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Spin Waves |
2 |
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Preface |
6 |
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Acknowledgments |
8 |
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Contents |
9 |
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Introduction to Magnetism |
14 |
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Magnetic Properties of Materials |
14 |
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Diamagnetism |
16 |
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Paramagnetism |
16 |
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Ferromagnetism |
16 |
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Ferrimagnetism and Antiferromagnetism |
17 |
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Spinning Top |
18 |
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Magnetism |
21 |
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Equation of Motion |
21 |
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Gyromagnetic Ratio |
23 |
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Angular Momentum in Quantum Mechanics |
25 |
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Basic Postulates of Quantum Mechanics |
26 |
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Eigenvalue Equations |
27 |
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Angular Momentum |
27 |
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Addition of Angular Momenta |
33 |
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Magnetic Moments of Atoms and Ions |
36 |
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Construction of Ground States of Atoms and Ions |
36 |
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Elements Important to Magnetism |
41 |
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Problems |
41 |
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References |
44 |
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Quantum Theory of Spin Waves |
45 |
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Charged Particle in an Electromagnetic Field |
45 |
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Zeeman Energy |
48 |
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Larmor Precession |
50 |
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Origins of Exchange: The Heisenberg Hamiltonian |
51 |
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Spin Wave on a Linear Ferromagnetic Chain |
58 |
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Harmonic Oscillator |
62 |
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Harmonic Oscillator Eigenfunctions |
62 |
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Raising and Lowering Operators |
64 |
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Magnons in a 3D Ferromagnet: Method of Holstein and Primakoff |
67 |
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Magnon Dispersion Relation |
67 |
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Magnon Interactions |
72 |
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Problems |
76 |
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References |
77 |
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Magnetic Susceptibilities |
79 |
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Diamagnetism |
79 |
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Paramagnetism |
82 |
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Weiss Theory of Ferromagnetism |
85 |
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Néel Theory of Ferrimagnetism |
88 |
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Exchange Field |
93 |
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Uniform Magnetization |
94 |
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Non-uniform Magnetization |
95 |
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Magnetocrystalline Anisotropy |
96 |
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Uniaxial Anisotropy |
96 |
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Cubic Anisotropy |
98 |
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Coordinate Transformations |
99 |
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Polder Susceptibility Tensor |
103 |
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Equation of Motion for the Magnetization |
103 |
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Susceptibility Without Exchange or Anisotropy |
103 |
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Susceptibility with Exchange and Anisotropy |
105 |
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Magnetic Damping |
106 |
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Magnetic Switching |
114 |
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Stoner--Wohlfarth Particle |
114 |
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Damped Precession |
116 |
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Problems |
118 |
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References |
120 |
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Electromagnetic Waves in Anisotropic-Dispersive Media |
123 |
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Maxwell's Equations |
123 |
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Constitutive Relations |
124 |
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Instantaneous Poynting Theorem |
126 |
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Complex Poynting Theorem |
128 |
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Energy Densities in Lossless Dispersive Media |
129 |
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Wave Equations |
131 |
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Polarization of the Electromagnetic Fields |
134 |
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Group and Energy Velocities |
136 |
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Plane Waves in a Magnetized Ferrite |
139 |
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Propagation Parallel to the Applied Field |
140 |
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Propagation Perpendicular to the Applied Field |
142 |
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The Magnetostatic Approximation |
144 |
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Problems |
146 |
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References |
149 |
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Magnetostatic Modes |
150 |
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Walker's Equation |
150 |
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Spin Waves |
152 |
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Uniform Precession Modes |
155 |
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Normally Magnetized Ferrite Film |
155 |
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Tangentially Magnetized Ferrite Film |
156 |
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Ferrite Sphere |
157 |
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Normally Magnetized Film: Forward Volume Waves |
162 |
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Tangentially Magnetized Film: Backward Volume Waves |
169 |
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Tangentially Magnetized Film: Surface Waves |
173 |
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Problems |
177 |
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References |
178 |
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Propagation Characteristics and Excitation of Dipolar Spin Waves |
180 |
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Energy Velocities for Dipolar Spin Waves |
180 |
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Propagation Loss |
182 |
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Relaxation Time for Propagating Modes |
182 |
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Surface Waves |
184 |
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Volume Waves |
185 |
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Summary of the Phenomenological Loss Theory |
187 |
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Mode Orthogonality and Normalization |
189 |
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Forward Volume Waves |
189 |
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Backward Volume Waves |
191 |
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Surface Waves |
193 |
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Excitation of Dipolar Spin Waves |
194 |
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Common Excitation Structures |
194 |
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Forward Volume Waves |
199 |
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Backward Volume Waves |
205 |
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Surface Waves |
206 |
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Discussion of Excitation Calculations |
208 |
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Problems |
210 |
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References |
212 |
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Variational Formulation for Magnetostatic Modes |
214 |
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General Problem Statement |
214 |
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Calculus of Variations |
215 |
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Formulation for One Independent Variable |
215 |
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Extensions to Three Independent Variables |
217 |
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Small-Signal Functional for Ferrites |
219 |
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Interpretation of the Functional |
221 |
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Stationary Formulas |
223 |
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Stationary Formula Examples with Forward Volume Waves |
225 |
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Large k-limit |
226 |
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Improved Approximation |
227 |
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Effect of Medium Inhomogeneity |
229 |
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Finite Element Analysis |
229 |
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Problems |
230 |
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References |
232 |
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Optical-Spin Wave Interactions |
234 |
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Symmetric Dielectric Waveguides |
235 |
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TE Modes |
235 |
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TM Modes |
238 |
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Optical Mode Orthogonality and Normalization |
239 |
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Magneto-Optical Interactions |
242 |
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Can You Tell the Difference Between and ? |
242 |
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Definition of Magnetization at High Frequencies |
245 |
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Symmetry Requirements on the Permittivity |
246 |
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Coupled-Mode Theory |
247 |
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Coupled-Mode Equations |
248 |
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Energy Conservation |
249 |
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Solutions to the Coupled-Mode Equations |
250 |
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Scattering of Optical-Guided Modes by Forward VolumeSpin Waves |
252 |
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Coupled-Mode Equations |
252 |
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Coupling Coefficients |
256 |
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Tightly Bound Optical Mode Approximation |
261 |
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Cotton--Mouton Effect |
263 |
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Anisotropic Bragg Diffraction |
264 |
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Problems |
267 |
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References |
271 |
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Nonlinear Interactions |
273 |
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Large-Amplitude Spin Waves |
273 |
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Foldover and Bistability |
277 |
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Hamiltonian Equations of Motion |
281 |
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Spin Wave Interactions |
283 |
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Decay Instability |
290 |
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H(2) Coefficients |
292 |
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Nonlinear Schrödinger Equation |
294 |
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Modulational Instability and Solitons |
295 |
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Split-Step Fourier Method |
297 |
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Anomalous Dispersion |
299 |
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Other Aspects |
301 |
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Routes to Chaos |
303 |
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Center Manifold Theory |
303 |
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Quantizing Low-Dimensional Chaos |
306 |
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Problems |
312 |
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References |
315 |
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Novel Applications |
319 |
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Nano-Contact Spin-Wave Excitations |
319 |
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Current-Induced Spin Torque |
320 |
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Magnetic Precession |
325 |
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Magnetic Precession in Patterned Structures |
332 |
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Inverse Doppler Effect in Backward Volume Waves |
335 |
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Problems |
339 |
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References |
340 |
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Appendix A Properties of Yttrium–Iron–Garnet (YIG) |
343 |
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References |
344 |
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Appendix B Currents in Quantum Mechanics |
345 |
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Density of States |
345 |
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Electric and Spin Current Densities |
347 |
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Reflection and Transmission at a Boundary |
348 |
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Tunneling Through a Barrier |
349 |
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References |
351 |
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Appendix C Characteristics of Spin Wave Modes |
352 |
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Constitutive Tensors |
352 |
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Polder Susceptibility Tensor |
352 |
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Permeability Tensor |
353 |
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Uniform Precession Mode Frequencies |
353 |
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Spin Wave Resonance Frequencies |
353 |
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General Magnetostatic Field Relations |
353 |
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Forward Volume Spin Waves |
354 |
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Backward Volume Spin Waves |
355 |
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Surface Spin Waves |
356 |
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Appendix D Mathematical Relations |
358 |
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Trigonometric Identities |
358 |
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Vector Identities and Definitions |
358 |
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Fourier Transform Definitions |
359 |
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Index |
360 |
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