Table Of ContentMagnetoacoustic Polarization
Phenomena in Solids
Springer Science+Business Media, LLC
V.V. Gudkov J.D. Gavenda
Magnetoacoustic Polarization
Phenomena in Solids
With 120 Figures
Springer
V.V. Gudkov J.D. Gavenda
Institute for Metal Physics Department of Physics
Ural Division of the Russian Academy University of Texas
of Sciences Austin, TX 78712
Yekaterinburg, 620219 USA
Russia
Library of Congress Cataloging-in-Publication Data
Gudkov, V.V.
Magnetoacoustic polarization phenomena in solids / V.V. Gudkov, J.D. Gavenda.
p. cm.
Includes bibliographical references and index.
ISBN 978-1-4612-7031-7 ISBN 978-1-4612-1168-6 (eBook)
DOI 10.1007/978-1-4612-1168-6
1. Acoustic magnetic resonance. 2. Polarization (Sound) I. Gavenda, J.D.,
1993- IL Tide
QC763 .G84 2000
538'.43—dc21 00-023806
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© 2000 Springer Science+Business Media New York
Originally published by Springer-Verlag New York, Inc. in 2000
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9 8 7 6 5 4 3 21
ISBN 978-1-4612-7031-7
To:
Janie Yeoman Gavenda
and
Alyosha Razletovskiy and Anya Gudkova
Preface
This book had its conception when Dr. Gudkov visited me in Austin in
the Fall of 1995 and urged me to join him in writing a review of the field
of magnetoacoustic polarization phenomena. I protested that, although my
students and I had done some early work on this topic, most of the later
work was done by researchers at the Institute for Metal Physics and by
other investigators in the former Soviet Union. He eventually persuaded me
that my initial contribution and general experience with magnetoacoustic
phenomena qualified me to serve as a co-author. When I considered the
fact that the extensive exploration of magnetoacoustic phenomena in the
former Soviet Union was relatively unknown to Western scientists, I agreed
to work with him on this project.
In order to make the material more accessible to nonspecialists, we have
adopted consistent notation throughout the text and redrawn the figures
from published papers in a consistent fashion.
Because our two institutions lie on opposite sides of the world, we needed
some financial support to bring the book to fruition. We are very grateful to
the Science Program for International Collaboration of the North Atlantic
Treaty Organization for financial support through Grant No. HTECH.CRG
951549.
I have dedicated this book to my wife, Janie, in recognition of the support
she has given me throughout my professional career.
J. D. Gavenda The University of Texas at Austin
viii Preface
I want to express my gratitude to all of the co-authors and colleagues
who have supported me during the more than 25 years devoted to the
investigation of magnetoacoustic polarization phenomena. In particular, I
appreciate the collaboration of my teacher, Dr. Kirill Borisovich Vlasov, the
theorist who developed the fundamentals of the phenomena; Dr. Albert
Mazgarovich Burkhanov, the most talented experimentalist I ever met;
and Dr. Anatoliy Bronislavovich Rinkevich, with whom the first and most
difficult part of the way was covered.
V. V. Gudkov Institute for Metal Physics
Contents
Preface vii
List of the Most Important Symbols Used in This Book xi
1 Introduction 1
1.1 The Role of Physical Acoustics in the Study of Solids 1
1.2 Magnetoacoustic Polarization Phenomena in Solids . 2
1.3 A Brief Historical Overview 5
1.4 Goals of the Present Work. . . . . . . . . . . . . . . 7
2 Experimental Techniques 11
2.1 General Equations . . . 11
2.2 The Faraday Effect . . . 14
2.3 The Cotton-Mouton Effect 16
2.3.1 The Phase-Amplitude Technique 17
2.3.2 The Amplitude Technique . 19
2.4 The Kerr Effect. . . . . . . . . . . . . . 21
3 Instrumentation 23
3.1 Setups for Phase-Amplitude Measurements 23
3.1.1 The Fixed-Frequency Bridge 24
3.1.2 Variable-Frequency Bridges 25
3.2 The Ultrasonic Field Visualizer . . . 31
x Contents
4~~ ~
4.1 The Classical Theory of Elasticity 33
4.2 Elastic, Magnetic, and Electric Variables . 35
4.3 Ferromagnets . . . . . . . . . . . . . . . . 37
4.3.1 Basics ofthe Phenomenological Theory of Ferromag-
netism . . . . . . . . . . . . . . . 37
4.3.2 Coupled Elastic and Spin Waves . . . . . . . . . 39
4.4 Nonmagnetic Metals . . . . . . . . . . . . . . . . . . . . 48
4.4.1 Fundamentals of the Electron Theory of Metals. 48
4.4.2 Electromagnetic Waves .............. 53
4.4.3 Coupled Electromagnetic and Elastic Waves. . . 56
4.5 Bulk Phenomena: The Faraday and Cotton-Mouton Effects 64
4.5.1 Weak Coupling . 64
4.5.2 Strong Coupling . . . . . . . . . . . . . . . . . . .. 66
4.6 The Kerr Effect. . . . . . . . . . . . . . . . . . . . . . . .. 67
4.6.1 Relations Among the Characteristic Parameters of
Incident, Reflected, and Transmitted Elastic Waves. 67
4.6.2 Shear Elastic Waves Incident on the Interface be
tween Dielectric and Ferromagnetic Media. . . . .. 71
4.6.3 Shear Elastic Waves Incident on the Interface be-
tween Dielectric and Metallic Media 80
4.7 The Faraday Effect in a Plate . . . . . . . . . . . . . . . .. 87
5 Experiments in Magnetic Materials 91
5.1 The Faraday Effect. . . . . 91
5.2 The Cotton-Mouton Effect 97
5.3 The Kerr Effect. . . . . . . 104
6 Experiments in Nonmagnetic Metals 109
6.1 The Faraday Effect: Doppler-Shifted Cyclotron Resonance 109
6.1.1 Anomalous Sound Propagation . 124
6.2 Magnetoacoustic Geometric Oscillations 128
6.3 Doppleron-Phonon Resonance. 137
6.4 Helicon-Phonon Resonance . 165
6.5 Giant Geometric Oscillations . 175
6.6 Quantum Oscillations ..... 179
6.7 The Cotton-Mouton Effect in the Classical High-Field Limit 191
References 193
Index 206
List of the Most Important Symbols
U sed in This Book
B magnetic induction
b magnetoacoustic constants, Sec. 4.3.2
i
C speed of light in vacuum
elastic coefficients (moduli), Sec. 4.1
Cijkl
D electric induction
Dmn transmission coefficients (m, n designate types of transmitted
and incident waves, respectively), Eq. (4.134)
e electron charge, Sec. 4.4.1
E electric field
e
electron energy, Sec. 4.4.1
eF
fermi energy, Sec. 4.4.1
unit vector along the i axis, Sec. 2.1
unit vectors defining the polarization of generating and receiving
piezo-electric transducers, respectively, Sec. 2.1
F body force per unit volume, Sec. 4.1
F(q) normalized nonlocal conductivity, Sec. 4.4.3
f frequency in Hz;
distribution function for conduction electrons, Sec. 4.4.1
group velocity of an electromagnetic wave, Sec. 4.4.2
magnetic field
effective field of anisotropy, Sec. 4.3.1
demagnetization field, Eq. (4.22)
effective magnetic field, Eq. (4.24)
internal magnetic field, Sec. 4.3.1
Kjeldaas field, Eq. (4.86)
