Daniel D. Stancil Anil Prabhakar. Spin Waves. Theory and Applications

Transcription

1 Spin Waves

2 Daniel D. Stancil Anil Prabhakar Spin Waves Theory and Applications 123

3 Daniel D. Stancil Carnegie Mellon University Pittsburgh, PA USA Anil Prabhakar Indian Institute of Technology Chennai India ISBN e-isbn DOI / Library of Congress Control Number: c Springer Science+Business Media, LLC 2009 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. While the advice and information in this book are believed to be true and accurate at the date of going to press, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper springer.com

4 To Kathy and Namita

5 Preface The properties and physics of spin waves comprise an unusually rich area of research. Under the proper circumstances, these waves can exhibit either dispersive or non-dispersive propagation, isotropic or anisotropic propagation, non-reciprocity, inhomogeneous medium effects, random medium effects, frequency selective nonlinearities, soliton propagation, and chaos. This richness has also led to a number of proposed applications in microwave and optical signal processing, and spin wave phenomena are becoming increasingly important to understand the dynamics of thin-film magnetic recording heads. 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 understanding of the microscopic origins of magnetism and exchange-dominated spin waves, motivate the equation of motion for the macroscopic magnetization, and to construct appropriate susceptibility models to describe the linear responses of magnetic materials to magnetic fields. The second part, Chapters 5 8, focuses on magnetostatic modes and dipolar spin waves, their properties, 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 from Chapter 3 can be used with Maxwell s equations to describe electromagnetic and magneto-quasi-static waves in dispersive anisotropic media. 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 material presented in the text. To enhance the book s usefulness as a reference, 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 treatment of magnetostatic excitations contained in the earlier volume, Theory of VII

6 VIII Preface Magnetostatic Waves. Major additions include quantum mechanical treatments of angular momentum, exchange, and spin waves; nonlinear phenomena such as solitons and chaos; and applications such as the generation of spin 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. August 2008 Daniel D. Stancil Pittsburgh, USA Anil Prabhakar Chennai, India

7 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 Magnetostatic Waves, were improved considerably by comments and suggestions 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, autooscillations, and soliton formation; from discussions with M. Widom on quantum mechanics; and from comments and suggestions relating to spin-transfer torques from J. C. Slonczewski. Of course, the remaining errors and idiosyncrasies 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. AP thanks his wife, Namita, for her encouragement and her indulgence during 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

8 Contents 1 Introduction to Magnetism Magnetic Properties of Materials Diamagnetism Paramagnetism Ferromagnetism Ferrimagnetism and Antiferromagnetism SpinningTop Magnetism Equation of Motion Gyromagnetic Ratio Angular Momentum in Quantum Mechanics Basic Postulates of Quantum Mechanics Eigenvalue Equations Angular Momentum Addition of Angular Momenta Magnetic Moments of Atoms and Ions Construction of Ground States of Atoms and Ions ElementsImportanttoMagnetism Problems References Quantum Theory of Spin Waves Charged Particle in an Electromagnetic Field ZeemanEnergy LarmorPrecession Origins of Exchange: The Heisenberg Hamiltonian Spin Wave on a Linear Ferromagnetic Chain Harmonic Oscillator Harmonic Oscillator Eigenfunctions Raising and Lowering Operators XI

9 XII Contents 2.7 Magnons in a 3D Ferromagnet: Method of Holstein and Primakoff Magnon Dispersion Relation Magnon Interactions Problems References Magnetic Susceptibilities Diamagnetism Paramagnetism Weiss Theory of Ferromagnetism Néel Theory of Ferrimagnetism ExchangeField Uniform Magnetization Non-uniform Magnetization Magnetocrystalline Anisotropy Uniaxial Anisotropy Cubic Anisotropy Coordinate Transformations Polder Susceptibility Tensor Equation of Motion for the Magnetization Susceptibility Without Exchange or Anisotropy Susceptibility with Exchange and Anisotropy MagneticDamping Magnetic Switching Stoner Wohlfarth Particle Damped Precession Problems References Electromagnetic Waves in Anisotropic-Dispersive Media Maxwell s Equations Constitutive Relations Instantaneous Poynting Theorem Complex Poynting Theorem Energy Densities in Lossless Dispersive Media Wave Equations Polarization of the Electromagnetic Fields Group and Energy Velocities Plane Waves in a Magnetized Ferrite Propagation Parallel to the Applied Field Propagation Perpendicular to the Applied Field The Magnetostatic Approximation Problems References

10 Contents XIII 5 Magnetostatic Modes Walker s Equation SpinWaves UniformPrecessionModes Normally Magnetized Ferrite Film Tangentially Magnetized Ferrite Film Ferrite Sphere Normally Magnetized Film: Forward Volume Waves Tangentially Magnetized Film: Backward Volume Waves Tangentially Magnetized Film: Surface Waves Problems References Propagation Characteristics and Excitation of Dipolar Spin Waves Energy Velocities for Dipolar Spin Waves Propagation Loss Relaxation Time for Propagating Modes Surface Waves Volume Waves Summary of the Phenomenological Loss Theory Mode Orthogonality and Normalization Forward Volume Waves Backward Volume Waves Surface Waves Excitation of Dipolar Spin Waves Common Excitation Structures Forward Volume Waves Backward Volume Waves Surface Waves Discussion of Excitation Calculations Problems References Variational Formulation for Magnetostatic Modes General Problem Statement Calculus of Variations Formulation for One Independent Variable Extensions to Three Independent Variables Small-Signal Functional for Ferrites Interpretation of the Functional Stationary Formulas Stationary Formula Examples with Forward Volume Waves Large k-limit

11 XIV Contents Improved Approximation Effect of Medium Inhomogeneity FiniteElementAnalysis Problems References Optical-Spin Wave Interactions Symmetric Dielectric Waveguides TE Modes TM Modes Optical Mode Orthogonality and Normalization Magneto-Optical Interactions Can You Tell the Difference Between μ and ε? Definition of Magnetization at High Frequencies Symmetry Requirements on the Permittivity Coupled-Mode Theory Coupled-Mode Equations Energy Conservation Solutions to the Coupled-Mode Equations Scattering of Optical-Guided Modes by Forward Volume SpinWaves Coupled-Mode Equations Coupling Coefficients Tightly Bound Optical Mode Approximation Cotton Mouton Effect Anisotropic Bragg Diffraction Problems References Nonlinear Interactions Large-AmplitudeSpinWaves Foldover and Bistability Hamiltonian Equations of Motion Spin Wave Interactions Decay Instability H (2) Coefficients Nonlinear Schrödinger Equation Modulational Instability and Solitons Split-Step Fourier Method Anomalous Dispersion Other Aspects RoutestoChaos Center Manifold Theory Quantizing Low-Dimensional Chaos Problems References

12 Contents XV 10 Novel Applications Nano-Contact Spin-Wave Excitations Current-Induced Spin Torque Magnetic Precession Magnetic Precession in Patterned Structures Inverse Doppler Effect in Backward Volume Waves Problems References Appendix A: Properties of YIG References Appendix B: Currents in Quantum Mechanics B.1 Density of States B.2 Electric and Spin Current Densities B.3 Reflection and Transmission at a Boundary B.4 Tunneling Through a Barrier References Appendix C: Characteristics of Spin Wave Modes C.1 Constitutive Tensors C.1.1 Polder Susceptibility Tensor C.1.2 Permeability Tensor C.2 Uniform Precession Mode Frequencies C.3 Spin Wave Resonance Frequencies C.4 General Magnetostatic Field Relations C.5 ForwardVolumeSpinWaves C.6 BackwardVolumeSpinWaves C.7 SurfaceSpinWaves Appendix D: Mathematical Relations D.1 Trigonometric Identities D.2 Vector Identities and Definitions D.3 Fourier Transform Definitions Index...351