Spin Waves: Problems and Solutions

✍ Scribed by Daniel D. Stancil, Anil Prabhakar

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 252
• Category: Library

✦ Synopsis

This book presents a collection of problems in spin wave excitations with their detailed solutions. Each chapter briefly introduces the important concepts, encouraging the reader to further explore the physics of spin wave excitations and the engineering of spin wave devices by working through the accompanying problem sets. The initial chapters cover the fundamental aspects of magnetization, with its origins in quantum mechanics, followed by chapters on spin wave excitations, such as the magnetostatic approximation, Walker's equation, the spin wave manifold in the three different excitation geometries of forward volume, backward volume and surface waves, and the dispersion of spin waves. The latter chapters focus on the practical aspects of spin waves and spin wave optical devices and use the problem sets to introduce concepts such as variational analysis and coupled mode theory. Finally, for the more advanced reader, the book covers nonlinear interactions and topics such as spin wavequantization, spin torque excitations, and the inverse Doppler effect.

The topics range in difficulty from elementary to advanced. All problems are solved in detail and the reader is encouraged to develop an understanding of spin wave excitations and spin wave devices while also strengthening their mathematical, analytical, and numerical programming skills.

✦ Table of Contents

Preface
Acknowledgments
Contents
1 Introduction to Magnetism
1.1 Analogy of the Spinning Top
1.2 Angular Momentum in Quantum Mechanics
1.3 Hund's Rules
2 Quantum Theory of Spin Waves
2.1 Hamiltonians for Coupled Spins
2.2 Harmonic Oscillator
2.3 Raising and Lowering Operators
2.4 Bra-Ket Notation
2.5 Spin Raising and Lowering Operators
2.6 Spin Waves
3 Magnetic Susceptibilities
3.1 Types of Magnetic Materials
3.1.1 Diamagnetism
3.1.2 Paramagnetism
3.1.3 Ferromagnetism and Antiferromagnetism
3.1.4 Ferrimagnetism
3.2 Exchange Fields
3.3 Crystal Structures
3.3.1 Miller Indices
3.4 Magnetocrystalline Anisotropy
3.4.1 Coordinate Transformations
3.5 Equation of Motion for the Magnetization
3.6 Susceptibility Without Exchange or Anisotropy
3.7 Stoner–Wohlfarth Model
4 Electromagnetic Waves in Anisotropic Dispersive Media
4.1 Maxwell's Equations
4.2 Constitutive Relations
4.3 Time Averages and Energy Conservation
4.4 Plane Waves
5 Magnetostatic Modes
5.1 The Magnetostatic Approximation
5.2 Uniform Precession Modes
5.3 Dipolar Spin Waves
5.3.1 Forward Volume Waves
5.3.2 Backward Volume Waves
5.3.3 Surface Waves
5.4 Exchange-Dominated Spin Waves
6 Propagation Characteristics and Excitation of Dipolar Spin Waves
6.1 Relaxation Time
6.1.1 Surface Waves
6.1.2 Volume Waves
6.2 Mode Orthogonality and Normalization
6.3 Radiation Resistance
6.3.1 Volume Waves
6.3.2 Forward Volume Waves
6.3.3 Backward Volume Waves
6.3.4 Surface Waves
7 Variational Formulation for Magnetostatic Modes
7.1 Calculus of Variations
8 Optical-Spin Wave Interactions
8.1 Optical Guided Modes of a Dielectric Thin Film
8.1.1 Transverse Electric Modes
8.1.2 Transverse Magnetic Modes
8.2 Magnetic and Electric Susceptibilities
8.3 Coupled-Mode Theory
8.4 Magneto-optic Coupling
9 Nonlinear Interactions
9.1 Complex Spin Wave Amplitudes
9.2 Bogoliubov Transformation
9.3 Nonlinear Schrödinger Equation
10 Novel Applications
10.1 Spin Transfer Torque
10.2 Poynting Vector and Backward Waves
A Appendix
Index