Spin waves: theory and applications

348 Pages·2009·2.09 MB·English

by  Anil Prabhakar

Spin Waves
·
Daniel D. Stancil Anil Prabhakar
Spin Waves
Theory and Applications
123
Daniel D. Stancil Anil Prabhakar
Carnegie Mellon University Indian Institute of Technology
Pittsburgh, PA Chennai
USA India
[email protected] [email protected]
ISBN 978-0-387-77864-8 e-ISBN 978-0-387-77865-5
DOI 10.1007/978-0-387-77865-5
LibraryofCongressControlNumber:2008936559
(cid:2)c SpringerScience+BusinessMedia,LLC2009
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To Kathy and Namita
Preface
The properties and physics of spin waves comprise an unusually rich area of
research. Under the proper circumstances, these waves can exhibit either dis-
persive or non-dispersive propagation, isotropic or anisotropic propagation,
non-reciprocity, inhomogeneous medium effects, random medium effects, fre-
quency selective nonlinearities, soliton propagation, and chaos. This richness
has also led to a number of proposed applications in microwave and opti-
cal signal processing, and spin wave phenomena are becoming increasingly
importanttounderstandthedynamicsofthin-filmmagneticrecordingheads.
The book can be divided into three major parts. The first is comprised
of Chapters 1–3 and is concerned with the physics of magnetism in magnetic
insulators. The principal goals of these chapters are to provide a basic un-
derstandingofthemicroscopicoriginsofmagnetismandexchange-dominated
spin waves, motivate the equation of motion for the macroscopic magnetiza-
tion,andtoconstructappropriatesusceptibilitymodelstodescribethelinear
responsesofmagneticmaterialstomagneticfields.Thesecondpart,Chapters
5–8,focusesonmagnetostaticmodesanddipolarspinwaves,theirproperties,
how to excite them, and how they interact with light. Chapter 4 serves as a
bridge between these two parts by discussing how the susceptibility models
fromChapter3canbeusedwithMaxwell’sequationstodescribeelectromag-
neticandmagneto-quasi-staticwavesindispersiveanisotropicmedia.Finally,
Chapters 9 and 10 treat nonlinear phenomena and advanced applications of
spin wave excitations.
The problems at the end of each chapter are often used to expand the
materialpresentedinthetext.Toenhancethebook’susefulnessasareference,
many of these problems are “show that” problems with the answer given. For
example, although the text discussion of dipolar spin waves in Chapter 5 is
limited to an isolated film without a ground plane, the dispersion relations in
the presence of a ground plane are given in the problems at the end of the
chapter.
The book represents a major expansion of the classical, linear treat-
ment of magnetostatic excitations contained in the earlier volume, Theory of
VII
VIII Preface
Magnetostatic Waves. Major additions include quantum mechanical treat-
ments of angular momentum, exchange, and spin waves; nonlinear phenom-
enasuchassolitonsandchaos;andapplicationssuchasthegenerationofspin
waves using current-induced spin torques.
This book has been fun to write. We hope you find it to be an interesting
and useful introduction to spin waves and their applications.
Daniel D. Stancil
Pittsburgh, USA
Anil Prabhakar
Chennai, India
August 2008
Acknowledgments
We are indebted to a number of people for helpful discussions and comments
on portions of this book.
The accuracy and readability of the earlier work, Theory of Magneto-
static Waves,wereimproved considerably bycomments andsuggestions from
N. Bilaniuk, N. E. Buris, S. H. Charap, D. J. Halchin, J. F. Kauffman,
T. D. Poston, A. Renema, S. D. Silliman, M. B. Steer, and F. J. Tischer. In
addition, the present volume benefited from our interactions with
C. E. Patton, P. E. Wigen, and A. N. Slavin on nonlinear excitations, auto-
oscillations,andsolitonformation;fromdiscussionswithM.Widomonquan-
tum mechanics; and from comments and suggestions relating to spin-transfer
torques from J. C. Slonczewski. Of course, the remaining errors and idiosyn-
crasies are ours.
One of us (DDS) would particularly like to thank his mentor, colleague,
and friend, Prof. F. R. Morgenthaler, for teaching him much of the material
in this book. He is also grateful to Kathy for her love, support, and patience.
APthankshiswife,Namita,forherencouragementandherindulgenceduring
the many stages of this manuscript. He is also grateful for assistance from
IIT-Madras under the Golden Jubilee Book Writing Scheme.
Finally, it has been a pleasure to work with A. Greene, K. Stanne, and
their capable team at Springer US.
IX
Contents
1 Introduction to Magnetism ................................ 1
1.1 Magnetic Properties of Materials .......................... 1
1.1.1 Diamagnetism .................................... 3
1.1.2 Paramagnetism ................................... 3
1.1.3 Ferromagnetism................................... 3
1.1.4 Ferrimagnetism and Antiferromagnetism ............. 4
1.2 Spinning Top ........................................... 5
1.3 Magnetism ............................................. 8
1.3.1 Equation of Motion................................ 8
1.3.2 Gyromagnetic Ratio ............................... 10
1.4 Angular Momentum in Quantum Mechanics ................ 12
1.4.1 Basic Postulates of Quantum Mechanics.............. 13
1.4.2 Eigenvalue Equations .............................. 14
1.4.3 Angular Momentum ............................... 14
1.4.4 Addition of Angular Momenta ...................... 20
1.5 Magnetic Moments of Atoms and Ions ..................... 23
1.5.1 Construction of Ground States of Atoms and Ions ..... 23
1.6 Elements Important to Magnetism......................... 28
Problems ................................................... 28
References .................................................. 31
2 Quantum Theory of Spin Waves ........................... 33
2.1 Charged Particle in an Electromagnetic Field ............... 33
2.2 Zeeman Energy ......................................... 36
2.3 Larmor Precession....................................... 38
2.4 Origins of Exchange: The Heisenberg Hamiltonian ........... 39
2.5 Spin Wave on a Linear Ferromagnetic Chain ................ 46
2.6 Harmonic Oscillator ..................................... 50
2.6.1 Harmonic Oscillator Eigenfunctions.................. 50
2.6.2 Raising and Lowering Operators..................... 52
XI
XII Contents
2.7 Magnons in a 3D Ferromagnet: Method of Holstein
and Primakoff........................................... 55
2.7.1 Magnon Dispersion Relation ........................ 55
2.7.2 Magnon Interactions............................... 60
Problems ................................................... 64
References .................................................. 65
3 Magnetic Susceptibilities .................................. 67
3.1 Diamagnetism .......................................... 67
3.2 Paramagnetism ......................................... 70
3.3 Weiss Theory of Ferromagnetism .......................... 73
3.4 N´eel Theory of Ferrimagnetism............................ 76
3.5 Exchange Field.......................................... 81
3.5.1 Uniform Magnetization............................. 82
3.5.2 Non-uniform Magnetization......................... 83
3.6 Magnetocrystalline Anisotropy ............................ 84
3.6.1 Uniaxial Anisotropy ............................... 84
3.6.2 Cubic Anisotropy ................................. 86
3.6.3 Coordinate Transformations ........................ 87
3.7 Polder Susceptibility Tensor .............................. 91
3.7.1 Equation of Motion for the Magnetization ............ 91
3.7.2 Susceptibility Without Exchange or Anisotropy ....... 91
3.7.3 Susceptibility with Exchange and Anisotropy ......... 93
3.8 Magnetic Damping ...................................... 94
3.9 Magnetic Switching......................................102
3.9.1 Stoner–Wohlfarth Particle ..........................102
3.9.2 Damped Precession................................104
Problems ...................................................106
References ..................................................108
4 Electromagnetic Waves in Anisotropic-Dispersive Media...111
4.1 Maxwell’s Equations .....................................111
4.2 Constitutive Relations ...................................112
4.3 Instantaneous Poynting Theorem ..........................114
4.4 Complex Poynting Theorem ..............................116
4.5 Energy Densities in Lossless Dispersive Media...............117
4.6 Wave Equations.........................................119
4.7 Polarization of the Electromagnetic Fields ..................122
4.8 Group and Energy Velocities..............................124
4.9 Plane Waves in a Magnetized Ferrite.......................127
4.9.1 Propagation Parallel to the Applied Field ............128
4.9.2 Propagation Perpendicular to the Applied Field .......130
4.10 The Magnetostatic Approximation.........................132
Problems ...................................................134
References ..................................................137