Theory of Magnetostatic Waves

Magnetic materials can support propagating waves of magnetization; since these are oscillations in the magnetostatic properties of the material, they are called magnetostatic waves (sometimes "magnons" or "magnetic polarons"). Under the proper circumstances these waves can exhibit, for example, either dispersive or nondispersive, isotropic or anisotropic propagation, nonreciprocity, frequency-selective nonlinearities, soliton propagation, and chaotic behavior. This rich variety of behavior has led to a number of proposed applications in microwave and optical signal processing. This textbook begins by discussing the basic physics of magnetism in magnetic insulators and the propagation of electromagnetic waves in anisotropic dispersive media. It then treats magnetostatic modes, describing how the modes are excited, how they propagate, and how they interact with light. There are problems at the end of each chapter; many of these serve to expand or explain the material in the text. To enhance the book's usefulness as a reference, the answers are given for many of the problems. The bibliographies for each chapter give an entry to the research literature. Magnetostatic Waves will thus serve not only as an introduction to an active area of research, but also as a handy reference for workers in the field.

Table of Contents:
1. Introduction to Magnetism.- 1.1. Magnetic Properties of Materials.- 1.1.1. Diamagnetism.- 1.1.2. Paramagnetism.- 1.1.3. Ferromagnetism.- 1.1.4. Ferrimagnetism and Antiferromagnetism.- 1.2. Spinning Top.- 1.3. Magnetism.- 1.3.1. Equation of Motion.- 1.3.2. Gyromagnetic Ratio.- 1.4. Magnetic Moments of Atoms and Ions.- 1.4.1. Angular Momentum in Quantum Mechanics.- 1.4.2. Construction of Ground States of Atoms and Ions.- 1.5. Elements Important to Magnetism.- Problems.- 2. Magnetic Susceptibilities.- 2.1. Diamagnetism.- 2.2. Paramagnetism.- 2.3. Weiss Theory of Ferromagnetism.- 2.4. Neel Theory of Ferrimagnetism.- 2.5. Exchange Interaction.- 2.5.1. Uniform Magnetization.- 2.5.2. Nonuniform Magnetization.- 2.6. Magnetocrystalline Anisotropy.- 2.6.1. Uniaxial Anisotropy.- 2.6.2. Cubic Anisotropy.- 2.6.3. Coordinate Transformations.- 2.7. Polder Susceptibility Tensor.- 2.7.1. Equation of Motion for the Magnetization.- 2.7.2. Susceptibility Without Exchange or Anisotropy.- 2.7.3. Susceptibility with Exchange and Anisotropy.- 2.8. Magnetic Damping.- Problems.- 3. Electromagnetic Waves in Anisotropic Dispersive Media.- 3.1. Maxwell's Equations.- 3.2. Constitutive Relations.- 3.3. Instantaneous Poynting Theorem.- 3.4. Complex Poynting Theorem.- 3.5. Energy Densities in Lossless Dispersive Media.- 3.6. Wave Equations.- 3.7. Polarization of the Electromagnetic Fields.- 3.8. Group and Energy Velocities.- 3.9. Plane Waves in a Magnetized Ferrite.- 3.9.1. Propagation Parallel to the Applied Field.- 3.9.2. Propagation Perpendicular to the Applied Field.- 3.10. The Magnetostatic Approximation.- Problems.- 4. Magnetostatic Modes.- 4.1. Walker's Equation.- 4.2. Spin Waves.- 4.3. Uniform Precession Modes.- 4.3.1. Normally Magnetized Ferrite Film.- 4.3.2. Tangentially Magnetized Ferrite Film.- 4.3.3. Ferrite Sphere.- 4.4. Normally Magnetized Film: Forward Volume Waves.- 4.5. Tangentially Magnetized Film: Backward Volume Waves.- 4.6. Tangentially Magnetized Film: Surface Waves.- Problems.- 5. Propagation Characteristics and Excitation of Magnetostatic Waves.- 5.1. Energy Velocities for Magnetostatic Waves.- 5.2. Propagation Loss.- 5.2.1. Relaxation Time for Propagating Modes.- 5.2.2. Surface Waves.- 5.2.3. Volume Waves.- 5.2.4. Summary of the Phenomenological Loss Theory.- 5.3. Mode Orthogonality and Normalization.- 5.3.1. Forward Volume Waves.- 5.3.2. Backward Volume Waves.- 5.3.3. Surface Waves.- 5.4. Excitation of Magnetostatic Waves.- 5.4.1. Common Excitation Structures.- 5.4.2. Forward Volume Waves.- 5.4.3. Backward Volume Waves.- 5.4.4. Surface Waves.- 5.4.5. Discussion of Excitation Calculations.- Problems.- 6. Variational Formulation for Magnetostatic Modes.- 6.1. General Problem Statement.- 6.2. Calculus of Variations.- 6.2.1. Formulation for One Independent Variable.- 6.2.2. Extensions to Three Independent Variables.- 6.3. Small-Signal Functional for Ferrites.- 6.4. Interpretation of the Functional.- 6.5. Stationary Formulas.- 6.6. Stationary Formula Examples with Forward Volume Waves.- 6.6.1. Large k Limit.- 6.6.2. Improved Approximation.- 6.6.3. Effect of Medium Inhomogeneity.- Problems.- 7. Optical-Magnetostatic Wave Interactions.- 7.1. Symmetric Dielectric Waveguides.- 7.1.1. TE Modes.- 7.1.2. TM Modes.- 7.1.3. Optical Mode Orthogonality and Normalization.- 7.2. Magneto-Optical Interactions.- 7.2.1. Can You Tell the Difference Between$$ \bar \mu $$ and $$ \bar \varepsilon $$?.- 7.2.2. Definition of Magnetization at High Frequencies.- 7.2.3. Symmetry Requirements on the Permittivity.- 7.3. Coupled-Mode Theory.- 7.3.1. Coupled-Mode Equations.- 7.3.2. Energy Conservation.- 7.3.3. Solutions to the Coupled-Mode Equations.- 7.4. Scattering of Optical Guided Modes by Magnetostatic Waves.- 7.4.1. Coupled-Mode Equations.- 7.4.2. Coupling Coefficients.- 7.4.3. Tightly Bound Optical Mode Approximation.- 7.5. Anisotropic Bragg Diffraction.- Problems.- Appendix: Properties of Yttrium Iron Garnet.