Table Of ContentM.S Sodha · N.C. Srivastava
Microwave
Propagation in
Ferrimagnetics
Microwave
ProP.agation _in
Fernmagnet1cs
Microwave
Prop_agation _in
FerrJmagnetJcs
M. S. Sodha andN. C. Srivastava
Indian Institute of·Technology
New Oelhi, lndia
SPRINGER SCIENCE+BUSINESS MEDIA, LLC
Library of Congress Cataloging in Publication Data
Main entry under title:
Microwave propagation in ferrimagnetics.
Bibliography: p.
Includes index.
I. Ferrites (Magnetic materials) 2. Microwaves. 3. Ferrimagnetism. I. Sodha, M. S.,
1932- . Il. Srivastava, N. C.
QC766.F3M5 538' .45 81-15364
ISBN 978-1-4757-5841-2 ISBN 978-1-4757-5839-9 (eBook) AACR2
DOI 10.1007/978-1-4757-5839-9
© 1981 Springer Science+Business Media New York
Originally published by Plenum Press, New York in 1981
All rights reserved
No part of this book may be reproduced, stored in a retrieval system, or transmitted
in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording, or otherwise, without written permission from the Publisher
Preface
During the last three decades, interest in the field of interaction of
microwaves with ferrimagnetics has steadily increased. Investigations in
tlris field have led to the development of a number of devices used for a
variety of applications. The initial emphasis of the investigators was on the
microwave behavior of ferrimagnetics placed in cavities and metallic
waveguides and associated devices. This work has been presented in
various books, monographs, and reviews written during the sixties. In
recent years, interest in microwave propagation in ferrimagnetics has
shifted from loaded waveguides to relatively new areas, e.g., magnetostatic
and magnetoelastic waves in layered structures, microwave propagation in
ferrimagnetic strip lines and microstrips, etc. Such investigations are
important from the viewpoint of devices such as delay lines, filters,
convolvers, guided wave amplifiers, striplines, and microstrip phase shif
ters, circulators, edge guided mode isolators, etc. As such, we feit the need
for a text (meant for graduate students starting work in these areas as weil
as practicing electrical engineers and applied physicists) which presents a
coherent account of the various aspects of propagation of microwaves
(electromagnetic as weil as magnetoelastic) in biased ferrimagnetics and
discusses the relatively recent developments in the theory and operation of
the aforementioned devices, and this book is the result.
A biased ferrimagnetic is, in the mathematical sense, a complicated
medium, electromagnetically as weil as elastically. Hence, the mathema
tical nature of the presentation is unavoidable but sufficient details are
given in the derivation of important results. Although the reader is
assumed to have a basic knowledge of electromagnetic theory, elastic field
theory, and solid state magnetism, seven appendices on the structure and
properties of common ferrimagnetics, the magnetic moments of atoms and
ions, coordinate transformation, elastic field theory, precessional mode
frequency of ellipsoids, Poynting's theorem and partially magnetized
ferrimagnetics have been included to make the book self-contained.
V
vi Preface
Chapters 1 to 3 present the basic concepts of electromagnetic and
magnetoelastic wave propagation in biased ferrif!Iagnetics. The response of
a ferrimagnetic to external electromagnetic and elastic fields is discussed in
Chapter 1. The permeability tensor has been obtained for magnetically
saturated ferrimagnetic, considering the various interactions present in a
real ferrimagnetic. The coupled magnetoelastic equations have also been
developed. Chapter 2 discusses electromagnetic and magnetoelastic plane
wave propagation in ferrimagnetics. Chapter 3 presents an analysis of
electromagnetic and magnetoelastic wave propagation across plane inter
faces; these studies provide a physical insight into the relevant phenomena
and serve as a background for the appreciation of more complex wave
propagation phenomena in ferrimagnetics (which is of practical impor
tance). In Chapter 4 we discuss the propagation oi magnetostatic waves in
layered planar structures; the analysis and experimental results pertaining
to a number of practical configurations are presented. The applications to
delay lines, filters, convolvers, and magnetostatic wave amplifiers are also
discussed. Chapter 5 considers magnetoelastic guided wave propagation in
layered planar structures and its applications. Gaussian units have been
used throughout the book.
We wish to thank our colleague Prof. A.K. Ghatak for providing the
inspiration to write this book. We are also grateful to Dr. I. Rattan for a
critical review of the manuscript, to Mr. S. S. Gupta and Mr. S. N. Bajpai
for helpful discussions, and to Mr. T. N. Gupta for his kind and ungrudging
assistance in the preparation of the manuscript. The financial support of
NSF (USA) for the original work reported in this book is gratefully
acknowledged.
Delhi M. S. Sodha
June 1981 N. C. Srivastava•
Contents
Notation ............ . xiii
Chapter 1. lntroduction.
1.1. Ferrimagnetics ............. .
1.2. Magnetic Dipole and Magnetization . 2
1.3. A Dipole in a Magnetic Field . 4
1.4. The Permeability Tensor .. . 8
1.5. Damping ............ . 10
1.6. Exchange Interaction . . . . . 18
1.7. Magnetocrystalline Anisotropy .. 22
1.7.1. Cubic Ferrimagnetics .......... . 24
1.7.2. Hexagonal Magnetopiumbites ... . 30
1.7.2.1. Uniaxial Magnetoplumbite .. . 30
1.7.2.2. Planar Magnetoplumbite ... . 31
1.8. Dipole-Dipole Interaction: Demagnetization. 33
1.9. Magnetoelastic Interaction ............ . 44
Chapter 2. Plane Waves in Ferrimagnetics 47
PART A. ELECTROMAGNETIC WAVES 47
2.1. Electromagnetic Field Equations . . . . . . . . . . . 47
2.2. Exchange-Free Plane Waves. . . . . . . . . . . . . . 50
2.2.1. The Propagation Constant . . . . . . . . . . . 50
2.2.2. Special Cases . . . . . . . . . . . . . . . . . . . . . . . . . . 52
2.2.2.1. Lossless Isotropie Ferrimagnetics . . . . . . . . . . 52
2.2.2.2. Lossless Hexagonal Planar Magnetopiumbites . . 61
2.2.3. Lossless Ferrimagnetics: The General Case . . . . . . . . 63
2.2.3.1. Mode Classification . . . . . . . . . . . . . . 63
2.2.3.2. Propagating and Nonpropagating Regions 64
2.2.4. Effect of Damping. . . . . . . . . . . . . . . . . . . . 67
2.2.5. Comparison with Waves in Magnetoplasmas. . . . 70
2.3. The Magnetostatic Approximation . . . . 71
2.4. Exchange-Dominated Plane Waves . . . . . . . . . . . . . . . . . 74
vii
viii Contents
PART B. MAGNETOELASTIC WAVES. 79
2.5. Magnetoelastic Field Equations .. 79
2.6. Exchange-Free Plane Waves .. 80
2.6.1. The Dispersion Relation 81
2.6.2. Special Cases ...... . 83
2.6.3. General Case ...... . 86
2.6.3.1. Dispersion Curves 86
2.6.3.2. Refractive Index Diagrams . 88
2.6.3.3. Polarization of Modes . 91
2.7. Effect of Exchange .. 93
2.8. Effect of Anisotropy . . . . . . . . . . . 95
Chapter 3. Wave Propagation Across Interfaces .... ....... 97
PART A. ELECTROMAGNETIC WA VE PROPAGATION. 97
3.1. Ferrimagnetic Half Space .............. . 97
3.1.1. Reflection and Transmission Coefficients . 98
3.1.2. Regions of Ordinary and Total Reftection 100
3.1.3. Phase Shift in Total Reflection ...... . 105
3.1.4. Reflection from Lossy Ferrimagnetics .. . 111
3.1.5. Energy Flow in Total Reflection: Lateral Shift 115
3.1.6. Ray Model for Attenuated Total Reflection . 122
3.2. Ferrimagnetic Slab ............ . 127
PART B. MAGNETOELASTIC W A VES . 133
3.3. Half Space Problem ............... . 133
Chapter 4. MagnetostaUe Waves in Layered Planar Structures 143
4.1. Ferrimagnetic Half Space. . . . . 144
4.1.1. Transverse Magnetization . 145
4.1.2. Arbitrary Magnetization . 150
4.1.3. Experimental Results. . . . 155
4.2. Isotropie Ferrimagnetic Slab . . . 160
4.2.1. Magnetization in the Slab Plane. 160
4.2.1.1. Transverse Propagation: Magnetostatic Analysis . 161
4.2.1.2. Transverse Propagation: Electromagnetic Analysis. 167
4.2.1.3. General Magnetostatic Analysis . . . . . 170
4.2.1.4. Experimental Results and Applications 174
4.2.2. Normal Magnetization . . . . . . . . . . . . . . . 180
4.2.2.1. Magnetostatic Field Analysis . . . . . . 181
4.2.2.2. Energy Distribution and Power Flow. 184
4.2.2.3. Zig-Zag Ray Model . . . . . . . . . . . 187
Contents ix
4.3. Metai-Backed Ferrimagnetic Slab ..................... . 194
4.3.1. Magnetization in Slab Plane .................... . 194
4.3.1.1. Transverse Propagation: Magnetostatic Analysis . . 195
4.3.1.2. Transverse Propagation: Electromagnetic Analysis .. 197
4.3.1.3. Arbitrary Propagation: Magnetostatic Analysis .... . 201
4.3.1.4. Effect of Finite Conductivity of Meta!. .... . 203
4.3.1.5. Experimental Results. . . . . . . . . ....... . 206
4.3.2. Normal Magnetization ............... . 208
4.4. Ferrimagnetic-Dielectric-Metal Structure ...... . 209
4.4.1. Transverse Magnetization in the Film Plane .. 211
4.4.2. Normal Magnetization .................... . 221
4.4.2.1. Dispersion Characteristics . 221
4.4.2.2. Energy and Power . . . 223
4.4.3. Arbitrary Magnetization ......... . 227
4.5. Metai-Ferrimagnetic-Metal Structure .. 235
4.5.1. Transverse Magnetization ... . 235
4.5.2. Normal Magnetization ...... . 240
4.6. Double Magnetic Layered Structures . 242
4.6.1. Air Gap Between Two Ferrimagnetic Substrates .. 242
4.6.2. Ferrimagnetic Layer Over Another Ferrimagnetic Substrate .. 246
4.7. Periodic Structures ............. . 248
4.8. Effect of Magnetocrystalline Anisotropy .............. . 252
4.8.1. YIG .................................... . 256
4.8.2. Zn Y Planar Magnetoplumbite .... : ............... . 262
2
4.9. Interaction of Magnetic Waves with Drifting Carriers. 266
4.9.1. Physical Explanation of Amplification ....... . 266
4. 9 .2. Air-Ferrimagnetic-Semiconductor Composite. . . . . . . . . . . 267
4.9.3. Metal-Dielectric-Semiconductor-YIG Structure ......... . 273
4.10. Magnetostatic Wave Oscillators .... 278
4.11. Transduction of Magnetostatic Waves ........ . 281
Chapter 5. Magnetoelastic Waves in Layered Planar Structures. 291
5.1. Transverse Magnetization ....................... . 292
5.1.1. Ferrimagnetic Half Space ................. . 292
5.1.2. Nonmagnetic Layer Over Ferrimagnetic Substrate . 297
5.1.3. Ferrimagnetic Slab ................. . 303
5.1.4. Ferrimagnetic Layered Nonmagnetic Substrate. 304
5.2. Longitudinal Magnetization. . . . . . . . . . . . . . . . . 308
5.2.1. The Dispersion Relation ............. . 308
5.2.2. Numerical Solution of the Dispersion Relation . 312
5.2.3. Energy Loss for Leaky Waves 316
5.2.4. Effect of Magnetic Loss ....................... . 319
5.2.5. Other Studies .............................. . 319
5.3. Normal Magnetization ............................. . 321
5.3.1. The Dispersion Equation ............. ·. ......... . 321
5.3.2. Dispersion Characteristics ...•. - .. - .............. . 323
x Contents
5.4. Experimental Results and Devices . . . . . . . . . . . . . . . 325
5.4.1. Excitation and Propagation Loss . . . . . . . . . . . . 325
5.4.2. Magnetoelastic Surface Wave Delay . . . 326
5.4.3. Magnetoelastic Surface Wave Isolator . . . . . . . . . . . . . . . 328
5.4.4. Magnetoelastic Surface Wave Oscillator. . . . . . . . . . . . . . . 328
5.4.5. Magnetoelastic Surface Wave Convolution . . . . . . . . . 331
5.4.6. Other Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335
Appendix A. Structure and Properfies of Common Ferrimagnetics 337
Al. Ferrimagnetic Gamet. 337
A.l.l. Structure .... 337
A.1.2. Magnetization . 338
A.l.2.1. Pure Gamet. 338
A.1.2.2. Mixed Gamets 340
A.1.2.3. Substituted Gamets 340
A.1.3. Magnetocrystalline Anisotropy. 341
A.1.4. Linewidth . . . . . 341
A.1.5. Other Properties 341
A.2. Spine! Ferrites ..... . 341
A.2.1. Crystal Structure 341
A.2.2. Magnetization . . 342
A.2.3. Magnetocrystalline Anisotropy . 343
A.2.4. Linewidth ........ . 343
A.3. Hexagonal Magnetopiumbites. 343
A.3.1. M-Type . 343
A.3.2. W-Type. 344
A.3.3. Y-Type . 344
A.3.4. Z-Type . 344
A.3.5. U-Type . 345
Appendix B. Magnetic Moment of Atoms and Ions . . . . . . . . 347
Appendix C. Coordinate Transformations. . . . . . . . . . . . 353
C.l. Eulerian Angles and Rotation Matrices 353
C.2. Transformation of Maxwell's Equations 357
C.3. The Transformed Permeability Tensor . 359
CA. Transformation of Anisotropy Fie!d. . . 360
C.5. Transformation of Magnetoelastic Interaction Energy. 361
Appendix D. Basic Elastic Wave Theory 363
D.l. Strain 363
D.2. Stress 365
