function of x. In 
the compositions that were selected for further study (x 



J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Battle et al. 6381 



T(K) 


FIG. 2. Magnetic susceptibility of Sr^ gLai 2 --;cNd;tMn 207 measured in an 
applied field of 1 kG for A:=(a) 0.2, (b) 0.7, and (c) 1.1. 


=0.2, 0,7, 1.1) the phase fractions were 40/60, 53/47, and 
97/3; thus the composition Srj gLao.iNdi iMn 207 appeared to 
be almost monophasic at the resolution of our powder dif¬ 
fraction apparatus. The data gave no indication of (Sr, La, 
Nd) cation ordering over the two crystallographically distinct 
sites available—one in the perovskite blocks and the other in 
the rock-salt layers. As expected, the unit cell volume 
showed a general decrease as the concentration of the 
smaller Nd^"^ cation increased. The magnetic susceptibility, 
measured in a field of 1 kG, of the three chosen compositions 
is plotted as a function of temperature in Fig. 2. The compo¬ 
sition x = 0.2 shows a rise in susceptibility below 20 K, but 
otherwise shows qualitatively similar behavior to x = 0.0^ 
(Fig. 3), with a Curie point apparent at 85 K and a suggestion 
of short range or two dimensional ordering below 230 K (cf. 
126 and 250 K for x = 0.0). A saturation magnetic moment of 
2.23 per Mn cation was measured in a field of 1 kG. The 
Curie point is not visible in the data collected on jc = 0.7, and 
the susceptibility of x=lA is very similar to that of the 
composition x= 1.2, although the marked rise in the magne¬ 
tization occurs at 290 K (270 K) in the former (latter); neu- 



FIG. 3. Magnetic susceptibility of Sri gLaj 2 -jcNdj^Mn 207 measured in 100 
G for x = 0.0 and 0.2. 

Iron diffraction experiments have previously failed to detect 
any long-range magnetic order in Srj gNdj 2 Mn 207 . 

The normalized resistance of Sr 2 NdMn 207 between 50 
and 300 K is shown in Fig. 4 as a function of pressure and 
applied field. The zero-field resistance is seen to increase by 
over three orders of magnitude between room temperature 
and 80 K, Neither the absolute value nor the temperature 
dependence of the zero-field resistance are affected signifi¬ 
cantly by the application of pressure. The temperature depen¬ 
dence of the zero-field resistance under pressure for 170 
=^r/K^300 can be fitted as an activated process, p 
= with an activation energy of 110±5 meV, inde¬ 

pendent of the applied pressure. This implies that the activa- 



FIG. 4. Normalized resistance of Sr 2 NdMn 207 for 50^T/K^300 at differ¬ 
ent magnetic fields and (a) ambient pressure, (b) 0.9, and (c) 1.5 GPa. 






6382 J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Battle et al. 



FIG. 5. (a) Normalized resistance of Sr 2 NdMn 207 at 1.8 GPa for different 
magnetic fields, (b) Normalized resistance of Srj 9 Ndi iMn 207 at ambient 
pressure for comparison purposes. 


tion energy of this system cannot depend sensitively on the 
unit cell dimensions. This is a surprising result, particularly 
in view of the decrease in activation energy observed when 
n = 00 perovskites are subjected to pressure.The magne¬ 
toresistance, however, is strongly dependent on the pressure 
applied, as illustrated in Fig. 4. Even at temperatures as high 
as 100 K, the magnetoresistance ratio at 12 T, (pg 

“Po)/p 5 , changes from-90% at 0 GPa to-200% at 

1.5 GPa, and there is a marked similarity between the behav¬ 
ior of Sr 2 NdMn 207 under pressure and Srj 9 Ndi iMn 207 at 
ambient pressure.^ This becomes particularly noticeable (Fig. 
5) at pressures in excess of 1.5 GPa and in high magnetic 
fields (^>12T). In this regime, Sr 2 NdMn 207 develops a 
local resistivity maximum at —70 K, similar to that observed 
in Sri 9 Ndi iMn 207 at high fields and ambient pressure [Fig. 
5(b)]. It is interesting to note that once this maximum has 
developed, its position and height are almost pressure inde¬ 
pendent. This could be an indication that the maximum is 
due to the completion of a pressure-field assisted ordering 
process among the Mn spins. 

The x-ray diffraction data collected on Sri gSm^ 2 Mn 207 
using a laboratory-based diffractometer indicated that we had 
been successful in preparing a monophasic, tetragonal n = 2 
RP sample, despite the fact that our previous attempts to 
prepare Sr 2 SmMn 207 had resulted in the formation of two 
n-2 phases with similar but different structural 
characteristics.^"^ However, close scrutiny of the high resolu¬ 
tion data collected at the synchrotron radiation source 
showed that the new sample was contaminated with 


TABLE II. Structural parameters of Sri gSmj 2 Mn 207 determined at SRS. 


Atom 

Site 

X 

y 

z 

“iso (A^) 

Occup. % 

Sr/Sm (I) 

2b 

0 

0 

1/2 

0.0053(7) 

81/19(1) 

Sr/Sm (2) 

4-e 

0 

0 

0.317 32(5) 

0.0057(4) 

50/50(1) 

Mn 

4e 

0 

0 

0.0976(1) 

0.0038(5) 


0 (1) 

2a 

0 

0 

0 

0.018(4) 


0 (2) 

4e 

0 

0 

0.2001(5) 

0.032(3) 


0(3) 


0 

1/2 

0.0981(3) 

0.013(1) 



Space group lAlmmm, reduced ;^^=1.56 for 32 variables 

Mn~0(l)= 1.965(2), Mn-O(2)-2.06( 1), Mn-0(3)= 1.912 59(4), 

Mn(z)-Mn(-z) = 3.931(5) A. 


— 2.8 wt % of a perovskite {n = ^) phase. The unit cell pa¬ 
rameters refined to the following values: for n = 2, a 
= 3.825 13(2), c = 20.1269(1)A; for n = oo, ^^ = 5.4205(5), 
i? = 7.6840(6), c = 5,4130(5) A. The Sr^"^ and Sm^*^ cations 
order in the n = 2 phase such that 84% of the smaller Sm^"'" 
cations are nine coordinate in the rock-salt layer [Sr/Sm(2)], 
with the majority of the Sr^^ cations being twelve coordinate 
within the perovskite blocks [Sr/Sm(l)]. The refined values 
of the atomic coordinates are presented in Table II, along 
with the most important bond lengths; note that 0(1) lies at 
the center of the perovskite block, the bond Mn-0(2) is 
directed along z into the rock-salt layer, and Mn-0(3) lies 
within the xy sheets; we have used the same labeling scheme 
previously. Although it is not ideal to determine these 
parameters by x-ray diffraction, the high absorption cross 
section of Sm renders a neutron diffraction study impractical. 
The magnetization of Sr^ gSmj 2 Mn 207 is plotted as a func¬ 
tion of temperature in Fig. 6. There is a sharp rise at 140 K, 
and some hysteresis is apparent below this temperature; a 
maximum is observed at — 35 K. A weak magnetization of 

— 0.06 fjiB per formula unit is seen at 5 K. The resistivity is 

plotted as a function of temperature and magnetic field in 
Fig. 7. The smooth curves are characteristic of an insulator, 
and no phase transition is apparent at 140 K. The magnetore¬ 
sistance [(Pfi-po/po)>^ 100^] apparently increases 
throughout the measured temperature range and reaches a 
maximum value of-10%. 



FIG. 6. FC and ZFC magnetization of Srj gSmj 2 Mn 207 , measured in 500 G. 








J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Battle et a!. 6383 



FIG. 7. Resistivity of Sf] 381111 2 Mn 207 as a function of temperature and 
magnetic field. 


IV. DISCUSSION 

The data described above suggest that it is possible to 
dope Srj 2 Mn 207 with Nd, thereby weakening the 
strength of the interactions producing long-range ferromag¬ 
netic ordering. Previous structural studies^^'^^ suggest that 
this is likely to involve a lengthening of the Mn~0(2) dis¬ 
tance, which will decrease the coupling between neighboring 
perovskite blocks and reduce the three-dimensional nature of 
the magnetic interactions. It is interesting to note that the 
change from one type of magnetic behavior to another occurs 
gradually with changing composition. As the Nd-content in¬ 
creases, the susceptibility begins to resemble that of 
Sri gNdi 2 Mn 207 , which does not show long-range magnetic 
ordering.However, this neat description is too simplistic 
because it does not take into account the fact that our x-ray 
data show that the samples are biphasic, and without a more 
detailed neutron diffraction study we cannot confidently de¬ 
scribe the differences in crystal structure and composition 
between the two phases, and we therefore cannot account 
fully for the weakening of the ferromagnetic interactions and 
the generally complex susceptibility behavior shown in Fig. 
2. It is likely, for example, that the ferromagnetic transition 
and the low temperature rise in susceptibility seen for x 
= 0.2 in Fig. 2(a) are attributable to the two different com¬ 
ponents of the sample. Nevertheless, Nd-doping clearly in¬ 
fluences the magnetic properties of this system, and our data 
give reason to believe that, for relatively low, but as yet 
badly defined (x<0.7), levels of Nd doping it may be pos¬ 
sible to tune in this system chemically by controlling the 


elemental distribution over the A sites within either the per¬ 
ovskite blocks or the rock-salt layers. This implies that it will 
also be possible to tune the temperature of maximum mag¬ 
netoresistance, but more magnetotransport measurements are 
needed to prove this point. The suggestion that the properties 
can be controlled by the La/Nd ratio should sound a warning 
to those who treat these compounds as a Mn-O network 
with benign lanthanide cations playing only a space-filling 
role in the structure. 

The results of our high pressure experiments suggest that 
the application of hydrostatic pressure to Sr 2 NdMn 207 has a 
similar effect, with regard to CMR, to increasing the Nd:Sr 
ratio. At ambient pressure, increasing the Nd content pro¬ 
duces a contraction of the unit cell parameter a, but an in¬ 
crease in c, and, given that pressure and increasing Nd con¬ 
tent have the same effect on CMR and that pressure will 
decrease both unit cell parameters, it is reasonable to assume 
that the change in a is of greater significance. Our samples of 
both Sr 2 NdMn 207 and Sr^ 9 Ndi iMn 207 are biphasic, and we 
have described them as containing both an antiferromagnetic 
phase and a spin-glass phase, with the spin-glass fraction 
being more significant in the Nd-rich sample. The occurrence 
of the latter phase was attributed to frustration caused by the 
presence of both ferromagnetic and antiferromagnetic inter¬ 
actions. Furthermore, the lower ordered magnetic moment 
per Mn cation and the lower Neel temperature of 
Srj 9 Ndi iMn 207 indicate that frustration-induced magnetic 
disorder is relatively large even in the magnetically ordered 
component of the Nd-rich sample. Our new results can then 
be taken to suggest that pressure produces an increase in the 
degree of frustration in antiferromagnetic Sr 2 NdMn 207 by 
enhancing the relative strength of any ferromagnetic interac¬ 
tions in the ordered phase. This is consistent with the mag¬ 
netic structure^^ which consists of ferromagnetic sheets per¬ 
pendicular to z; the decrease in a will increase the strength 
of the ferromagnetic coupling and hence increase the degree 
of frustration in the antiferromagnetic structure. Susceptibil¬ 
ity or neutron measurements under pressure are necessary to 
test this proposal further. 

Finally, our data on Srj gSm^ 2 Mn 207 demonstrate the 
need for careful diffraction studies in order to identify the 
phases present in manganate samples. Damay et al?^ have 
reported that perovskite compositions Smj show 

a Curie temperature at ~ 140 K, with a saturation moment 
per Mn cation of 1 for x=0.44 in a field of 500 G. 
Thus the magnetization of our sample can be attributed to the 
presence of 3% of the perovskite Smo.56Sro.44Mn03, essen¬ 
tially the fraction estimated from our x-ray study. This would 
not have been observed had we relied on our laboratory- 
based powder diffractometer, although it is a relatively mod¬ 
ern, high-resolution machine. Indeed, the presence of this 
phase was not taken into account in our discussion of mag¬ 
netic data collected before high resolution x-ray studies had 
been performed,and our earlier discussion is therefore 
flawed. The perovskite phase dominates the magnetization 
data, but it is present at too low a concentration to influence 
the magnetotransport data, as can be seen from a comparison 
of our data with those of Damay et al , which show a metal- 
insulator transition. We can conclude that the majority, n 




6384 J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Battle et ai 


=2 phase does not show magnetoresistance on the scale of 
the La and Nd analogs, even though we cannot describe the 
temperature dependence of the susceptibility. As in 
Sr 2 HoMn 207 , the preferential occupation of the perovskite 
block site by the larger Sr^"^ cation results in a large Mn-Mn 
distance (3.931 A) along z within a double layer, and this is 
likely to weaken the interatomic interactions along the axis 
in comparison to those within the xy plane; it is also likely to 
prevent the exchangestriction which stabilizes the antiferro¬ 
magnetic phase in Sr 2 NdMn 207 . Although we cannot draw 
any firm conclusions about the magnetic properties of the n 
= 2 phase from our susceptibility data, the similarity be¬ 
tween the structural data described above and those reported 
previously for Sr 2 HoMn 207 and Sr 2 YMn 207 ^^ leads us to 
predict spin glass behavior at low temperatures (<50 K) in 
n-2 SrigSmj 2 Mn 207 . It is possible that the susceptibility 
maximum at 35 K (Fig. 6) corresponds to the glass transition 
temperature. It should be noted that the Ho- and Y- 
containing compounds show a slight distortion from the ideal 
RP structure. This involves oxide ion displacements arising 
from the rotation of MnOg octahedra, and is easily detected 
in neutron diffraction experiments. However, we would not 
expect to have detected it in our x-ray experiments on the Sm 
compound. 

Finally, we wish to emphasise that, having attempted to 
prepare a number of n = 2 RP phases, and having paid care¬ 
ful attention to synthesis conditions, we have never suc¬ 
ceeded in preparing a monophasic material. We have pre¬ 
pared samples free of n = oo perovskite, but they have always 
contained two n = l phases, for example Sr 2 NdMn 207 . We 
have made highly crystalline n = 2 phases, but they have 
always been contaminated by perovskite, for example 
Sri gSmi 2 Mn 207 as described above. Furthermore, even 
samples which appear to contain only one n = 2 phase show 
a relatively high concentration of intergrowths of other RP 
phases.^^ Our final conclusion is thus that any attempt to 
make an unambiguous interpretation of the physical proper¬ 
ties of these materials is fraught with difficulty. The prob¬ 
lems may diminish if single crystals become available, but 
they are unlikely to disappear altogether. 

ACKNOWLEDGMENTS 

This research is supported by EPSRC and the Donors of 
the Petroleum Research Fund, administered by the American 
Chemical Society. 


*A. Urushibara, Y. Moritomo, T. Arima, A. Asamitsu, G. Kido, and Y. 
Tokura, Phys. Rev. B 51, 14 103 (1995). 

^C. N. R. Rao, A. K. Cheetham, and R. Mahcsh, Chem. Mater. 8, 2421 
(1996). 

^S. N. Ruddlesden and P. Popper, Acta Crystallogr. 11, 541 (1958). 

^W. Bao, C. H. Chen, S. A. Carter, and S.-W. Cheong, Solid State Com- 
mun. 98, 55 (1996). 

^J. C. Bouloux, J. L. Soubeyroux, A. Daoudi, and G. L. Flem, Mater. Res. 
Bull. 16, 855 (1981). 

^Y. Moritomo, Y. Tomioka, A. Asamitsu, and Y. Tokura, Phys. Rev. B 51, 
3297 (1995). 

^B. J. Stemlieb, J. P. Hill, U. C. Wildgruber, G. M. Luke, B. Nachumi, Y. 
Moritomo, and Y. Tokura, Phys. Rev. Lett. 76, 2169 (1996). 

®Y. Moritomo, A. Asamitsu, H. Kuwahara, and Y. Tokura, Nature (Lon¬ 
don) 380, 141 (1996). 

®P. D. Battle, S. J. Blundell, M. A. Green, W. Hayes, M. Honold, A. K. 
Klehe, N. S. Laskey, J. E. Millbum, L. Murphy, M. J. Rosseinsky, N. A. 
Samarin, J. Singleton, N. A. Sluchanko, S. P. Sullivan, and J. F. Vente, J. 
Phys.: Condens. Matter 8, L427 (1996). 

‘°R. Seshadri, C. Martin, A. Maignan, M. Hervieu, B. Raveau, and C. N. R. 

Rao, J. Mater. Chem. 6, 1585 (1996). 

^‘P. D. Battle, S. J. Blundell, D. E. Cox, M. A. Green, J. E. Millbum, P. G. 
Radaelli, M. J. Rosseinsky, J. Singleton, L. E. Spring, and J. F. Vente, 
Mater. Res. Soc. Symp. Proc. 453, 331 (1997). 

‘^P. D. Battle, M. A, Green, N. S. Laskey, J. E. Millbum, P. G. Radaelli, M. 
J. Rosseinsky, S. P. Sullivan, and J. F. Vente, Phys. Rev. B 54, 15 967 
(1996). 

^^P. D. Battle, J. Hepburn, J. E. Millbum, P. G. Radaelli, M. J. Rosseinsky, 
L. E. Spring, and J. F. Vente, Chem. Mater. 9, 3215 (1997). 

‘"^P. D. Battle, D. E. Cox, M. A. Green, J. E. Millbum, L. E. Spring, P. G. 
Radaelli, M. J. Rosseinsky, and J. F. Vente, Chem. Mater. 9, 1042 (1997). 

F. Mitchell, D. N. Argyriou, J. D. Jorgensen, D. G. Hinks, C. P. Potter, 
and S. D. Bader, Phys. Rev. B 55, 63 (1997). 

’^P. D. Battle, M. A. Green, N. S. Laskey, N. Kasmir, J. E. Millbum, L. E. 
Spring, S. P. Sullivan, M. J. Rosseinsky, and J. F. Vente, J. Mater. Chem. 
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^^P. D. Battle, J. E. Millbum, M. J. Rosseinsky, L. E. Spring, and J. F. 

Vente, and P. G. Radaelli, Chem. Mater. 9, 3136 (1997). 

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^®M. Eremets, High Pressure Experimental Methods (Oxford University 
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Phys. Chem. Ref. Data 1, 773 (1972). 

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Phys. Rev. Lett. 76, 295 (1996). 

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Rosseinsky, S. P. Sullivan, and J. F. Vente, Chem. Mater. 9, 552 (1997). 
^^F. Damay, N, Nguyen, A. Maignan, M. Hervieu, and B. Raveau, Solid 
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JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Role of intergrowths in the properties of naturally layered 
manganite single crystals (invited) 

S. D. Bader R. M. Osgood III, D. J. Miller, J. F. Mitchell, and J. S. Jiang 

Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439 

Two-layered Ruddlesden-Popper phase Sr 0 (Lai„;^Sr^Mn 03 ) 2 , with x=0.3 and 0.4, exhibits 
colossal magnetoresistance, a magnetic anisotropy which is strongly composition-dependent, very 
little remanence, and an anomalous low-field magnetization (M) plateau between the Curie 
temperature (Tc) and 7*^300 K. The resistivity peaks near Tc for both in-plane and out-of-plane 
currents. The magnetization plateau is not intrinsic to the crystal, but is attributed to intergrowth 
defects, consisting of one additional or missing SrO blocking layers, as observed in transmission 
electron micrographs. The intergrowths exhibit interesting two-dimensional magnetic behavior, for 
both the x = 0.3 and 0.4 compositions. For x = 0.4, M scales as (l-T/T*)^, with /3=0.25 
±0.02. For x = 0.3, the intergrowths exhibit an easy axis in the a-b plane due to the shape 
anisotropy, while for T<Tq, M lies along the c axis. © 1998 American Institute of Physics. 
[80021-8979(98)43311-5] 

L INTRODUCTION 

Manganites, based on the perovskite structure type, are a 
fascinating class of materials, exhibiting both the colossal 
magnetoresistance (CMR) phenomenon^ and a host of inter¬ 
esting magnetic properties.Recently, Moritomo et al fab¬ 
ricated these materials in the two-layered form;^ i.e., the n 
= 2 variant of the Ruddlesden-Popper series 
(La, Sr)„ 4 .iMn„ 03 „+i, and there have been a number of 
subsequent investigations of this material.^"^ Figure 1 illus¬ 
trates the n = 1 , 2,00 members of this family. The unit cell 
may be written: SrO(Lai _;^,Sr;,Mn 03 ) 2 , where it is clear that 
two Mn06 octahedra are separated from one another by an 
insulating layer of SrO. The structure is tetragonal, with the 
a-b plane parallel to the layers of MnOg and the c axis 
perpendicular.^ The n = 2 variant of this family was found to 
have a ~20 000% CMR at 129 K with //=7 T, while at low 
fields (0.3 T), a CMR of —200% was found (at 129 K).^ 

These materials (including the n = oo variety) exhibit a com¬ 
petition between antiferromagnetism due to superexchange, 
and ferromagnetism due to double exchange. For x = 0, the 
material is antiferromagnetic, while in the region jc 
^0.2-0.4, the materials are ferromagnetic and exhibit a 
metal-insulator transition at Tc moves appreciably in 
an external field H, which in turn shifts and broadens the 
metal-insulator transition and causes CMR. An external 
field is thought to align the Mn sites and therefore allow the 
electron (via the double exchange mechanism) to delocalize 
and “hop” between the Mn sites. 

As in the cuprate superconductors,^^ not all of the inter¬ 
esting physics for the manganites is confined in the tempera¬ 
ture region T<Tc- Several studies have reported short-range 
magnetic order for T>Tc in these layered materials (both 
x=0.3 and 0.4).^’"^’^^’^^ One naturally asks the question: “to 
what extent is this magnetic order intrinsic to the layered 
structure of the material?” We find that the CMR occurs at 
low fields 2iiT=Tc for the current both in the plane and 


^^Electronic mail: bader@anl.gov 


along the c axis. The high temperature magnetization is, 
however, interesting in its own right; it is attributed to inter¬ 
growth defects extrinsic to the crystal, which exhibits novel, 
two-dimensional magnetic behavior. 

II. EXPERIMENT 

Crystals of L3i2-2x^^i + 2 x^^ 2^7 (;c = 0.3,0.4) were 
grown from polycrystalline rods of the same nominal com¬ 
position using the traveling-floating-zone technique in an op¬ 
tical image furnace (NEC model SC-M15HD). The precursor 
rods were prepared by solid-state synthesis from high purity 
(>99.99%) starting materials: La 203 (prefired in flowing O 2 
at 1000 °C for 12 h), Mn02, and SrC 03 . After several firings 
at 1000-1350 °C, the powders were isostatically pressed into 
rods suitable for zone melting. The growth atmosphere was 
20% O 2 for x = 0.3 and 0.4. In each case, the crystals grew 
with the c axis normal to the zone travel direction. The re¬ 
sulting highly textured polycrystalline boules can be cleaved 
readily to yield shiny black crystals of layered manganite. 
Typical dimensions of the cleaved crystals are 2X2 
XO.lmm*^. Back-reflection x-ray Laue photographs estab¬ 
lish that in all cases the cleaved crystals have the c axis 
oriented normal to the thin plates. Magnetization and suscep- 



n=l n=2 


FIG. 1. Diagram of the structure Sr 0 (Lai_j,Sr^Mn 03 ) 2 , reproduced from 
Ref. 2. The variable n refers to the number of MnOg octahedra layers in the 
bilayer. The shaded atoms are the La, Sr cations, the white atoms are O, and 
the black atom in the center of the 0^ octahedron is the Mn atom. 


0021 -8979/98/83(11 )/6385/5/$15.00 


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© 1998 American Institute of Physics 



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J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Bader et al. 




Temperature (K) 

FIG. 2. Magnetic moment vs temperature for (a) .x: = 0.4 (H~30Oe\\ab)\ 
(b).r = 0.3 (//-SOOellc). 


tibility (x) measurements were made on both a 
superconducting-quantum interference device (SQUID) and 
an extraction magnetometer from Quantum Design, equipped 
with with a 7 and 9 T superconducting solenoid, respec¬ 
tively. The trapped flux in the solenoid ('^10 Oe) was moni¬ 
tored, so that the field values given are correct to within 
±0.5 Oe. Measurements were made with the applied field 
both parallel to the plane (HWab) and parallel to the c 
axis (HWc). Resistivity measurements were made on thin 
platelets obtained by crushing the boule; leads were con¬ 
nected by attaching Cu wires to sputtered Au contacts. An¬ 
other platelet from the same boule was ion-milled and used 
for transmission electron microscope (TEM) measurements. 

III. MAGNETIZATION AND TRANSPORT 

Figure 2(a) displays M vs 7 (H = 30OQ\\ab) for 
=0.4; Figure 2(b) illustrates M vs T {H=100 OcWab) for 
x = 0.3. For both compositions, there are two plateaux below 
the two transitions. The lower transition is Tc ('~94 K for 
x=03 and 116 K for jc = 0.4); the upper transition is at T 
= r*~300K. In Fig. 2b, 7* is not as visible for the x 
= 0.3 sample as it is for x = 0.4 because of the higher field 
employed for this measurement (100 Oe), which tends to 
smear out the transition. A measurement of M vs 7 with H 
= 15 Oe near 7* is displayed in Fig. 3. Measurements of M 
vs H below Tc yield a ferromagnetic hysteresis loop, albeit 
one with virtually no remanence [see Fig. 4(a) for H\\ab and 



Temperature (K) 

FIG. 3. Magnetic moment vs temperature for .x = 0.3 {H~15 OcWab, T 
^T*). Three transitions are identified. 


HWc injc = 0.4; see Fig. 4(b) for H\\ab and//Ik inA: = 0.3, all 
at 5 K]. The easy axis, determined by the saturation field, lies 
in the a~b plane for jc = 0.4 and along c for ;r = 0.3, in agree¬ 
ment with Ref. 3. Measurements of M vs // for 7c<7 
<7* yield a small ferromagnetic loop superimposed on a 


x = 0.4 



H(T) x = 0.3 



H(T) 


FIG. 4. Magnetization (normalized to the saturation magnetization M J vs 
H for (a) ;c = 0.4, (b) jc-0.3 (HWab: filled symbols, HWc: clear symbols, 
r=5 K for both compositions). Measurements were made sweeping H from 
negative to positive values and back to A/=0. 








J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Bader et al. 


6387 



H(T) 


FIG. 5. (a) Magnetic moment vs applied field (H) at 250 K for HWab (filled 
symbols) and H\\c (clear symbols). Both measurements are superimposed on 
a linear paramagnetic background from the intrinsic portion of the crystal, 
which is displayed in (b) for HWab. Two lines in (b) indicate the kink near 
H=0 which is due to the ferromagnetic response of the extrinsic material. 
All measurements in this figure are from the same sample. 


paramagnetic background, in agreement with neutron dif¬ 
fraction experiments, which have been able to sense mo¬ 
ments only for T<Tc.^ The high-temperature paramagnet¬ 
ism therefore must represent short range order. Figure 5(a) 
displays M vs HWab and M vs HWc in jc = 0.3, while Fig. 
5(b) displays the M vs HWab data on a larger scale; the 
ferromagnetic part of the signal manifests itself here as a 
kink near H—0. These measurements are all from the same 
sample. Note the scales on Figs. 5(a) and 5(b); the ferromag¬ 
netic signal is masked by the paramagnetic signal from the 
intrinsic material. 

Associated with the Tc illustrated in Fig. 2 for jc = 0.3 
are peaks in the resistivity p and in the CMR, displayed in 
Fig. 6 for two different directions of the current j. There was 
a slight difference in Tc^90K between the two separate 
samples measured in Fig. 6; this difference has been normal¬ 
ized out. Note that the resistance was much higher along the 
c axis, in agreement with Ref. 3. Note that peaks for both 
Pab Pc at H=0 are at The authors of Ref. 3 

observed a large peak in p^b , the resistivity measured in the 
a-b plane, for T>Tc, This was considered a sign of ferro¬ 
magnetic correlations within the MnO^ planes and lack of 
correlation between the planes. Below Tc, where M lies 



T/T 

c 


FIG. 6. Measurement of resistivity vs applied field for (a) j\\ab and (b) j\\c 
for the X = 0.3 composition. Measurements were made on separate samples, 
both of whom had Tc^90 K; the minor difference between the Tc’s was 
normalized out. 


only along c, Kimura et al rationalized the drop in p^b they 
observed as being due to the disappearance of spin disorder 
in the a-b plane.^ We did not observe such as a peak in p^b 
for T> rcforx = 0.3.We conclude that the high-temperature 
magnetism is an extrinsic phenomenon, due to an inter¬ 
growth phase, which was presumably also present in the 
similarly prepared samples used in Ref. 3. 






S',. » ; I 

, Vs ' - - V < xf .i X 




1 


4' i If r' 'UU !►»*»»*»»».) HiH SI u ;■ ? 

if; u I*» H ;*■ * * ^ ’• 


.J - , , XX. x,. . , X- • 




FIG. 7, High-resolution TEM micrograph showing one intergrowth (marked 
with a pointer) with n~5 for the x = 0.4 composition. 



















6388 J. AppL Phys., Vol. 83, No. 11, 1 June 1998 


Bader et a!. 



FIG. 8. High-resolution TEM micrograph showing two intergrowths 
(marked with a pointer) with n — 1 for the x = 0.4 composition. 

IV. INTERGROWTHS 

Seshadri et al have demonstrated the presence of inter¬ 
growths in these materials, using TEM7 Intergrowths can be 
due to missing or extra layers of SrO atoms between the 
Mn06 octahedra. Such defects represent variants of the 
Ruddlesden-Popper series. Figures 7 and 8 diplay high- 
resolution TEM images from samples with x = 0.4. The in¬ 
sulating double SrO layer is the white band. In Fig. 7, the 
regular series of white bands is interrupted by a n = 5 inter¬ 
growth; in Fig. 8, an extra white band divides two n = 1 
intergrowths. Such intergrowths are also observed in the x 
= 0.3 samples (see Fig. 9). An estimate of the intergrowth 
volume fraction can be made by dividing the height of the 
hysteresis loop measured at 250 K by the saturation magnetic 
moment (measured with H large enough to saturate M at 7 
<Tc)‘ We obtain a volume fraction of —0.1% intergrowths 
in the x = 0.4 samples and —0.6% intergrowths in the x 


=0.3 samples, although there was a variation of ±0,3% 
among samples with x = 0.3 (four with this composition were 
measured). 

Potter et al^ have given evidence that the magnetism of 
the intergrowths is two dimensional. For M scales as 

(1-7/7*)^, where /3=0.25±0.02 for the x = 0.4 composi¬ 
tion, which is reminiscent of two-dimensional (2D) behavior. 
For the x = 0.3 composition, three transitions in the M vs 7 
data are observed, as displayed in Fig. 3, indicating the pres¬ 
ence of three different distributions of intergrowths. It was 
therefore not possible to obtain an exponent for x = 0.3. 

Another experimental observation that strongly supports 
the influence of the intergrowths above 7^ is the fact that 
hysteresis loops measured with the field along the c axis are 
much harder than those measured with the field in iht a-b 
plane [see Fig. 5(a)]. This is consistent with the picture of 
two-dimensional intergrowths running parallel to the a-b 
plane. Such inclusions are magnetically hard along the c 
axis, due to shape anisotropy, in contrast with the easy axis 
anisotropy along the c axis observed below Tc for the intrin¬ 
sic material. Were the magnetic signal above 7^ to be due to 
intralayer correlations only (the model proposed in Ref. 3), 
there would not necessarily be an anisotropy in the magne¬ 
tization loops. 

V. CONCLUSIONS 

The two-layered Ruddlesden-Popper phase 
Sr 0 (Lai_^Srj,.Mn 03 ) 2 , with x = 0.3 and 0.4, exhibits CMR 
at Tc at low H and a magnetic anisotropy which is strongly 
composition-dependent. The magnetic order observed for 7 
> Tc includes not only the short-range order response of the 
intrinsic material, but a minor ferromagnetic signal evident at 
low fields due to intergrowths. These intergrowths are clearly 
visible in TEM images and exhibit novel two-dimensional 
magnetism. The intergrowths are magnetically hard along 
the c axis in the x = 0.3 material, despite the fact that the c 
axis is easy for this composition. We find that the x = 0.3 and 




FIG. 9. Bright-field micrograph of the .r=0.3 composition showing (a) perfect crystal, (b) crystal with intergrowths. In (b) the intergrowths are visible as 
vertical streaks in the photograph running parallel to the a-b plane. 














































J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Bader et al. 


6389 


0.4 compositions differ strongly only in the magnetic anisot¬ 
ropy of the intrinsic material, not in the temperature depen¬ 
dence of the resistivity or magnetization. 

*R. van Helmolt, J. Wecker, B. Holzapfel, L. Schultz, and K. Samwer, 
Phys. Rev. Lett. 71, 2331 (1993). 

^Y. Moritomo, A. Asamitsu, H. Kuwahara, and Y. Tokura, Nature (Lon¬ 
don) 380, 141 (1996). 

^T. Kimura, Y. Tomioka, H. Kuwahara, A. Asamitsu, M. Tamura, and Y. 
Tokura, Science 274, 1698 (1996). 

D. Potter, M. Swiatek, S. D. Bader, D. N. Argyriou, J. F. Mitchell, D. 
J. Miller, D. G. Hinks, and J. D. Jorgensen, Phys. Rev. B (in press). 

^ J. F. Mitchell, D. N. Argyriou, J. D. Jorgensen, D. G. Hinks, C. D. Potter, 
and S. D. Bader, Phys. Rev. B 55, 63 (1997). 

^D. N. Argyriou, J. F. Mitchell, J. B. Goodenough, O. Chmaissem, S. 


Short, and J. D. Jorgensen, Phys. Rev. Lett. 78, 1568 (1997). 

^R. Seshadri, M. Hervieu, C. Martin, A. Maignan, B. Domenges, B. 
Raveau, and A. N. Fitch, Chem. Mater. 9, 1778 (1997). 

^P. D. Battle, M. A. Green, N. S. Laskey, J. E. Millbum, P. G. Radaelli, M. 
J. Rosseinsky, S. P. Sullivan, and J. F. Vente, Phys. Rev. B 54, 15967 
(1996). 

^P. Laffez, G. Van Tendeloo, R. Seshadri, M. Hervieu, C. Martin, A. Maig¬ 
nan, and B. Raveau, J. Appl. Phys. 80, 5850 (1996). 

^®H. Ding, T. Yokoya, J. C. Campuzano, T. Takahashi, M. Randeria, M. R. 
Norman, T. Mochiku, K. Hadowaki, and J. Giapintzakis, Nature (London) 
382, 51 (1996). 

^ ’ T. G. Perring, G. Aeppli, Y, Moritomo, and Y. Tokura, Phys. Rev. Lett. 
78, 3197 (1997). 

^^J. B. MacChesney, J. F. Potter, and R. C. Sherwood, J. Appl. Phys. 40, 
1243 (1969). 


JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Rare Earth and Boride Hard Magnets Andrew S. Kim, Chairman 


The development of high performance Nd-Fe-Co-Ga-B die 
upset magnets 

T. Saito®* 

Department of Metallurgical Engineering, Chiba Institute of Technology, 2-17-1 Tsudanuma, Narashino, 
Chiba 275, Japan 

M. Fujita and T. Kuji 

Corporate R&D Center, Mitsui Mining and Smelting Co. Ltd., 1333-2 Haraichi, Ageo, Saitama 362, Japan 

K. Fukuoka and Y. Syono 

Institute for Materials Research, Tohoku University, Katahira, Sendai 980, Japan 

The magnetic properties and the microstructure of Nd-Fe-B and Nd-Fe-Co-Ga-B die upset 
magnets produced from amorphous materials were studied. The Nd-Fe-B die upset magnets had 
fine polygonal Nd 2 Fei 4 B grains and showed magnetic anisotropy. The compositional modification 
and optimization of the die upset condition led to the increase in the remanence and coercivity 
values of the Nd-Fe-B die upset magnets. The optimally deformed Nd-Fe-Co-Ga-B die upset 
magnets showed the maximum energy product of 54.4 MGOe. © 1998 American Institute of 
Physics. [80021-8979(98)15011-9] 


INTRODUCTION 

The maximum energy products of Nd-Fe-B magnets, 
which are usually produced by sintering and melt- 
spinning,^’^ are dependent on the degree of the crystallo¬ 
graphic alignment of the Nd 2 Fei 4 B phase. In the sintered 
magnets, alignment of the Nd 2 Fei 4 B phase is achieved by the 
prior green compaction of the crushed ingot powders in an 
applied magnetic field.^ Nd-Pr-Dy-Fe-B sintered magnets 
with the highest maximum energy product of 54.2 MGOe 
have been reported.^ On the other hand, alignment of the 
Nd 2 Fei 4 B phase is achieved by die upsetting in the melt¬ 
spinning approach."^ Amorphous melt-spun ribbons are com¬ 
minuted and then are consolidated into bulk form by hot 
pressing before die upsetting. Although as-hot-pressed mag¬ 
nets have randomly oriented Nd 2 Fei 4 B grains, subsequent 
die upsetting gives rise to the crystallographic alignment of 
the Nd 2 Fei 4 B phase.^’^ Even though the die upset magnets 
have some advantages such as the finer Nd 2 Fei 4 B grains and 
lower oxygen content than the sintered counterparts, the 
maximum energy product of the die upset magnets are not 
yet comparable to those of the sintered counterparts. The 
optimization of the processing will lead to further improve¬ 
ment of the crystallographic alignment of the Nd 2 Fei 4 B 
phase in the die upset magnets, thereby enhancing the maxi¬ 
mum energy product. 

In the die upset magnets, the inhomogeneity of the as- 
hot-pressed magnets deteriorates the crystallographic align¬ 
ment of the Nd 2 Fei 4 B phase during the die upsetting.^ It has 
been reported that the Nd-Fe-B die upset magnets produced 
from the amorphous materials with the homogeneous micro- 


^^Electronic mail: tetsuji@cc.it-chiba.ac.jp 


structure exhibit the higher maximum energy products than 
those produced from the as-hot-pressed magnets.^ In this 
study, we are trying to improve the maximum energy prod¬ 
ucts of the die upset magnets produced from the amorphous 
materials by optimizing the composition and the processing 
conditions. The magnetic properties and the crystallographic 
alignment of the die upset magnets produced from the amor¬ 
phous materials are compared to those of the die upset mag¬ 
nets produced from the as-hot-pressed magnets. 

EXPERIMENT 

Ndi3 5Fe80.5B6, Ndi3 5(Feo.975COo.o25)80.5B6» 
Ndi 3 . 5 (Feo. 975 Coo.o 25 ) 8 oG^^. 5 B 6 ^Hoy ingots were melt-spun in 
argon onto a copper substrate rotating at a surface velocity of 
52 m s“^ The melt-spun ribbons were comminuted and filled 
into a steel container. The powders were dynamically com¬ 
pacted at a shock pressure of 21 GPa by the impact of a flyer 
launched by a 25 mm propellant gun. The propellant gun 
facilities and process have been described in detail 
elsewhere.^ The consolidated powders were taken out from 
the container by lathing. Typical dimensions of the bulk ma¬ 
terials were 20 mm thick and 25 mm in diameter. For com¬ 
parison, the melt-spun ribbons were consolidated into bulk 
form by hot pressing. The bulk materials and the as-hot- 
pressed materials were deformed by die upsetting at a reduc¬ 
tion rate of about 5X10“^ mm s“*. The thicknesses of the 
specimens were successfully reduced from 20 to 4 mm at 
temperatures between 963 and 1073 K in an argon atmo¬ 
sphere. 

The specimens were examined by x-ray diffraction 
(XRD) using Cu radiation. The microstructures of the 
specimens were examined under a transmission electron mi- 


0021 -8979/98/83(11 )/6390/3/$15.00 


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© 1998 American Institute of Physics 



J. Appl. Phys., Vo!. 83, No. 11, 1 June 1998 


Saito et al. 


6391 



20 30 40 50 60 

20 (deg) 

FIG. 1. XRD patterns of (a) bulk materials of Nd |3 5 Fego. 5 B 5 alloy and (b) 
those die upset at 1023 K. 

croscope (TEM). In the die upset specimen, the cross- 
sectional microstructures parallel to the die upset direction 
were investigated. The magnetic properties of the specimens 
were determined by a recording fluxmeter with a maximum 
applied field of 25 kOe after premagnetization in a field of 
150 kOe. 

RESULTS AND DISCUSSION 

Figure 1 shows the XRD patterns of the bulk materials 
of the Ndi 3 5 Fe 8 o. 5 B 6 alloy and those die upset at 1023 K. 
The XRD pattern of the bulk materials shows only a fairly 
broad peak at around 40°, which is a characteristic of an 
amorphous structure. This indicates that the bulk material 
produced from the melt-spun ribbons maintains the amor¬ 
phous state. On the other hand, the XRD pattern of the die 
upset specimen is well indexed according to the tetragonal 
Nd 2 Fei 4 B phase. This suggests that the heat exposure during 
the die upsetting of the amorphous bulk materials results in 
the crystallization of the Nd 2 Fei 4 B phase as is the case for 
the die upsetting of the as-hot-pressed magnets."^’^ 

Figure 2 shows the TEM micrographs of the bulk mate¬ 
rials of the Ndi 3 5 Fe 8 o. 5 B 6 alloy and those die upset at 1023 
K. The microstructure of the bulk material is featureless, and 
the corresponding selected area diffraction (SAD) pattern of 
the specimen shows a diffuse halo. This suggests that the 
bulk material consists of the amorphous phase. In the die 
upset specimen, the polygonal crystallites with an average 



FIG. 2. TEM micrographs of (a) bulk materials of Ndi 3 jFcso.sBe and 
(b) those die upset at 1023 K. 


^ ^ _ . 

-15 -10 -5 0 5 

H (kOe) 

FIG. 3. Demagnetization curves of (a) bulk materials of Ndi 3 5 Fe 8 o. 5 B 6 alloy 
and those die upset at 1023 K. The die upset specimens were measured in 
the (b) parallel and (c) normal to the die upset direction. 

diameter of about 0.1 /nm are seen in the microstructure. 
This indicates that the die upset magnets produced from the 
amorphous bulk materials consists of fine Nd 2 Fei 4 B grains 
with the polygonal shape. 

Figure 3 shows the demagnetization curves of the bulk 
materials of the Ndi 3 5 Fe 8 o. 5 B 6 alloy and those die upset at 
1023 K. The coercivity of the bulk material remains as low 
as that of amorphous melt-spun ribbons. The die upset speci¬ 
men shows the high coercivity value. This is due to the fine 
Nd 2 Fei 4 B grains of the die upset magnets. The anisotropy of 
the die upset magnets is characterized by the significantly 
higher remanence in the parallel direction than in the normal 
direction. The Ndi 3 5 Fe 8 o. 5 B 6 die upset magnets show a maxi¬ 
mum energy product of 47.7 MGOe with an intrinsic coer¬ 
civity of 7.3 kOe. The increase in the coercivity value of 
Ndi 3 5 Fe 8 o. 5 B 6 die upset magnets would give the magnets 
with the excellent high maximum energy products. 

Figure 4 shows the dependence of the maximum energy 
product of the die upset magnets on the die upset tempera¬ 
ture. The substitution of Co or Ga for Fe of the 
Ndi 3 5 Fe 8 o. 5 B 6 alloy results in the increase of the optimal die 
upset temperature to obtain the high maximum energy prod- 



Temperature (K) 


FIG. 4. Dependence of the maximum energy product, , of the die 

upset magnets on the die upset temperature. 







6392 


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Salto et al. 



FIG. 5. XRD patterns of Ndi 3 5 (Feo 975 Coo,o 25 ) 8 oGao. 5 B 6 die upset magnets 
produced from (a) amorphous bulk materials and (b) as-hot-pressed 
magnets. 


ucts. The TEM studies revealed that the resultant die upset 
magnets consisted of the polygonal Nd 2 Fei 4 B grains as fine 
as the Ndi 3 5 Fe 8 o. 5 B 6 die upset magnets. The substitution of 
Co or Ga for Fe of the Ndi 3 5 Fego. 5 B 6 die upset magnets led 
to the improvement of the coercivity and the maximum 
energy products of the Nd-Fe-B die upset magnets as 
is the case for the die upset magnets produced from 
the as-hot-pressed magnets.^ The resultant 
Ndi 3 , 5 (Feo. 975 Coo.o 25 ) 8 oGao. 5 B 6 die upset magnets exhibit a 
maximum energy product of 54.4 MGOe with an intrinsic 
coercivity of 12.5 kOe. 

The XRD patterns of the Ndi3,5(Feo,975Coo.o25)8oGao,5B6 
die upset magnets produced from the amorphous bulk mate¬ 
rials and the as-hot-pressed magnets are shown in Fig. 5. The 
polished surfaces of the die upset specimens were examined. 
Even though both XRD patterns show the pronounced c-axis 
alignment of the Nd 2 Fei 4 B phase, which is characterized by 
the prominent (004) and (006) peaks, the die upset magnets 
produced from the amorphous bulk materials have the higher 
ratio of the (006) to (105) peaks than those produced from 
the as-hot-pressed magnets. This indicates that the die upset 
magnets produced from the amorphous bulk materials have 
the higher crystallographic alignment of the Nd 2 Fei 4 B phase 
than those produced from the as-hot-pressed magnets, which 
are characterized with the platelike Nd 2 Fei 4 B grains.^ 

The demagnetization curves of these die upset magnets 
are shown in Fig. 6. The Nd,3 5(Feo.975Coo.o25)8oGao.5B6 die 
Upset magnets produced from the as-hot-pressed magnets 
show a maximum energy product of 50.2 MGOe with an 
intrinsic coercivity of 13.2 kOe, This value is almost compa¬ 
rable to that of the best die upset magnets.^® The observed 
higher remanence value of the die upset magnets produced 


4jtl (kG) 



FIG. 6. Demagnetization curves of Nd ,3 5 (Feo. 975 Coo.o 25 ) 8 oGao, 5 B 6 die upset 
magnets produced from (a) amorphous bulk materials and (b) as-hot-pressed 
magnets. 

from the amorphous bulk materials is due to the higher crys¬ 
tallographic alignment of the polygonal Nd 2 Fei 4 B grains. 
The detailed XEM studies revealed that the die upset mag¬ 
nets produced from the as-hot-pressed magnets contained 
similar polygonal Nd 2 Fei 4 B grains together with the typical 
platelet shaped grains.^* Therefore, the further optimization 
of the hot pressing and die upsetting conditions would lead 
to an increase in the maximum energy product of the die 
upset magnets produced from the as-hot-pressed magnets. 

ACKNOWLEDGMENTS 

This work was performed under the Research and De¬ 
velopment Program on “Advanced Chemical Processing 
Technology,” conducted under a program set by New En¬ 
ergy and Industrial Technology Development Organization. 

^ M. Sagawa, S. Fujimura, N. Togawa, H. Yamamoto, and Y. Matsuura, J. 
Appl. Phys. 55, 2083 (1984). 

J. Croat, J. F. Herbst, R. W. Lee, and F. E. Pinkerton, J. Appl. Phys. 55, 
2078 (1984). 

^K. Kaneko, K. Tokuhara, and N. Ishigaki, J, J, Soc. Powder Powder Met¬ 
allurgy 41, 695 (1994). 

'^R. W. Lee, E. G. Brewer, and N. A. Schaffel, IEEE Trans. Magn. MAG- 
21, 1958 (1985). 

^R. K. Mishra, E. G. Brewer, and R. W. Lee, J. Appl. Phys. 63, 3528 
(1988). 

^C. D. Fuerst and E. G. Brewer, J. Appl. Phys. 73, 5751 (1993). 

’Y. Nozawa, S. Tanigawa, and M. Tokunaga, IEEE Trans. Magn. MAG- 
26, 1724 (1990). 

^T. Harada, M. Fujita, and T. Kuji, J. Alloys Compd. 243, 139 (1996). 

^T. Harada, T. Kuji, K. Fukuoka, and Y. Syono, J. Mater. Sci. Lett. 11, 
1072 (1992). 

Panchanathan, J. Mater. Eng. Performance 4, 423 (1995). 

R. K. Mishra, T. Y. Chu, and L. K. Rabenberg, J. Magn. Magn. Mater. 84, 
88 (1990). 




JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER II 


1 JUNE 1998 


Plastic deformation modeling of die-upset process for magnequench 
NdFeB magnets 

S. Guruswamy and Y. R. Wang 

Department of Metallurgical Engineering, University of Utah, Salt Lake City, Utah 84112 

V. Panchanathan 

Magnequench International, Anderson, Indiana 46013 

The die upset of hot pressed NdFeB magnets modifies the equiaxed grains to platelets, develops the 
c-axis texture parallel to press direction, and improves magnetic properties. The mechanism of 
c-axis alignment has been suggested to be a combination of grain-boundary sliding and anisotropic 
grain growth in a direction normal to the applied stress. To clearly understand the role of 
deformation process in grain-boundary sliding or anisotropic grain growth simulations of the 
die-upset process were performed using anatares, a three-dimensional finite element method 
based deformation modeling software. The stresses and strains in the different regions of a 
cylindrical Nd-Fe-B magnet at different stages of the die-upset process were determined. The 
average value of the maximum principal stress (parallel to the upset direction) and total effective 
strain increased as the upset increased from 50% to 70%. The maximum principal stress and total 
effective strain show a maximum at the center and decrease in both the thickness and the radial 
direction due to friction at the die-wall/magnet interface. The stress and effective strain uniformity 
improves with increase in upset. The data agree well with the variations of texture in the magnet 
observed using pole figure measurements in this study and texture studies using a synchrotron 
source. © 1998 American Institute of Physics. [S002l-S979{9S)l65ll-S] 


I. INTRODUCTION 

The magnequench process for the production of Nd-Fe- 
B-based magnets consists of melt spinning the alloy to pro¬ 
duce ribbons, milling of melt-spun ribbons to powder, fol¬ 
lowed by hot pressing and die upsetting. The optimally 
quenched melt-spun ribbons have equiaxed and randomly 
oriented Nd 2 Fei 4 B (2-14-1) grains. Hot pressing of ribbon 
powder achieves complete densification and a desired shape 
while maintaining essentially an isotropic structure and mag¬ 
netic properties. The subsequent hot deformation process 
modifies the equiaxed grains to platelets with increase in 
grain size. These platelets are stacked with the c axis perpen¬ 
dicular to the face of the grains. The mechanism of c-axis 
alignment has been suggested to be by a combination of 
grain-boundary sliding and anisotropic grain growth in a di¬ 
rection normal to the applied stress.^’^ The amount of c-axis 
alignment with the press direction, measured using x-ray dif¬ 
fraction techniques, has been shown to depend on the 
amount of deformation. In addition, the strain distribution in 
a magnet deformation at a given level is expected to be non- 
uniform due to friction between the die wall and the magnet. 
The friction coefficient between the die wall and magnet is 
sensitive to the surface conditions, deformation temperature, 
the lubricant, and the load. Thus, depending on the die-upset 
process conditions, the stress and strain distribution will vary 
and this is expected to influence the texture, and hence, the 
magnetic properties. The nature of the strain and stress dis¬ 
tribution in the magnet during the different stages of the 
upset deformation is very critical in understanding the tex¬ 
ture development in these magnets. To the best of our knowl¬ 
edge, no detailed analysis of how the local stress and strain 


influence the crystallographic alignment by grain-boundary 
sliding and anisotropic grain growth has thus far been per¬ 
formed. In this work, an assessment of stresses and strains in 
the magnet is made by a simulation of the die-upset process 
and is correlated with texture measurements made using x- 
ray diffraction. 

II. EXPERIMENTAL WORK 

NdFeB magnets were die upset to 50%, 60%, and 70% 
deformation and the texture in these magnets were evaluated 
using x-ray pole figures. Simulation of the die-upset process 
for NdFeB magnets was done using “ANTARES,” a finite- 
element-based plastic deformation modeling software for the 
cases of 50%, 60%, and 70% upsets. An initial strain rate of 
2X10“^ and a temperature of deformation of 800 °C was 
assumed. The material was assumed to exhibit a deformation 
behavior by the equation 

a=a° + k€^e^, 

where (7® = flow stress at e^O, = constant, 6= strain, e 
= strain rate, n = strain hardening factor, and m = strain rate 
sensitivity factor. For the die material, the property data used 
corresponded to H-11 tool steel. The data for Nd-Fe-B used 
were obtained from the work of Yoshikawa et alJ A friction 
coefficient of 0.3 was used for the magnet/die interface lu¬ 
bricated with graphite. 

III. RESULTS AND DISCUSSION 

Typical deformation geometry used for die-upset simu¬ 
lation is shown in Fig. 1(a). The diameter of the billet is 18 
mm and the length of the billet varies slightly depending on 


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© 1998 American Institute of Physics 



6394 J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Guruswamy, Wang, and Panchanathan 



(a) 



MPa 


-144.0113 


-158.0030 

-172.1747 

-186.2564 

-200.3381 

-214.4198 

-228.5015 




FIG. 2. Principal stress contours at the end of 60% die-upset deformation. 



FIG. 1. Typical deformation (a) at the end of the die upset and (b) at an 
intermediate stage of the die upset. Axis of symmetry is along the left edge. 
A, B, and C refer to the magnet, top punch, and bottom die, respectively. 


the die upset required. Each % upset requires a different die 
set with appropriate diameter and depth of the cavity. The 
geometry of the billet at each incremental step of the punch 
movement can be obtained, and Fig. 1(b) presents the billet 
mesh geometry at an intermediate stage of the die-upset pro¬ 
cess. The barreling of the billet results from (i) the friction at 
the top punch/billet interface and the die/billet interface, and 
(ii) the temperature variation across the billet due to heat 
transfer across the die-billet interfaces and billet/protective 
gas interface. Near the end of the deformation process, the 
barreled surface of the billet makes contact with the lateral 
faces of the die, and the flow patterns in peripheral regions 
become complex. The values of different stress, strain, strain 
energy, temperature, and other parameters are obtained at 
every stage of the process. Of importance are the principal 
stress and effective strain values. The principal stress is 
nearly parallel to the axis of the magnet and the effective 
strain is proportional to the strain in the direction parallel to 


the axis of the billet (e^^). Figures 2 and 3 present the prin¬ 
cipal stress and effective strain contours in the magnets at the 
end of deformation for the 60% die-upset magnets. It has 
been observed that grain growth along the a axes that are 
normal to the applied stress is favored. The principal stress- 
time-temperature profile is thus important in assessing the 
contribution of the anisotropic growth. The effective strain 
could also be more directly correlated with the grain rotation 
and anisotropic grain growth, and the crystalline alignment. 
For the case of the 50% die-upset magnet (Fig. 4), the effec¬ 
tive plastic strain varies from 53.27% at the center of the 
bottom and top face to a value of 79.81% at the central 
region of the magnet. This suggests that the crystalline tex¬ 
ture must vary significantly across the magnet. For the case 
of 60% deformation (Fig. 3), the effective strains at all the 
different locations have increased. At the center of the bot¬ 
tom and top faces, the effective strain is 59.29% compared to 
the value of 53.27% for 50% deformation. The center of the 
magnet experienced an effective strain of 107.62%. For the 
70% upset magnet (Fig. 5), these values increased to 71.74% 
for the center of the top and bottom faces and 145.91% for 
the central region of the magnet. In these three figures, the 
lateral confinement by the cylindrical bottom die face, and 

1.5594 
1.4904 
1.4213 
1.3S23 
1.2833 
1.2142 
1.1452 
1.0762 
1.0071 
0.9381 
0.8601 
0.8000 
0.7310 
0.6620 
0.5829 
0.5239 

FIG. 3. Effective strain contour at the end of 60% die-upset deformation. 























J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Guruswamy, Wang, and Panchanathan 6395 



Z.3905 
2.2570 
2.1 ZS1 
1.SS2<1 
1.0597 
1.7270 
15943 
1.4618 
15209 
1.1062 
1.0635 
0.9308 
0.7901 
0.6654 
05327 
0.4000 



FIG. 4. Effective strain contour at the end of 50% die-upset deformation. 


the extrusion of the magnet through the clearance between 
the punch and bottom die result in a highly nonuniform 
strain distribution in the comer regions. The average strain 
level increases with the increase in the percentage of the die 
upset, and therefore, the overall texture should increase with 
percentage of the die upset. However, the large variation in 
the effective strain should also lead to extensive variation in 
texture across the magnet, and therefore, the magnetic prop¬ 
erties are expected to be nonuniform. There may, however, 
be a critical effective strain level above which there is no 
further improvement in texture. If this critical level is ex¬ 
ceeded at all the locations of the magnet, then a complete or 
limiting (006) texture would have been achieved. The effec¬ 
tive strain variation in the radial direction is much less com¬ 
pared to the variation in the thickness direction, except for 
the region near the edge of the magnet. 

The deformation modeling work is consistent with the 
texture measurements made in these die-upset magnets. The 





(b) 

FIG. 6. Three-dimensional partial (006) pole figure from (a) 0.5 mm depth 
and (b) 1.0 mm depth of the 60% die-upset magnet. 

(006) pole figures from a 0.5 mm depth are shown in Fig. 
6 (a) and those for a 1.0 mm depth are shown in Fig. 6(b). 
Their values are 26.3° and 24.0° for the 0.5 and 1.0 mm 
depths, respectively. They again show that the crystallo¬ 
graphic alignment is enhanced as one moves from the sur¬ 
face toward the center of the magnet. This observation is as 
expected from the deformation modeling. The larger strain 
produced a stronger (006) texture. It also suggests that fric¬ 
tion between the sample and punch affects the crystal align¬ 
ment near the sample surface. The results from the modeling 
work are also consistent with the study of texture variation 
across the die-upset magnets by Lewis et al? 

^ J. Croat, J. F. Herbst, R. W. Lee, and F. E. Pinkerton, Appl. Phys. Lett. 44, 
148 (1984). 

^J. Croat, J. F. Herbst, R. W. Lee, and F. E. Pinkerton, J. Appl. Phys, 55, 
2078 (1984). 

3r. W. Lee, Appl. Phys. Lett. 46, 790 (1985). 

^R. W. Lee, N. Schaffel, and L. Brewer, IEEE Trans. Magn. MAG-21, 
1958 (1985). 

^R. K. Mishra, Mater. Sci. Eng. B 7, 297 (1991). 

^K. Ohmori, L. Li, and C. D. Graham, Jr., IEEE Trans. Magn. MAG-28, 
2139 (1992). 

^N. Yoshikawa, Y. Kasai, T. Watanabe, S. Shibata, V. Panchanathan, and 
J. J. Croat, J. Appl. Phys. 69, 6049 (1991). 

^L. H. Lewis, W. 0. Welch, T. R. Thurston, and V. Panchanathan, Pro¬ 
ceedings of the 9th International Symposium on Magnetic Anisotropy and 
Coercivity in RE-TM Alloys (1996), p. 278. 





















JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Microstructural analysis of strip cast Nd-Fe-B alloys for high (BH)max 
magnets 

J. Bernardi®^ and J. Fidler 

Institute of Applied and Technical Physics, University of Technology, A~1040 Wien, Austria 

M. Sagawa 

Intermetallies Company Ltd., Nishikyo-ku, Kyoto 615, Japan 

Y. Hirose 

Showa Denko K.K, Chichibu Research Laboratory, Saitama 369-18, Japan 

High energy density magnets >400 kJ/w? are increasingly used in many applications. Conventional 
casting techniques for sintered magnets reveal the formation of a high quantity of a-Fe and large 
Nd-rich regions. New techniques, like strip casting, produce homogeneous and fine scaled 
microstructures and are already used for producing high magnets. The fast cooling rate 

during strip casting suppresses the formation of a-Fe dendrites and of large Nd-rich pockets. 
Directional solidification causes a formation of columnar grains containing a typical arrangement of 
hard magnetic Nd 2 Fei 4 B regions and Nd-rich regions. The Nd regions occur as intragranular 
platelets as well as intergranular phases. Intragranular lamellae show a periodicity which 
corresponds to a eutectoidal solidification according to the composition of the liquid and are directed 
parallel to the temperature gradient during solidification. The lamellae show an average width of 
150 nm, a spacing of 3 yam, and a length up to the size of the hard magnetic grains. The fine 
separation of the hard magnetic and Nd phases is advantageous for the milling of the alloy after 
hydrogen decripitation and improves sinterability of magnets. Although the microstructure of strip 
cast alloys is much finer than that of ordinary cast alloys, the alignment of the powder is not 
deteriorated and B^ is not reduced due to a sufficient large interlamellar spacing between the Nd-rich 
platelets that enables the formation of single crystal powder particles after milling. © 1998 
American Institute of Physics. [80021-8979(98)18911-9] 


L INTRODUCTION 

Sintered Nd-Fe-B-type permanent magnets are widely 
used in applications that require a high energy product/ 
volume ratio in order to reduce weight.^ In addition there is a 
rising demand for magnets with higher than 

400kJ/m^. This goal can be reached by shifting the alloy 
composition more towards the stoichiometric Nd 2 Fei 4 B com¬ 
position as well as by improving the alignment of the hard 
magnetic grains during compacting. In addition the distribu¬ 
tion of phases in the starting alloy can be significantly im¬ 
proved. Conventional casting techniques reveal the forma¬ 
tion of a high quantity of precipitated a-Fe that deteriorates 
the powder alignment^ and large Nd-rich regions that are 
very sensitive to oxidation. The a-Fe is formed according to 
the pseudo-binary Fe-(Nd,B) phase diagram, with Nd:B 
=2:1, where the solidification path passes through a region 
(Liq. + Fe) and Fe particles are formed within the liquid.^ 
The formation of dendritic a-Fe in cast alloys can be reduced 
by additives like M2=Ti, Nb, Zr, V, Mo, or W that form 
M2-Fe”B borides'^ as well as by optimizing the casting 
technique. It has been previously shown that flat cast ingots 
consist of fine grains near the mold surface, columnar grains 
in the central portions, and coarse grains near the free 
surface.^ Reducing the thickness of the ingots from 8.7 to 4.4 
mm resulted in an increase of the amount of columnar grains 


“taectronic mail: bemardi@emaiLtuwien.ac.at 


and in a decrease of dendritic a-Fe in the ingot. An improve¬ 
ment of Br by 5% and (BH)niax by 10% of magnets produced 
from that ingot were attributed to a significantly reduced 
presence of dendritic a-Fe causing a better grindability of the 
powder and a better grain alignment. In this article we report 
on the effect of strip casting on the microstructure of Nd- 
Fe-B magnetic material. Materials produced by strip casting 
are already used for high (BH)„iax magnets. This new tech¬ 
nique allows large scale production of ingots with a homo¬ 
geneous and fine scaled microstructures without a significant 
precipitation of a-Fe. The fine dispersion of the rare earth- 
rich phase is important not only for high energy magnets 
having of over 400kJ/m^, but also for high coer- 

civity magnets that include high Dy concentrations. In such 
strip cast high Dy alloys B^ and (BH),„ax improved keep¬ 
ing the coercive field high because the total rare earth content 
can be substantially decreased without the formation of rare 
earth depleted regions that can deteriorate the squareness of 
the demagnetization curve of sintered magnets. 

II. EXPERIMENT 

The investigated samples with the composition 
(Nd,Dy)i 4 i(Fe,Al) 8 oB 5 9 were produced by strip casting, a 
technique similar to melt spinning, using a wheel speed of 1 
m/s. The platelike casted alloy shows a typical thickness of 
250-350 fim and a width of several centimeters. The 
samples were investigated by optical microscopy with polar- 


0021 -8979/98/83(11 )/6396/3/$15.00 


6396 


© 1998 American Institute of Physics 



J. AppL Phys., Vol. 83, No. 11, 1 June 1998 


Bernardi et al. 


6397 



FIG. 1. Optical micrograph of the cross section of strip cast 
(Nd,Dy)i 4 i(Fe,Al) 8 oB 5.9 showing the columnar growth of hard magnetic 
grains starting at nucleation centers (C) and the magnetic domains structure 
inside the columnar grains. 

ized light as well as by scanning electron microscopy (SEM) 
and transmission electron microscopy (TEM). 

III. RESULTS AND DISCUSSION 

The typical microstructure of the strip cast alloy parallel 
to the direction of solidification observed with polarized light 
is shown in Fig. 1. Solidification of the melt starts at nucle¬ 
ation centers (C) at the wheel side of the strips. The distance 
between individual centers is 50-120 /x-m. Starting from 
these nucleation sites, a columnar structure of hard magnetic 
grains is formed due to directional solidification. The growth 
direction of the grains is typically the direction of the heat 
flow during solidification. The columns grow within a cone 
with an opening angle 60°-80° towards the free surface of 
the strips. The diameter of the individual grains perpendicu¬ 
lar to the growth direction is 5-25 /xm close to the wheel 
side and 25-60 /xm close to the free surface side (Fig. 2), 
respectively. 

The columnar grains consist of a hard magnetic phase, 
which is proven by the existence of the magnetic domain 
pattern in that structure. The orientation of the domain walls 
visible with polarized light indicates that the growth direc¬ 
tion of these columns within the cone does not correspond 
with either (100), the easy growth axis of the tetragonal 
2:14:1 structure,^’^ or (001). A columnar dendritic 2:14:1 
structure with a growth direction parallel to (001) was pre- 



FIG. 2. Optical micrograph taken parallel to the surface of the strips near the 
free surface side. 



FIG. 3. SEM micrograph of the polished cross section of the strip cast alloy 
showing the distribution of hard magnetic phase (dark) and Nd-rich phase 
(bright) in backscattered mode. 


viously observed in splat cooled Ndi 5 Fe 77 B 8 magnets.^ A 
preferred c axis texture normal to the ribbon plane was also 
observed in melt spun Ndi 6 Fe 76 B 8 ribbons.^ Close to the 
wheel side between the nucleation sites, smaller elongated 
grains are formed with a growth direction more parallel to 
the surface. In these grains the domain walls tend to be ori¬ 
ented perpendicular to the surface, indicating a preferred 
(100) growth direction of the magnetic grains in that region. 
Within the large dendritic columns of the 2:14:1 phase a thin 
plateletlike phase is formed parallel to the growth direction. 
The occurrence of this intragranular layered structure does 
not usually influence the domain structure of the hard mag¬ 
netic grains (compare Fig. 1). Figure 3 shows a SEM back- 
scattered electron micrograph of a strip cast sample perpen¬ 
dicular to the wheel side. The hard magnetic grains appear as 
dark areas. Thin bright regions which occur with a certain 
periodicity within the hard magnetic grains and at grain 
boundaries consist of the Nd-rich phase. There is no indica¬ 
tion for the formation of dendritic a-Fe or a significant 
amount of additional phases like Ndi+fFe 4 B 4 formed during 
solidification. The lamellar arrangement of the two phases 
that are oriented parallel to the temperature gradient is char¬ 
acteristic for a eutectoidal solidification. The interlamellar 
spacing between the Nd-rich platelets is about 3 jxm and is 
controlled by the temperature gradient during solidification 
as well as the composition of the liquid. 

The orientation relationship between the Nd-rich intra¬ 
granular platelets and hard magnetic matrix grains was fur¬ 
ther investigated by TEM. Figure 4 shows the typical micro¬ 
structure of a columnar 2:14:1 grain in the center of a strip 
viewed perpendicular to the direction of solidification. Hard 
magnetic grains are separated by intragranular Nd-rich 
lamellae with a thickness of 60-150 nm. Within a grain all 
hard magnetic regions show the same crystallographic orien¬ 
tation. Close to grain boundaries the Nd-rich intragranular 
regions are also found with more irregular shapes. 

At grain boundaries and especially at grain boundary 
junctions, intergranular Nd-rich phases are found. Selected 
area electron diffraction (SAD) confirms that the Nd-rich 
platelets as well as the intergranular Nd-rich phases mainly 
occur as fee Nd and less frequently as Nd oxide. X-ray spec¬ 
tra show that there is usually a significant amount of Fe 





6398 J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 



FIG. 4. TEM micrograph of strip cast (Nd,Dy)i 4 i(Fe,Al) 8 oB 5 9 showing 
intragranular Nd-rich platelets embedded in a hard magnetic grain. The dif¬ 
fraction pattern of the marked region shows diffraction spots from the te¬ 
tragonal Nd 2 Fei 4 B phase and of the fee Nd-rich lamella. 

dissolved within the Nd-rich phases. During the TEM inves¬ 
tigation no a-Fe or Ndi+^Fe 4 B 4 was detected. The analysis of 
various diffraction patterns revealed that most of the lamel¬ 
lae are formed parallel to the {1,1,-1} plane of the tetragonal 
2:14:1 phase. 

Good magnetic properties require a homogeneous distri¬ 
bution of all phases and dopant elements throughout the cast 
material. Traditional casting techniques can cause a segrega¬ 
tion of individual phases depending, e.g., on the geometry of 
the casting mold, composition, or cooling rate, and therefore 
lead to strong inhomogeneities of the microstructure and the 
chemical composition.^’^’^^ The strip casting technique en¬ 
ables a fine separation of hard magnetic and rare earth-rich 
phases in the cast alloys. The merits of using strip cast alloys 
as a starting material for high performance Nd-Fe-B mag¬ 
nets are as follows: 

(1) The rapid solidification process prevents the forma¬ 
tion of large dendritic a-Fe grains in the cast alloy without 
the need of isothermal annealing even if the total rare earth 
content is reduced in order to produce high mag¬ 


Bernardi et a!. 

nets. The sufficiently large interlamellar spacing of about 3 
fim between the Nd-rich platelets in the columnar Nd 2 Fei 4 B 
grains is crucial in order to enable the formation of single 
crystal powder particles after HD treatment and jet milling 
necessary for optimum alignment of the particles and for 
high Br in the magnets. 

(2) The homogeneous fine scale microstructure, contain¬ 
ing a high amount of thin rare earth-rich platelets, leads to a 
high density of fine pre-cracks after hydrogen decrepitation. 
That and the lack of large dendritic o'-Fe grains improves the 
crushability of strip cast alloys significantly. 

(3) The good dispersion of rare earth-rich phases in the 
strip cast alloys leads to an optimum distribution of liquid 
phase during sintering and enables the production of high 
density magnets with high coercive fields even at lower sin¬ 
tering temperatures. The total rare earth content can be de¬ 
creased by using strip casting without the formation of rare 
earth depleted zones in the magnets. That is essential for 
high (BH),„ax magnets but also in the case of magnets with 
high Dy content in order to improve the remanence and 
(BH)n,^x while keeping high . 

'H. Nagel and W. E. Kronen, Proceedings of the 13th International Work¬ 
shop on Rare Earth Magnets and their Applications, Birmingham, UK, 
1994, edited by C. A. F. Manswaring, D. G. R. Jones, A. J. Williams, and 
1. R. Harris (University of Birmingham, Birmingham, UK, 1994), p. 391. 
^D. W. Scott, B. M. Ma, Y. L. Liang, and C. 0. Bounds, J. Appl. Phys. 
4830 (1996). 

^G. Schneider, E. T. Henig, H. H. Stadelmaier, and G. Petzow, Proceed¬ 
ings of the 5th International Symposium on Magnetic Anisotropy and Co- 
ercivity in Rare Earth Transition Metal Alloys, Part II, Bad Soden, Ger¬ 
many, 1987, edited by C. Herget, H. Kronller, and R. Poerschke (Deutch 
Physikalische Gesellschaft, Bad Honnef, FRG 1987), p. 347. 

'‘j. Fidler, J. Bernardi, and T. Schrefl, Scr. Metall. Mater. 33, 1781 (1995). 
^B. M. Ma and C. 0. Bounds, J. Appl. Phys. 70, 6471 (1991). 

^G. Schneider, E. Th. Henig, F, P. Missell, and G. Petzow, Z. Metallkd. 81, 
322 (1990). 

^A. Fujita and I. R. Harris, IEEE Trans. Magn. 29, 2803 (1993). 

^T. Harada, T. Ando, R. C. O’Handley, and N. J. Grant, J. Appl. Phys. 70, 
6468 (1991). 

^D. Dadon, Y. Gefen, and M. P. Dariel, IEEE Trans. Magn. 23, 3605 
(1987). 

*^H. Lemailre, P. Tenaud, F. Vial, and B. Labulle, J. Magn. Magn. Mater. 
83, 234 (1990). 


JOURNAL OF APPLIED PHYSICS VOLUME 83, NUMBER 11 I JUNE 1998 

Extension of the primary solidification region of Nd2Fei4B by levitation 
of undercooied meits 

R. Hermann®* and W. Loser 

Institute of Solid State and Materials Research (IFW), Institute of Metallic Materials, 

Helmholtzstrasse 20, D-01069 Dresden, Germany 

Undercooied Nd-Fe-B melts with compositions near the Nd2Fej4B phase (<I> phase) were studied 
by the electromagnetic levitation technique. In situ measurements of the solidification kinetics were 
accomplished and melt drops with controlled undercooling were quenched onto chill substrates in 
order to reveal the solidification sequence and microstructure formation processes. Crystal growth 
velocities of the $ phase of the order of 1 mms“^ were estimated from in situ measurements. 

Consistent with the nucleation theory, which predicts primary y-Fe phase crystallization up to 650 
K undercooling for the stoichiometric alloy, y-Fe nucleation could not be avoided during 
undercooling but the quenching of the melt drops led to dissolution of the y-Fe nuclei during 
0-phase formation. The y-Fe phase growth was suppressed in a seam adjacent to the chill surface, 
whereas Fe dendrites occurred in the remaining parts of the quenched samples. Reduced solute 
rejection on growth is believed to be responsible for the preferred metastable 0-phase formation 
from the undercooied melt on chill substrates. The investigation gives some clues to understand 
different microstructures and magnetic properties of powder precursors for permanent magnets 
obtained from different rapid solidification routes. © 1998 American Institute of Physics. 
[80021-8979(98)15111-3] 


I. INTRODUCTION 

Commercial Nd-Fe-B permanent magnets are usually 
prepared by sintering or rapid quenching methods.The 
Nd2Fei4B compound exhibits a high saturation magnetiza¬ 
tion and a strong magnetocrystalline field. These properties 
are the physical conditions for excellent permanent magnets. 
However, different magnetic properties are obtained using 
various processing techniques due to different microstruc¬ 
ture. The determination of the crystallization behavior and 
the resulting microstructure are still under study. Detailed 
knowledge of the solidification behavior is essential espe¬ 
cially for the development of alloys with novel properties. 
The solidification processes in rapid solidification techniques 
are hardly accessible to direct observation. Therefore, the 
purpose of this article was a study of crystallization pro¬ 
cesses of Nd-Fe-B melts by the containerless electromag¬ 
netic levitation method. This technique permits in situ mea¬ 
surements of the solidification kinetics of undercooied melt 
drops during the recalescence stage. Moreover, melt drops 
with controlled undercooling levels have been quenched onto 
copper substrates and copper-tin-coated substrates, respec¬ 
tively, in order to reveal the as-solidified microstructure. 

II. EXPERIMENT 

Three different Nd-Fe-B master alloys were prepared 
from pure Nd and Fe-B alloy by arc melting under argon 
atmosphere. Composition A is the stoichiometric 
Ndji gFeg2.3B59 alloy. Composition B is a hypostoichiomet- 
ric NdnFeg3 5B5 5 alloy and composition C is a hyper- 
stoichiometric Ndi5 gFe76 3B7 9 alloy. Spheres of about 6 mm 


^^Electronic mail: R.Hermann@IFW-Dresden.de 


in diameter and about 1.2 g mass were containerless melted 
and solidified in an electromagnetic levitation facility under 
helium gas atmosphere. The molted samples were cooled by 
a gas stream enabling cooling rates of about 10 K s“^ The 
temperature of the sample was monitored by a two- 
colorpyrometer with a sampling rate of 50 Hz and a relative 
accuracy of ± 3 K. For measuring and resolving the fast re¬ 
calescence time a modified single-reflex camera with a sili¬ 
con diode in its focal plane was used enabling sample rates 
of 500 MHz. The sampling rate of the transient recorder was 
1.5 MHz. A detailed description of the facility is given 
elsewhere.^ Melt drops of well defined undercooling level 
were quenched on a copper substrate and a copper substrate 
which was coated with tin to enhance the interfacial heat 
transfer. Immediately after nucleation the drops solidify with 
a preferred heat flow into the undercooied melt but with a 
heat transfer into the chill substrate as well. The as-solidified 
melt drops were investigated by digitally enhanced Kerr mi¬ 
croscopy and scanning electron microscopy. 

III. RESULTS 

A. Time-temperature characteristic 

The solidification of the undercooied melt drop starts by 
spontaneous nucleation or can be initiated by triggering at a 
well defined undercooling level. The photodiode does not, in 
principle, allow one to determine an absolute temperature, 
but the two-color pyrometer could be used to set the tem¬ 
perature scale in order to compare the results with the equi¬ 
librium phase diagram. Figure 1 shows typical temperature¬ 
time profiles of the three investigated Nd-Fe-B compounds. 
The stoichiometric sample [Fig. 1(a)] was melted at 
= 1520 K and initially superheated. After cooling down be- 


0021-8979/98/83(11 )/6399/3/$15.00 


6399 


© 1998 American Institute of Physics 



6400 J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


R. Hermann and W. Loser 



FIG. 1. Temperature-time characteristic of double recalescence events of: 
(a) a stoichiometric Nd-Fe-B alloy at an undercooling level of 170 K (with 
respect to the liquidus temperature), (b) a hypostoichiometric Nd-Fe-B 
alloy at an undercooling level of 165 K, (c) a hyperstoichiometric Nd-Fe-B 
alloy at an undercooling level of 130 K. 

low the melting temperature, the solidification of the sample 
occurs at 1350 K, corresponding to an undercooling level of 
A7= 170 K. The solidification process consists of two steps. 
The first step can be attributed to a small amount of y-Fe 
phase nuclei at about 1460 K, whereas the drop is still under 
undercooling. The second step starts with the solidification 
of the <!> phase. Assuming that the solidification front is pla¬ 
nar, the growth velocity of the $ phase can be estimated to 
1.2 mm 8“^ The resulting time of crossing the planar front 
through the viewing field of the diode (0.88 mmXO.88 mm) 
was measured to 720 ms. Figures 1(b) and 1(c) show the 
corresponding temperature-time profile of the hypostoichio¬ 
metric and hyperstoichiometric sample, respectively. It is of 
interest to note that all three alloys show the small recales¬ 
cence step of y-Fe phase nucleation independent of the 
achieved undercooling level. 

B. Phase analysis of as-solidified samples 

The in situ observation of undercooled melts is an im¬ 
portant tool for investigation of rapid solidification. Never¬ 
theless, the microstructure of the as-solidified sample has to 
be investigated. The arc-melted master alloys show different 
microstructures. In alloys A and B y-Fe dendrites are clearly 
visible whereas alloy C does not contain any y-Fe dendrites. 
Figure 2 shows the backscattering electron (BSE) micro¬ 
graphs of a sample of alloy B, undercooled at about 150 K 
prior to solidification and subsequently quenched on a 
copper-tin-coated substrate. Immediately on the strongly 
separated tin layer a nonfeatured layer of about 100 /mm has 
been developed, responsible for pure metastable $ phase 
electron probe microanalysis investigation, Fig. 2(a)]. The 
relatively sudden transition to the structured layer shows the 
beginning decomposition into Fe-rich phases and the growth 
of Nd 2 Fei 4 B needles [see Figs. 2(a) and 2(b)]. Finally, the 
growth of Fe dendrites and the separation of Nd-rich phases 
in the interdendritic region indicate the transition to equilib¬ 
rium solidification [Fig. 2(c)]. 



FIG. 2. BSE micrographs of alloy B, undercooled at about 150 K prior to 
chilling on a copper-tin-coated substrate: (a) featureless Nd 2 Fe| 4 B phase 
layer near the chill substrate, (b) growth of Nd 2 Fe| 4 B needles and Fe-rich 
phases, (c) growth of Fe dendrites near the top of the sample. 








J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


R. Hermann and W. Loser 6401 


On the other hand BSE micrographs of samples 
quenched on a copper substrate prior to solidification, show 
that Fe dendrites have been grown directly in the quenched 
region. The heat transfer was not sufficient for the formation 
of pure metastable phase even at the stoichiometric alloy. 
These microstructures indicate that both critical undercool¬ 
ing and rapid quenching are necessary for the growth of the 
metastable O phase. 

IV. DISCUSSION 

The as-solidified microstructure of Nd-Fe-B alloys is 
determined by nucleation and growth processes of the com¬ 
petitive phases, notably y-Fe and O phase, and post¬ 
solidification transformations as well. The homogeneous 
nucleation rates of y and 0 phase, I y and , respectively 
were estimated as functions of melt undercooling on the ba¬ 
sis of thermodynamic and kinetic data given by Clavaguera 
and Diego."^ For the stoichiometric melt composition, the 
nucleation of the properitectic y-Fe phase dominates in a 
wide undercooling range below the liquidus temperature 
Ti^y. The crossing point with the /(j, is about 650 K below 
the liquidus temperature, outside the range of experimental 
accessibility. In principle, the nucleation and growth of the O 
phase can arise in the primary y-Fe phase field well above 
the peritectic temperature if a critical undercooling below the 
metastable liquidus temperature T/ ^ is achieved.^’^ The time- 
temperature characteristics of levitated samples indicate that 
y-Fe nucleation could not be avoided on slow cooling of the 
levitated samples. This becomes apparent from the small dip 
near the liquidus temperature T; The residual melt, how¬ 
ever could be undercooled by a considerable amount of 
>170K below Ti y. Accordingly a very distinct recales- 
cence event was obtained due to the growth of the ^ phase 
from the undercooled melt. The microstructural features in¬ 
dicate that both melt undercooling and fast cooling were nec¬ 
essary for the growth of the metastable phase. Quenching 
of the undercooled melt drops onto the copper-tin-coated 
substrate led to a wide seam of more than 100 /mi thickness 
free of y-Fe dendrites even for hypo stoichiometric melt al¬ 
loys. More distant from the chill surface the growth of 
Nd 2 Fei 4 B needles continued with apparent Fe segregation in 
the interdendritic regions before y-Fe dendrites indicate the 
transition to the equilibrium solidification mode. The reason 


for the possible suppression of the y-Fe equilibrium phase 
dendrites and preferred growth of the metastable O phase is 
its smaller composition deviation from the melt, which leads 
to less solute rejection at the growth front.^ This behavior is 
typical of various peritectic alloys.^ This first attempt of Nd- 
Fe-B melt undercooling experiments shed some light onto 
the obvious differences in microstructure and magnetic prop¬ 
erties of powder precursors for Nd-Fe-B hard magnetic ma¬ 
terials obtained from different rapid solidification techniques. 
In hyperstoichiometric inert-gas-atomized Nd-Fe-B par¬ 
ticles properitectic y-Fe precipitations depending on droplet 
size were found,® whereas thin melt spun ribbons often ex¬ 
hibit an overquenched amorphous state from which the ^ 
phase can evolve. There is an apparent difference in the ther¬ 
mal history of both rapid solidification techniques. IGA par¬ 
ticles are exposed to moderate cooling rates of 
10^-10^ Ks“^ by the gas stream. High undercooling of 
droplets prior to solidification is expected, which is a behav¬ 
ior similar to levitated samples. In melt spinning there is a 
vigorous heat transfer from a thin melt film to the chill sub¬ 
strate, which can lead to a dynamic undercooling and finally 
quenching the melt into the amorphous state before nucle¬ 
ation of crystalline phases because of cooling rates as high as 
10^ Ks"'. 

ACKNOWLEDGMENTS 

The authors wish to thank H.-G. Lindenkreuz, M. From- 
mel, S. Schinnerling, and 1. Bacher for carrying out under¬ 
cooling experiments and microstructure investigations. The 
support of the Deutsche Forschungsgemeinschaft is grate¬ 
fully acknowledged. 

^M. Sagawa, S. Fujimura, N. Togawa, H. Yamamoto, and Y. Matsuura, J. 
Appl. Phys. 55, 2083 (1984). 

^ J. J. Croat, J. F. Herbst, R. W, Lee, and F. E. Pinkerton, J. Appl. Phys. 55, 
2078 (1984). 

^ W, Loser, H. Genest, and H.-G. Lindenkreuz, Ann. Report, IFW Dresden, 
27 (1994). 

Clavaguera and J. A. Diego, Intermetallics 1, 187 (1993). 

^G. Schneider, E.-T. Henig, G. Petzow, and H. H. Stadelmaier, Z. Met- 
allkd. 77, 755 (1986). 

^T. Umeda, T. Okane, and W. Kurz, Acta Mater. 44, 4209 (1996). 

^H. W. Kerr and W. Kurz, Int. Mater. Rev. 41, 129 (1996). 

^C. H. Sellers, T. A. Hyde, D. J. Braganan, L. H. Lewis, and V. Pancha- 
nathan, J. Appl. Phys. 81, 1351 (1997). 



JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER II 


1 JUNE 1998 


High performance Nd-Fe-B sintered magnets made by the wet process 

M. Takahashi K. Uchida, and F. Taniguchi 

Magnetic and Electronic Materials Research Laboratory, Hitachi Metals, Ltd. 5200 Mikajiri, Kumagaya, 

Saitama 360, Japan 

T. Mikamoto 

Production System Laboratory, Hitachi Metals, Ltd., 6010 Mikajiri, Kumagaya, Saitama 360, Japan 

The wet process for the fabrication of Nd-Fe-B sintered magnets has been developed on the mass 
production scale. In this process, mineral oil is used as a solvent to prevent the milled powder and 
green bodies from oxidation. It is removed before sintering. As a result, the oxygen uptake during 
storage is less than 0.01 wt %/day. By reducing the oxygen content and the total rare earth (TRE) 
content in sintered magnets to less than 0.2 and 29.3 wt %, respectively, magnets with 
greater than 50 MGOe/10 kOe, 45 MGOe/15 kOe, and 32 MGOe/32 kOe were obtained with high 
reliability. The magnets produced by this wet process also show better corrosion resistance and 20% 
higher mechanical strength than those made by conventional methods. These characteristics may be 
explained by a smaller grain size, smaller TRE content, and higher density produced by the wet 
process. © 1998 American Institute of Physics. [80021-8979(98)15211-8] 


I. INTRODUCTION 

Nd-Fe-B sintered magnets with higher magnetic prop¬ 
erties have been required as their applications decrease in 
size. Minimizing nonmagnetic secondary phases (rare earth 
oxide, B-rich phase etc.), maximizing grain alignment, and 
optimizing alloy design are ways to increase of 

Nd-Fe-B sintered magnets, and concrete methods based on 
these principles have been presented. Improving the mag¬ 
netic properties by minimizing nonmagnetic secondary 
phases requires a reduction in the oxygen content in sintered 
magnets. To reach this goal, various methods have been de¬ 
veloped for the powder metallurgy process. However, it is 
difficult to prevent oxidation in chemically active fine pow¬ 
der and green compacts that are exposed to the air with con¬ 
ventional methods. A low oxygen content of around 0.2 
wt % in a sintered body could be achieved only on the labo¬ 
ratory scale by a wet process using an organic solvent such 
as n-hexane or a dry process using oxygen-free chambers 
and containers. 

We have developed a wet process (HILOP, HITACHI 
low oxygen process) using mineral oil as a solvent and have 
obtained Nd-Fe-B sintered magnets with less than 0.2 wt % 
oxygen in sintered bodies on the production scale. In this 
article, the procedure of the developed wet process and the 
characteristics of the resultant magnets will be presented. 

II. EXPERIMENT 

The developed wet process is based on conventional 
powder metallurgy techniques, but is distinguished from the 
conventional technique by handling the milled powders and 
green bodies in oil from milling to sintering. The wet process 
procedure is illustrated in Fig. 1 in comparison with the con¬ 
ventional dry process. Cast alloys were annealed at 1100 °C 
for 6 h, and then ground to less than 500 pm after the hy¬ 


^taectronic mail: Masahiroj_Takahashi@po.hitachi-metals.co.jp 


drogen decrepitation process. The oxygen content in the ni¬ 
trogen gas used in the mill chamber for conventionally pro¬ 
cessed materials is commonly around 1000 ppm to stabilize 
the surface of the fine powder to prevent rapid oxidation in 
air. In the wet process, however, the prepared coarse pow¬ 
ders were jet milled with no oxygen (less than the detection 
limit, i.e., <0ppm). Milled powders were put in mineral oil 
without being exposed to the air, mixed into slurries, and 
stored for pressing. The slurries were die-pressed in a mag¬ 
netic field of 14 kOe applied perpendicular to the axis of the 
press. The extremely low vaporization rate of the oil com¬ 
pared to that of organic solvents such as «-hexane enables 
the green bodies to be handled in air. The oil present in the 
green bodies was removed in the temperature range 100 °C 
^7^300 °C for 1 h in a vacuum of 10“ * Torr before sin¬ 
tering. Sintering was carried out at temperatures from 1050 
to 1080 °C in a vacuum of 10“^ Torr for 5 h. Sintered bodies 
were heat-treated at 900 °C for 2 h followed by another heat 
treatment at temperatures from 460 to 560 °C for 1 h. Mag¬ 
netic properties were measured by ?l B-H tracer. Corrosion 
rates were determined by measuring the weight losses after 
exposing the magnets in an autoclave under conditions of 
120 °C, 100% relative humidity, and 2 atm. 


conventional 

wet process(HILOP) 

coarse powder 

1 

coarse powder 

I 

1 

jet milling in N2 

I 

jet milling in N2 

{with 0.1 %02) 

I 

(with 0%O2) 

I 

I 

dry pressing 

wet pressing 



(solvent :oil) 

I 



I 

desolvent 

I 

sinte 

‘ring 

I 

sintering 


FIG. 1. A comparison of the wet process (HILOP) with the conventional dry 
process. 


0021 -8979/98/83(11 )/6402/3/$15.00 


6402 


© 1998 American Institute of Physics 




J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Takahashi et al. 


6403 


TABLE L Typical oxygen and carbon contents of HILOP-processed and 
conventionally processed materials. 


Process 

Oxygen (wt %) 

Carbon (wt %) 

HILOP 

0.16 

0.061 

Conventional 

0.58 

0.055 


III. RESULTS AND DISCUSSION 

A. Oxygen contents and magnetic properties 

The typical oxygen and carbon contents of magnets with 
compositions of 

Nd27.3Pro.5Dy 15 Fet,ai C02.oNbo.7Gao. 1 Cuo. iB 10 
and 

Nd23.9Pr6 gDy 1.4Febai Nbo.7Gao. 1B ^ 0 

in wt % produced by the wet process and the conventional 
dry process, respectively, are shown in Table L The final 
carbon content of the wet-processed magnets is only around 
0.01 wt % greater than that of conventionally processed 
magnets. This indicates that the oil remaining in the green 
body was well removed by the desolvent process. The oxy¬ 
gen content of wet-processed materials is less than a third of 
that of the magnets produced by the conventional process. 
The oxygen content increased by only 0.02 wt % from the 
starting coarse powder with 0.14 wt % oxygen during jet 
milling, pressing, desolventing, and sintering process steps. 
The oxygen uptake rate for wet-processed powders stored in 
oil was much lower than that for powders stored in organic 
solvent (n-hexane): 0.007 and 0.016 wt %/day, respectively. 
The characteristics of oxidation prevention and low vapor¬ 
ization rate of the oil contribute to the adaptation of the wet 
process to mass production with high reliability. The low 
final oxygen levels provided by the wet process raised the 
possibility of a reduction of total rare earth (TRE) content. 

Figure 2 shows variations of with oxygen content for 
sintered magnets with different TRE contents. The coercivity 

decreased with the increase of oxygen content. As TRE 
decreased from 29.8 to 28.9 wt %, the decrease rate for 
the oxygen content in the range 0.15 wt %^O^0.25 wt % 
became higher and was deteriorated to zero with a lower 



FIG. 2. Variations of with oxygen content for sintered magnets with 
different TRE contents: (a) 29.8 wt %, (b) 29.3 wt %, (c) 28.9 wt %. 



FIG. 3. Magnetic properties of HILOP materials (a) in comparison with 
conventionally processed materials (b). 

oxygen content. This is due to a reduction of the Nd-rich 
phase caused by the change from Nd to Nd oxide. To obtain 
a high enough for practical use, a TRE of more than 29.3 
wt % is required. 

Figure 3 shows the magnetic properties of HILOP 
materials for 29.3 wt % TRE 

[Nd(28.8-;c)Bro.5Dy;cB^baiCo2.oNbojGao,iCuo,iBi 0 

{x = 1.5, 3.0,4.5, 5.5, 7.5, 9.5) in wt %] in comparison with 
conventional compositions (TRE^31.5-32.5 wt %) on the 
production scale. From high Br to high iH ^, Br of HILOP 
materials is 800 G higher than that of conventionally pro¬ 
cessed materials, due to lower oxygen content and lower 
TRE content. The HILOP process is also applicable to ma¬ 
terials with a much higher . The magnetic properties 

of MGOe with iHc= 13.1 kOe were obtained 

for the composition of 

Nd28.86Dyo.75B®bal.Nbo.43Alo.08CUo.05Bi.oi- 

B. Corrosion resistance 

The corrosion resistance of the HILOP materi¬ 
als containing less than 0.2 wt % oxygen was in¬ 
vestigated. The weight loss of the HILOP material 
(Nd27.iPro.6Dyi.5FebaiCo2.iNbo.7Gao.iCuo.iBi.i) is shown in 
Table II in comparison with a conventionally processed ma¬ 
terial (Nd 23 , 9 Pr 6 6 Dyi 4 Febai.Nbo. 7 Gao 4 Bi 0 ) and a reference 
material (Nd 28 . 2 Pi‘ 2 . 2 Dyi. 2 FebaiNbo. 5 Gao 4 Bi 1 ) that has al¬ 
most the same TRE as the conventionally processed material 
and almost the same oxygen content as HILOP material. The 
weight loss rate of the magnet with a TRE of around 32 wt % 
increased with decreased oxygen content. This trend is in 
agreement with those reported by Kim^ and Camp."^ How- 


table II. Weight loss of HILOP material by pressure cooker test (P.C.T.) 
for 96 h in comparison with the conventionally processed material. The 
materials’ compositions are given in the text. 


Process 

TRE (wt %) 

Oxygen (wt %) 

Weight loss (mg/cm^) 

Conventional 

31.7 

0.75 

0.67 

Ref. 

31.9 

0.15 

21.12 

HILOP 

29.2 

0.15 

0.53 





6404 J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Takahashi et af. 



FIG. 4. Photos showing the microstructure of HILOP material (a) in com¬ 
parison with a conventionally processed magnet (b). 


ever, the HILOP material shows a lower weight loss rate 
even compared to that of the conventionally processed ma¬ 
terial in spite of its low oxygen content. 

Figure 4 shows optical micrographs of the HILOP ma¬ 
terial and the conventional material. Compared to the con¬ 
ventional material, the HILOP material has a smaller and 
more homogeneous grain size, so the Nd-rich phases (black 
or gray regions in the micrographs) at the triple junctions are 
smaller and more homogeneously distributed. According to 
the article by Scott et al,^ the weight loss rate decreases with 
the decrease of grain size. Since the corrosion of Nd-Fe-B 
sintered magnets is initiated in the Nd-rich grain boundary 
phase,the above result may be explained by the fact that 
the magnet possesses a lower TRE and that the Nd-rich 
phases are more evenly distributed, with smaller grain size. 

C. Mechanical strength 

Table III shows the three-point bending strength 
and the density of sintered bodies of HILOP material 
(Nd2i.3Pro.5Dy7 5Fe5ai Co2.oNbo,7Gao.iCuo.iBi o) the con¬ 
ventionally processed material 

(Ndi9 2Pr5.2Dy7 jFebai C04 5Nb 1 _ 4 Gao. 1 B 12 ) . 

The mechanical strength of HILOP material is improved by 
around 25%. This result may be attributed to the smaller 


TABLE III. Three-point bending strengths and densities (p s) of HILOP 
material in comparison with those of the conventionally processed material. 



ps 

Three-point bending strength 

Process 

(g/cm"^) 

(kgf/mm^) 

Conventional 

7.62 

26.2 

HILOP 

7.70 

32.8 


grain size mentioned above, higher density (i.e., fewer voids) 
and fewer inclusions in the Nd-rich phase, such as rare-earth 
oxides. This issue requires further investigation. 

IV. CONCLUSION 

The wet process using mineral oil to prevent milled 
powder and green bodies from oxidation has been estab¬ 
lished. As a result, magnets with oxygen content of less than 
0.2 wt % and of higher than 45 MGOe were ob¬ 

tained in production. The above magnets also have a better 
corrosion resistance and a higher mechanical strength mainly 
due to a smaller grain size and a smaller TRE content in the 
sintered bodies. This process has produced a reduction in the 
final oxygen content during production, and is one approach 
for the production of high performance Nd-Fe-B sintered 
magnets. Additional improvements in the crystallographic 
alignment of the magnets will produce magnets with much 
higher magnetic properties. 

*E. Otuki, T. Otsuka, and T. Imai, in Proceedings of the I Ith Workshop on 
RE Magnets and their Applications, edited by S. G. Sanker (Carnegie 
Mellon University Press, Pittsburgh, PA, 1990), pp. 328-340. 

^M. Sagawa and H. Nagata, IEEE Trans. Magn. MAG-29, 2747 (1993). 
^A. S, Kim, F. E. Camp, and E. J. Dulis, IEEE Trans. Magn. MAG-26, 
1936 (1990). 

'^F. E. Camp and A. S. Kim, J. Appl. Phys. 70, 6348 (1991). 

^D. W. Scott, B. M. Ma, Y. L. Liang, and C. O. Bounds, J. Appl. Phys, 79, 
5501 (1996). 

^K. Tokuhara and S. Hirosawa, J. Appl. Phys. 69, 5521 (1991). 

^A. S. Kim and F. E. Camp, J. Mater. Eng. 13, 175 (1991). 



JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER II 


1 JUNE 1998 


Hydrogen absorption and desorption behavior in Pr-Fe-B type alloys 

Yoon B. Kim and W. Y. Jeung 

Center for Metal Processing, Korea Institute of Science and Technology, P.O. Box 131 Cheongryang, 

Seoul 130-650, Korea 

In this study, the hydrogen absorption and desorption behavior of Pr-Fe-B type alloys with 
addition of Co, Ga, and Zr was investigated focusing on the disproportionation and recombination 
reaction in HDDR process. In Pri 3 B 6 Febai. alloy, the second hydrogen absorption reaction which 
corresponds to the disproportionation reaction in HDDR process occurs at about 620 ®C, and the 
recombination reaction was not observed below 1000 °C in hydrogen atmosphere. In alloys with Co 
content of 12 at.%, the second hydrogen desorption reaction, which corresponds to the 
recombination reaction in HDDR process, occurs at about 955 °C and the occurring temperature of 
the recombination reaction is further decreased with increasing Co content. The Ga addition to 
Pri 3 BbFe 5 ai. alloy also reduces the recombination reaction temperature and has no significant 
influence on the disproportionation reaction. Moreover, the lowering of the recombination reaction 
temperature is remarkable when Ga and Co are added simultaneously. On the contrary, Zr addition 
to Pr^B^Febai. alloy may not cause the recombination reaction but make the disproportionation 
reaction sluggish. The Pr~Fe-B type magnet powder which has a remanence of 9.8 kG and 
coercivity of 4.8 kOe, was obtained by HDDR treatment. © 1998 American Institute of Physics. 
[80021-8979(98)34611-3] 


I. INTRODUCTION 

Hydrogen treatment such as hydrogenation, dispropor¬ 
tionation, desorption, and recombination (HDDR) process is 
now well established as a method of producing Nd-Fe-B 
type anisotropic magnetic powder through a hydrogen in¬ 
duced phase transformation. The effects of such minor 
elements as Co, Ga, and Zr on the HDDR process of Nd- 
Fe-B type alloy have been intensively studied.However, 
the research on applying the HDDR treatment to Pr-Fe-B 
type alloy and HDDR phenomena with such additive ele¬ 
ments in Pr-Fe-B type alloy were not available. 

In Pr-Fe-B based alloys where Pr is used as the rare 
earth instead of Nd, Pr 2 Fei 4 B compound may disproportion¬ 
ate into the mixture of PrH 2 , Fe 2 B, and a-¥t at the dispro¬ 
portionation reaction stage of HDDR treatment. At the re¬ 
combination reaction stage in HDDR treatment, these 
decomposed mixtures could be recombined into the fine 
grained Pr 2 Fei 4 B phase. In the present study, the effects of 
such minor elements as Co, Ga, and Zr on the hydrogen 
absorption and desorption behavior of Pr-Fe-B type alloys 
were investigated focusing on the disproportionation and re¬ 
combination reaction in HDDR process. In addition to this, 
magnetic properties of HDDR treated Pr-Fe-B type alloy 
were investigated. 


II. EXPERIMENT 

Pr-Fe-B alloy ingots of various composition were pre¬ 
pared by arc melting and induction melting weighed amounts 
of constituent elements. The alloy ingots were then homog¬ 
enized at 1000 ®C for 20 h in vacuum. After homogenization, 
alloy ingots were mechanically crushed down to powders of 
under 200 yLtm. These powders were used for investigating 


the hydrogen absorption and desorption behavior. The 
chemical composition of alloys used in this study are shown 
in Table I. 

For investigating the hydrogen absorption and desorp¬ 
tion characteristics, the samples were heated from room tem¬ 
perature to 1000 °C at an initial hydrogen pressure of 760 
Torr and then the pressure changes as well as temperature 
changes were monitored. At each measurement, an 8 g 
sample was used and the heating rate was 5 °C/min. The 
expansion of hydrogen at an elevated temperature was taken 
into account by performing blank test. The phase changes 
during hydrogen absorption and desorption were examed us¬ 
ing a x-ray diffractometer with C\x-ka radiation. 

The samples for HDDR treatment were prepared by hy¬ 
drogen decrepitation at room temperature and subsequent 
milling. For HDDR treatment, the disproportionation treat¬ 
ment was carried out at 800 °C and subsequent evacuating 
was performed at 820 ®C. The disproportionation time was 
varied. The bonded magnets were made by aligning and 
pressing after mixing the HDDR treated powders with solid 
phenol. This compacts were then cured at 120 °C for 2 h. 
The magnetic properties of bonded magnets were measured 
by a D.C Fluxmeter. 


TABLE I. The chemical composition of alloys (at.%). 


No. 

Pr 

B 

Co 

Zr 

Ga 

Fe 

1 

13.0 

6.0 




bal. 

2 

13.0 

6.0 

6.0-35.0 



bal. 

3 

13.0 

6.0 


O.l-i.O 


bal. 

4 

13.0 

6.0 



0.5-L5 

bal. 

5 

13.0 

6.0 

12.0 

0.5-1.0 


bal. 

6 

13.0 

6.0 

12.0 


1.5 

bal. 


0021-8979/98/83(11 )/6405/3/$15.00 


6405 


© 1998 American Institute of Physics 



6406 J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Y. B. Kim and W. Y. Jeung 



FIG. 1. The hydrogen absorption and desorption behavior in Pr] 3 B 5 Feba]. 
type alloys. 

III. RESULT AND DISCUSSION 

The pressure and the temperature changes in Pri 3 B 6 Febai. 
alloy, which is the standard composition in this study, on 
heating from room temperature to 1000 °C is shown in Fig. 
1. The pressure change curve for this alloy consists of three 
regions, two hydrogen absorption regions (designated as a 
and c) and one hydrogen desorption region (designated as b). 
The first hydrogen absorption reaction of this alloy, which 
correspond to hydrogen absorption into Pr-rich and Pr 2 Fe| 4 B 
phases, starts at about 80 This is followed by broad hy¬ 
drogen desorption reaction. Another hydrogen absorption re¬ 
action corresponding to disproportionation reaction in 
HDDR process occurs at around 620 °C. The recombination 
reaction was not observed below 1000 °C in hydrogen atmo¬ 
sphere in Pr-Fe“B three component system. The two exo¬ 
thermic peaks on the temperature change curve correspond to 
the hydrogen absorption reaction. 

Figure 2 shows the hydrogen absorption and desorption 
behavior of Co added Pr-Fe-B alloys. In order for investi¬ 
gation of effect of Co addition on the hydrogen absorption 
and desorption behavior, the contents of Co addition was 
varied from 6 to 24 at.%. The starting temperature of first 



FIG. 2. The hydrogen absorption and desorption behavior in Pri 3 B 6 COxFehai. 
(ji:=6,12,18,24) type alloys. 



FIG. 3. X-ray diffraction pattern of powders after second hydrogen desorp¬ 
tion reaction in Pr| 36 ^ 00 i 2 Feh,ji type alloys. 

hydrogen absorption reaction were varied 70 to 100 with 
the addition of Co. However, the occurring temperatures of 
second hydrogen absorption reaction corresponding to dis¬ 
proportionation reaction are almost the same as those in the 
alloys with or without Co, which is around 620 °C. So, the 
addition of Co to Pr-Fe-B type alloy may not affect the 
disproportionation reaction. On the contrary, in the alloy 
with Co content of 12 at.%, the second hydrogen desorption 
reaction (designated as d) occurs at 955 °C, which corre¬ 
sponds to the recombination reaction in HDDR process. The 
x-ray diffraction pattern of the powder after this desorption 
reaction in Fig. 3 shows that the diffraction peaks of 
Pr 2 Fej 4 B phase, which were recombined from the decom¬ 
posed mixture of PrH 2 , Fe 2 B, and a-Fe, are dominant. The 
second hydrogen desorption reaction in Pri^BgCoisFeb-j and 
Pri 3 B 6 Co 24 Fe 5 yi alloys occurred at 940 and 925 °C, respec¬ 
tively. So, the occurring temperature of recombination reac¬ 
tion is further decreased with increasing Co content. The 
recombination reaction was not observed in the alloys with 
Co content below 6 at.%. 

Figure 4 shows the hydrogen absorption and desorption 
behavior of Ga added Pr-Fe-B alloys. Ga was added from 
0.5 to 1.5 at.%. The Ga addition to Pri 3 B 6 Febai. alloy also 



FIG. 4. The hydrogen absorption and desorption behavior in Pr| 3 B(iGaxFe|,;,| 
(Ga=0.5,1.5) type alloys. 














J. Appl. Phys., Vol. 83, No. 11, 1 June 1998 


Y. B. Kim and W. Y. Jeung 6407 



Time(sec,) 


FIG. 5. The hydrogen absorption and desorption behavior in 
Pri3B6Coi2(Gai 5)Febai. type alloys. 



FIG. 6. The hydrogen absorption and desorption behavior in Pri 3 B 6 ZrxFet 
(Zr= 0.1,0.5,1.0) type alloys. 


causes the recombination reaction below 1000 °C in hydro¬ 
gen atmosphere, which is the same behavior as that observed 
in Co added alloys. In Pri 3 B 6 Gai 5 Febai. the recombination 
reaction was occurred at about 940 °C, but small addition of 
Ga (0,5 at.%) does not cause the recombination reaction. The 
addition of Ga to Pri 3 B 5 Febai has no significant influence on 
disproportionation reaction. 

As shown in Fig. 2 and Fig. 4, the most distinct effects 
of Co and Ga addition to Pr-Fe-B system is the lowering of 
the recombination reaction temperature below 1000 °C in 
comparison with Pri 3 B 6 Fe 5 ai. alloy. The decomposed mixture 
is considered to be less stable by the addition of Co and Ga 
and hence the recombination reaction starts at a lower tem¬ 
perature. This result indicates that the addition of Co and Ga 
to Pr-Fe-B alloy enhances the recombination reaction by 
lowering the recombination reaction temperature. 

Figure 5 shows the hydrogen absorption and desorption 
behavior of Pri 3 B 6 Coi 2 Gai. 5 Fe 5 ai alloy. In this alloy, the re¬ 
combination reaction starts at about 890 °C. In comparison 
with Prj 3 B 6 Coi 2 Febai, the starting temperature of recombina¬ 
tion reaction was further decreased by Ga addition. The low¬ 
ering of the occurring temperature is remarkable when Ga 
and Co are added simultaneously. 

The hydrogen absorption and desorption behavior of Zr 
added Pr-Fe-B alloys is shown in Fig. 6. The Zr content 
was varied from 0.1 to 1.0 at %. The shape of second hydro¬ 
gen absorption curve corresponding to disproportionation re¬ 
action for alloy with 0.1 at % Zr is broadened in comparison 
with Pr| 3 B 6 Febai. alloy. This disproportionation curve is fur¬ 
ther broadened with increasing Zr content and both the start¬ 
ing and finishing temperature of disproportionation reaction 
were changed. So, it can be said that the addition of Zr to 
Pr-Fe-B alloy may retard the disproportionation reaction. In 
opposition to Co and Ga added Pr-Fe-B alloys, Zr addition 
to Pri 3 B 6 Febai. alloy does not cause the recombination reac¬ 
tion below 1000 °C in hydrogen atmosphere. 

HDDR treatment was employed to the 
Pr|^ 3 B 6 Zro iGai oCo 24 Febai. alloy. The samples for HDDR 
treatment were prepared by hydrogen decrepitation at room 


temperature and subsequent milling. HDDR treatment was 
carried out by keeping the sample at 800 °C in hydrogen and 
evacuating hydrogen from the sample at 820 "^C. As a result, 
Pri 3 B 6 Zro.iGai oCo 24 Febai. magnet powder having a rema- 
nence of 9.8 kG and a coercivity of 4.8 kOe was obtained by 
employing the HDDR treatment to Pr-Fe-B system. 

IV, CONCLUSION 

From the investigation of hydrogen absorption and de¬ 
sorption behavior of Pr-Fe-B type alloys and magnetic 
properties of HDDR treated Pr-Fe-B type magnetic powder, 
the following conclusions can be drawn. 

The second hydrogen desorption reaction, which corre¬ 
sponds to recombination reaction in HDDR process, occurs 
at about 955 ""C in Pri 3 B 6 Coi 2 Febai. alloy and the occurring 
temperature of recombination reaction is further decreased 
with increasing Co content. The Ga addition to Pri 3 B 6 Febai. 
alloy also reduces the recombination reaction temperature. 
So, the addition of Co and Ga to Pr-Fe-B alloy enhances 
the recombination reaction. Moreover, the lowering of the 
recombination reaction temperature is remarkable when Ga 
and Co are added simultaneously. The addition of Co and Ga 
to Pri 3 B 6 Fe 5 ai. alloy has no significant influence on dispro¬ 
portionation reaction. On the contrary, Zr addition to 
Pri 3 B 6 Febai. alloy may not cause the recombination reaction 
but make the disproportionation reaction sluggish. The Pr- 
Fe-B type magnet powder which has a remanence of 9.8 kG 
and coercivity of 4.8 kOe, was obtained by HDDR treatment. 

^T. Takeshita and R Nakayama, in Proc. of the 12th Int. Workshop on 
Rare-Earth Magnets and Their Application, Canberra, July 670 (1992), 
^I. R. Harris and P. J. Mcguiness, J. Less-Common Met. 172, 1273 (1991). 
^R Nakayama and T. Takeshita, J. Appl. Phys. 74, 2719 (1993). 

R. Harris, in Proc. of the 12th Int. Workshop on Rare-Earth Magnets 
and Their Application. Canberra, July, 347 (1992). 

^R Nakayama and T. Takeshita, J. Alloys Compd, 193, 259 (1993). 

^T. Takeshita and R Nakayama, in Proc. of the 11th Int. Workshop on 
Rare-Earth Magnets and Their Application. Pittsburgh, Oct. 49 (1990). 
^M. Uehera, P. Choi, T. Tomida, U. Tomizawa, S. Hirosawa, and Maehera, 
IEEE Trans. Magn. 31, 3632 (1995). 








JOURNAL OF APPLIED PHYSICS 


VOLUME 83, NUMBER 11 


1 JUNE 1998 


Coercivity of sintered Nd(Feo,92-xG3xBo.o8)5.5 permanent magnets 

X. C. Kou^> and F. R. de Boer 

Van der Waals-Zeeman Institute, University of Amsterdam, 1018 XE Amsterdam, The Netherlands 

H. Kronmuller 

Max-Planck Institut fur Metallforschung, Institut fur Physik, Heisenbergstrafie 1, 70569 Stuttgart, Germany 

The temperature dependence of the coercive field of Nd(Feo 92 -;cGa;rBo.o 8 ) 5.5 compounds with x 
= 0 and 0.01 has been measured from 10 K up to the Curie temperatures in fields applied parallel 
or perpendicular to the magnetic alignment direction and has been analyzed in terms of a 
micromagnetic model. Two temperature ranges in which different mechanisms control the 
coercivity can clearly be distinguished. At temperatures above 170 K, a nucleation process of 
reversed domains determines the coercivity mechanism. From the micromagnetism point of view, 
partial substitution of Fe by Ga into NdFeB magnets leads to a reduction of the local effective 
demagnetization field (-N^ffM^) which makes the nucleation of reversed domains more difficult, 
and therefore enhances the coercivity. © 1998 American Institute of Physics, 
[80021-8979(98)15311-2] 


Anisotropic NdFeB permanent magnets are mainly pro¬ 
duced by the sintering technique.^ The magnetic phase in 
NdFeB magnets is the tetragonal Nd 2 Fei 4 B phase which has 
exciting intrinsic magnetic properties. However, the coercive 
field realized in NdFeB magnets depends strongly on the 
microstructure. The main disadvantage of the NdFeB magnet 
is its large temperature coefficient of the coercivity. The way 
to reduce the temperature coefficient of a magnet is to in¬ 
crease either its coercive field or its Curie temperature. Par¬ 
tial substitution of Nd in NdFeB magnets by Tb and/or Dy 
results in a large enhancement of the coercive field. This is 
because of the huge uniaxial magnetic anisotropy of 
Tb 2 Fei 4 B or Dy 2 Fei 4 B. However, substitution of Tb and/or 
Dy leads to a drastic reduction of the saturation magnetiza¬ 
tion. On the other hand, the Curie temperature of NdFeB 
magnets can be drastically increased by partial substitution 
of Fe by Co, however, at a cost of the coercive field. Ga is 
the only nonmagnetic element which simultaneously raises 
the Curie temperature^ and the coercive field of NdFeB mag¬ 
nets. It is one of the main subjects of the present article to 
understand why the coercive field is enhanced in Ga- 
containing NdFeB magnets. In addition, the mechanism 
which controls the magnetization reversal process in NdFeB 
and Nd(Fe,Ga)B magnets will be studied with the main em¬ 
phasis on the comparison of the temperature dependence of 
the coercive field measured with the field applied parallel 
and perpendicular to the magnetic-alignment direction. 

Much effort was made to obtain magnets with a high 
degree of the grain alignment. A number of cylindrical 
samples with a diameter of 4 mm and a length of 6 mm 
were cut out from the bulk Nd(Feo. 92 Bo.o 8 ) 5.5 
Nd(Feo. 9 iGao.oiBo.o 8 ) 5.5 sintered magnets with the cylindrical 
axis parallel or perpendicular to the magnetic alignment di¬ 
rection. Magnetic hysteresis loops were measured from 10 to 
800 K in a vibrating-sample magnetometer equipped with a 


Author to whom correspondence should be addressed; electronic mail: 
kou@phys.uva.nl 


superconducting coil providing a maximum field strength of 
6.4 MA/m. The value of the coercive field is defined as 
the field where the irreversible susceptibility of the demag¬ 
netization curve has a maximum. According to this defini¬ 
tion, the coercive field corresponds to the field where most 
domains reverse their magnetization direction under the ac¬ 
tion of the applied inverse field. 

Figure 1 shows the magnetic hysteresis loops of 
Nd(Feo. 9 iGao.oiBo.o 8 ) 5.5 measured at 300 K in external fields 
applied parallel and perpendicular to the magnetic-alignment 
direction. The presence of a fairly good grain alignment fol¬ 
lows from the very pronounced difference of the magnetic 
hysteresis loops measured in the two directions. The hyster¬ 
esis loop in the parallel measurements is predominantly due 
to magnetization reversal of the grains which are magneti¬ 
cally aligned. However, the hysteresis loop in the perpen¬ 
dicular measurements is only due to the presence of grains 
which are misaligned. This is because the magnetic moments 
of the aligned grains will be rotated to the direction of the 
applied field only when the external field exceeds the anisot¬ 
ropy field, which is about 7 MA/m at 300 K for Nd 2 Fei 4 B. 
According to the micromagnetic model of coercivitythe 
presence of misaligned grains in permanent magnets leads to 
lowering coercivity. This is because the nucleation field is 
lower in misaligned single-domain particles. From the 
present measurement, however, it becomes evident that the 
coercive field is larger when the magnetic hysteresis loop is 
measured in a perpendicular field. This experimental fact 
suggests the coercivity in misaligned grains to be larger than 
in perfectly aligned grains. It must be noted that it is a com¬ 
mon feature of NdFeB sintered magnets that an improvement 
of the degree of grain alignment results in a reduction of the 
coe