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عدد المساهمات : 18994 التقييم : 35488 تاريخ التسجيل : 01/07/2009 الدولة : مصر العمل : مدير منتدى هندسة الإنتاج والتصميم الميكانيكى
| موضوع: كتاب Magnetics, Dielectrics, and Wave Propagation with MATLAB Codes - Second Edition الجمعة 29 مارس 2024, 1:12 am | |
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أخواني في الله أحضرت لكم كتاب Magnetics, Dielectrics, and Wave Propagation with MATLAB Codes - Second Edition Carmine Vittoria
و المحتوى كما يلي :
Contents Preface xii Preface to the Second Edition xv Acknowledgments .xvi Author xvii Chapter 1 Review of Maxwell Equations and Units .1 Maxwell Equations in MKS System of Units 1 Major and Minor Magnetic Hysteresis Loops 2 Tensor and Dyadic Quantities 6 Maxwell Equations in Gaussian System of Units 10 External, Surface, and Internal Electromagnetic Fields . 11 Problems . 14 Appendix 1.A: Conversion of Units . 15 References 18 Solutions . 18 Chapter 2 Classical Principles of Magnetism .27 Historical Background 27 First Observation of Magnetic Resonance .27 Definition of Magnetic Dipole Moment .28 Magnetostatics of Magnetized Bodies . 33 Electrostatics of Electric Dipole Moment 39 Relationship between B and H Fields . 41 General Definition of Magnetic Moment .44 Classical Motion of the Magnetic Moment 46 Problems .49 Appendix 2.A .50 Bibliography . 51 Solutions . 51 Chapter 3 Introduction to Magnetism .59 Energy Levels and Wave Functions of Atoms 61 Spin Motion 64 Intra-Exchange Interactions . 67 Heisenberg Representation of Exchange Coupling 72 Multiplet States 72 Hund Rules . 75 Spin–Orbit Interaction 77 Lande gJ-Factor 78 Effects of Magnetic Field on a Free Atom .80viii Contents Crystal-Field Effects on Magnetic Ions 85 Superexchange Coupling between Magnetic Ions .89 Double Superexchange Coupling .99 Ferromagnetism in Magnetic Metals 101 Problems . 106 Appendix 3.A: Matrix Representation of Quantum Mechanics . 108 Bibliography 110 Solutions . 111 Chapter 4 Deposition of Ferrite Films at the Atomic Scale by the ATLAD Technique . 119 Historical Background to the Development of the ATLAD Technique . 119 Deposition of Ferrite Films by the Laser Ablation Technique .120 Deposition of Spinel Ferrite Films at the Atomic Scale— ATLAD Technique 121 Deposition of Hexaferrite Films at the Atomic Scale— ATLAD Technique 126 Concluding Remarks 134 Problems . 135 References 135 ATLAD References 135 Supplemental References 136 Solutions . 136 Chapter 5 Free Magnetic Energy 137 Thermodynamics of Noninteracting Spins: Paramagnets 137 Ferromagnetic Interaction in Solids . 139 Ferrimagnetic Ordering 144 Spin Wave Energy 147 Effects of Thermal Spin Wave Excitations . 151 Free Magnetic Energy 152 Single Ion Model for Magnetic Anisotropy . 153 Pair Model 155 Demagnetizing Field Contribution to Free Energy 156 Numerical Examples 160 Cubic Magnetic Anisotropy Energy . 164 Uniaxial Magnetic Anisotropy Energy . 165 Problems . 167 Bibliography 167 Solutions . 168 Chapter 6 Phenomenological Theory 182 Smit and Beljers Formulation . 182 Examples of Ferromagnetic Resonance . 184Contents ix Simple Model for Hysteresis 196 General Formulation . 201 Connection between Free Energy and Internal Fields 203 Static Field Equations .204 Dynamic Equations of Motion .205 Microwave Permeability . 211 Normal Modes 214 Magnetic Relaxation . 218 Free Energy of Multi-Domains 223 Problems .227 Appendix 6.A: Magnetic Damping Parameter Calculated from First Principles .227 Bibliography .229 Solutions .229 Chapter 7 Electrical Properties of Magneto-Dielectric Films 244 Basic Difference between Electric and Magnetic Dipole Moments .244 Electric Dipole Orientation in a Field 244 Equation of Motion of Electrical Dipole Moment in a Solid .246 Free Energy of Electrical Materials 247 Magneto-Elastic Coupling 249 Microwave Properties of Perfect Conductors . 252 Principles of Superconductivity: Type I . 253 Magnetic Susceptibility of Superconductors: Type I .259 London’s Penetration Depth .259 Type II Superconductors 261 Microwave Surface Impedance 264 Conduction through a Non-Superconducting Constriction 265 Isotopic Spin Representation of Feynman Equations .268 Problems . 272 Bibliography 274 Solutions . 275 Chapter 8 Kramers–Kronig Equations .282 Problems .287 Bibliography 288 Solutions .288 Chapter 9 Electromagnetic Wave Propagation in Anisotropic Magneto-Dielectric Media .292 Spin Wave Dispersions for Semi-Infinite Medium .296 Spin Wave Dispersion at High k-Values .297 The k = 0 Spin Wave Limit .298 Sphere .298 Thin Films 300x Contents Parallel FMR Configuration .300 Needle . 301 Surface or Localized Spin Wave Excitations 302 Pure Electromagnetic Modes of Propagation: Semi-Infinite Medium 305 Coupling of the Equation of Motion and Maxwell’s Equations .306 Metals . 314 Dielectrics . 315 Solution for k2 . 315 Normal Modes of Spin Wave Excitations 318 Magnetostatic Wave Excitations . 323 M Perpendicular to Film Plane 323 a. θ k = 0: . 323 b. θ k = π/2: 326 H in the Film Plane 330 a. θ k = 0: . 330 b. θ k = π/2: 331 Case 1 . 331 Case 2 . 332 Ferrite Bounded by Parallel Plates . 333 Problems . 336 Appendix 9.A . 337 Empty Microwave cavity 337 At Resonance 337 Perpendicular Case .340 In-Plane Case 341 Bibliography 342 Solutions .342 Chapter 10 ATLAD Deposition of Magnetoelectric Hexaferrite Films and Their Properties 346 Basic Definitions of Ordered Ferroic Materials .346 Parity and Time Reversal Symmetry in Ferroics 347 Tensor Properties of the Magnetoelectric Coupling in Hexaferrites .347 Deposition of Single-Crystal ME Hexaferrite Films of the M-Type by the ATLAD 351 Magnetometry and Magnetoelectric Measurements 354 Free Magnetic Energy Representation of the Spin Spiral Configuration . 359 Free Energy of ME Hexaferrite 360 Electromagnetic Wave Dispersion of Magnetoelectric Hexaferrite .362 Analog to a Semiconductor Transistor Three-Terminal Network 363 Problem 365 Solution 366 Bibliography .366Contents xi Chapter 11 Spin Surface Boundary Conditions .367 A Quantitative Estimate of Magnetic Surface Energy . 369 Another Source of Surface Magnetic Energy . 370 Static Field Boundary Conditions 372 Dynamic Field Boundary Conditions . 373 Applications of Boundary Conditions 375 H ⊥ to the Film Plane 375 H // to the Film Plane 380 Electromagnetic Spin Boundary Conditions 380 Problems . 384 Appendix 11.A . 385 Perpendicular Case . 385 In-Plane Case 394 Bibliography . 405 Solutions . 405 Chapter 12 Matrix Representation of Wave Propagation . 414 Matrix Representation of Wave Propagation in Single Layers 414 (//) Case 414 (⊥) Case 419 The Incident Field 420 Ferromagnetic Resonance in Composite Structures: No Exchange Coupling 423 Ferromagnetic Resonance in Composite Structures: Exchange Coupling 428 (⊥) Case 428 Boundary Conditions . 431 Procedure for Solution . 433 (//) Case 436 Boundary Conditions (// FMR) . 436 Problems . 439 Appendix 12.A .440 Calculation of Transmission Line Parameters from [A] Matrix .440 Microwave Response to Microwave Cavity Loaded with Magnetic Thin Film 453 References 458 Solutions . 458 Index 467 Index Note: Bold page numbers refer to tables and italic page numbers refer to figures. alternate target laser ablation deposition (ATLAD) technique 119–135, 346–366 deposition of ME hexaferrite films 346–366 development of 119–120 hexaferrite films deposition at atomic scale 126–134 spinel ferrite films deposition at atomic scale 121–126 A matrix 417, 420, 425, 426, 429, 431, 434, 440–453 angular momentum 44–46, 61, 77, 82, 83, 85, 253, 355 angular momentum quantum number 63–65, 75, 137 angular velocity 48, 58 antiferroelectrics 346 antiferromagnetic ordering 173 antiferromagnetic state 71, 72, 91, 97, 98, 102, 103, 346 anti-resonance FMR (AFMR) frequency 213 atomic number 61, 77, 114 atoms 61–64, 85, 246, 369 band gap energy 255 bandwidth 222 barium hexaferrite (BaFe12O19) 351 magnetoplumbite hexagonal structure 162 single crystal film deposition 127–131 Bernoulli’s equation 137 B-field 7, 14, 31, 41–44 Bloch–Bloembergen model 221 body center cubic (BCC) 137, 140, 171, 171, 370 Bohr magneton 32, 46, 58, 64, 137 Bohr’s radius 32, 62 Boltzmann statistics 137 Boltzman’s constant 245 boson operators 268 boundary condition 13, 14, 212, 367–404, 414, 419, 422, 424, 430, 431–433, 436, 445, 462 applications 375–380 dynamic field 373, 373–375 electromagnetic spin 380–384 spin-pinning 424 spin surface 367–384 static field 372–373 wave propagation in single layers 414 Brillouin function 138, 151, 172 Brillouin zone 297–298 bubble domains 223, 224, 225 Cauchy probability function 197, 198, 200 characteristic impedance 11, 264, 417, 419, 432, 440, 443, 454, 464 charge density 50, 258 circular coil 33, 33 circular polarization 2, 5, 376, 420 coaxial line 420 cobalt ions 352, 358 coercive field 199, 201, 365 collinear magnetic sublattice 144, 144 commutation relations 268, 270 composite structures, FMR in 423–438 conduction 43, 254, 259, 265–268, 270 current 43 through non-superconducting constriction 265, 265–267 conductivity 2, 101, 252, 253, 379, 380, 424 conductors 252–253 constitutive relations 1, 9, 10 constriction 266, 268 contour integral 291 converse ME effect 348 conversion of units 15, 16, 17 Cooper pair 253, 254, 257, 258 Coulomb force 62 Coulomb interaction 67 Coulomb repulsion energy 118 coupling constant 266 critical magnetic fields 261 crystal-field effects, on magnetic ions 85–89 electrostatic interaction 86 multiplet splittings 88, 88–89 3d electronic configuration 89, 89 3d wave functions 88 wave functions 86–88, 90 cubic magnetic anisotropy energy 164–165, 166 CuFe2O4, single crystal film deposition of 124–126 Curie’s law 139 Curie temperature 142 current density 1, 2, 31, 42, 43, 267 db 8, 328, 329 DC permeability 193 DC susceptibility 190, 193 De Broglie’s equation 59468 Index degeneracy 65, 68, 70, 75, 85, 87, 99–101 degrees of freedom 64, 65 delay time 328 delta splitting 89 demagnetizing energy 39, 186, 225, 226, 325–327, 331, 332, 360 demagnetizing factors 157, 158, 186, 212, 225 demagnetizing field 156–160, 159, 187, 187, 292–294 density 129 diamagnetic energy 84 diamagnetism 169, 258 dielectric constant 2, 12, 335, 355 dielectrics 315 dielectric tensor 273, 278 dipole–dipole interaction 39, 157, 174, 369, 409–412 Dirac’s equation 64 direct ME effect 348 discrete 59, 61, 227, 327, 329 dispersion 132, 207, 292, 296–302, 305, 306, 308, 310, 311, 313–333, 340, 345, 362–363, 423, 428, 461 dielectrics 315 magnetic metals 314–315 relation 318, 320 resonant spin wave mode 318 displacement current 43 dissipation loss 4 domain wall 225 double exchange 99, 101 double superexchange coupling 99–101 dyadic operator 309 dyadic permeability 43 dyadic quantities 6–10 dyadic susceptibility 44 dyadic vector 9 dynamic equations of motion 205–211 dynamic field boundary condition 373, 373–375 dynamic magnetic field 130, 203 dynamic motion 147 Dzyaloshinskii–Morya interaction 347, 359 Earth’s field 56 effective conductivity 441, 444 effective permeability 288, 444 effective propagation constant 419, 443 E-field 272, 275, 344, 355, 463 eigen energies 96 eigen function 69, 70 elastic constants 247 electrical bridge technique 28 electric dipole moment 39–41, 40, 347 definition 244 electric displacement 247 in field 244–246 lattice motion 246, 246 in solid 246–247 electric displacement 247 electric field 17, 21, 23, 40, 40, 41, 81, 244, 252, 347, 348, 362, 380 electric susceptibility 2, 247 electromagnetic energy 14 electromagnetic fields 48 external 11–14, 12 internal 11–14, 12 surface 11–14, 12 electromagnetic spin boundary condition 380–384 electromagnetic wave propagation 292–336 dielectrics 315 equation of motion and Maxwell’s equations 306–314 ferrite bounded by parallel plates 333–336, 334 high k-values, spin wave dispersion at 297–298, 298 in insulator 305, 305 magnetic metals, dispersion for 314–315 magnetoelectric hexaferrite 362–363 magnetostatic wave excitations 323–333 for metal 305, 306 semi-infinite medium 305–306 solution for k 2 315–317 sphere 298–299 spin wave dispersions for semi-infinite medium 296, 297 spin wave excitations, normal modes of 318–323 spin wave limit 298 surface spin wave excitations 302–305 electron 32, 56, 59 electron beam deposition 119 electronic configuration 75, 91, 100, 160 electrostatic interaction 28, 85, 86 electrostatic repulsion energy 68, 71 electrostatics, of electric dipole moment 39–41, 40 electrostriction 346 energy dispersive X-ray spectroscopy (EDS) 352 energy levels 61–64, 71, 88, 89, 153 EPR equipment 340 equation of motion 47, 82, 183, 306–314 equilibrium condition 184, 185, 188, 191, 193–195, 204, 373 equivalent circuit 14, 14, 337, 453, 459 exchange coupling, Heisenberg representation of 72 exchange energy 103, 140, 152 exchange field 141, 293 exchange integral 93, 140 exchange interaction 28, 75, 80, 139, 140, 147, 346, 369Index 469 exchange stiffness constant 150, 228, 307, 361, 363, 424 excitation matrix 434 extended X-ray absorption fine structure (EXAFS) technique 125, 132, 133 face center cubic (FCC) 137, 384, 411 Faraday’s law 256, 308 Fermi energy 103, 254, 256 Fermi’s correlation probability function 72 Fermi’s radius 103 Fermi velocity 255 ferrimagnetic ordering 144–147, 172 ferrimagnetics 346 ferrite films deposition, by ATLAD technique 119–135 hexaferrite films 126–134 spinel ferrite films 121–126 ferrites 27, 86, 119–122, 127, 131, 227 ferroelectrics 346 ferroics, parity and time reversal symmetry in 347 ferromagnetic interaction, in solids 139–144 Curie temperature 142 exchange field 141 magnetic potential energy 140 magnetization vs. temperature 142 normalized magnetization 143, 143 susceptibility ratio 142 thermal magnetization 141 ferromagnetic resonance (FMR) 119, 184–196, 329, 355, 423–439 in composite structures 423–438 exchange coupling 428–438, 435 magnetostatic wave excitation 323, 324, 326, 329–330 needle-shaped magnetic sample 187, 187–188 no exchange coupling 423–428 semi-infinite magnetic medium 184–186, 185 spherical magnetic sample 186–187 thin-film magnetic sample 188–192, 189 uniaxial magnetic anisotropy energy 192, 192–196, 194–196 ferromagnetic state 71, 91, 97, 100–103, 146, 346 ferromagnetism, in magnetic metals 101–106 Feynman equations, isotopic spin representation of 268–272 Fourier transform 282 free atom 80, 85 free electron gas 103 free energy 182, 184, 202 of electrical materials 247–249 and internal fields connection 203–204 Maxwell’s equations 307 of ME hexaferrite 360–362 of multi-domains 223–226 spin spiral configuration 359–360, 360 surface anisotropy energy density 374 free magnetic energy 137–181 cubic magnetic anisotropy energy 164–165, 166 demagnetizing field 156–160, 159 ferrimagnetic ordering 144–147 ferromagnetic interaction in solids 139–144 Gibbs free energy 152 Helmholtz free energy 152 noninteracting spins, thermodynamics of 137–139 pair model 155–156 single ion model for magnetic anisotropy 153–155 spin wave energy 147–150 thermal spin wave excitations 151, 151–152 uniaxial magnetic anisotropy energy 165–166 Gaussian system of units 10–11 Gauss law 294 general formulation 201–203 g-factor 136, 372 giant magnetoresistance (GMR) 364, 364 Gibbs free energy 152 Gilbert damping parameter 218, 220, 222, 228, 228, 308, 377, 378 Gilbert relaxation model 308 Green’s theorem 368 ground state energy 63, 91, 102, 255, 257 ground-state multiplet for rare earth ions 76 for transition metal ions 76 gyromagnetic ratio 45 Hamiltonian 61, 78, 80, 81, 90, 102, 203, 255, 256, 268 Hamilton–Jacobi equation 246, 252 Heisenberg Exchange model 72, 103 Helmholtz free energy 152 hexaferrite films deposition, by ATLAD technique 126–134 BaFe12–xMnxO19 131–134 barium hexaferrite (BaFe12O19) 127–131, 130 hexaferrites 120, 122, 126–134, 166, 208–211, 346–366 crystal structure 162, 163 magnetoelectric coupling in 347–351 M-type 351–353 single-crystal ME films 351–353 hexagonal symmetry 160, 412, 413 H-field 41–44 Hund’s rule 75–76, 160 hysteresis model 196–200 Cauchy probability function 197, 198, 200 ferromagnetic resonance 199, 201 loop 197, 200 saturation field effects 196, 197470 Index incident electric field 420 incident electromagnetic field 420–423 incident voltage 420, 454 induced current 281 induced magnetization 258, 356 interfacial region 304 internal energy 152 internal magnetic field 203, 307, 380 internal supercurrents 259 intra-exchange interactions 67–72 Coulomb interaction 67 eigen functions 69, 70 electrostatic repulsion energy 68, 71 energy levels 71, 71 Fermi’s correlation probability function 72 Pauli’s exclusion principle 71 Schrodinger equation 68 spin angular momentum 70 ionic bonding 154 iris cavity hole 337, 418 iron 140–142, 146, 150, 370 isotopic spin 268–272 Josephson equation 267, 268, 271, 272 kinetic energy 81–83, 102 Kramers–Kronig equations 282–288 contour of integration 284, 284 Fourier transform 282 magnetic flux density 283 magnetic system 282 mathematical poles 284, 284 Kramer’s rule 417 Lame constants 252 Landau–Lifshitz damping parameter 218–221, 308, 359, 360 Lande gJ-factor 78–80 Langevin function 245 Larmor frequency 48, 270, 271 lattice displacement 248 lattice motion 246, 254, 357 Laurent series 275 Legendre polynomial expansion 155 Lenz law 84 linear momentum 59 linear polarization 5, 419 linewidth 27, 119, 133, 222, 227, 328 liquid phase epitaxy (LPE) 119 lithium ferrite (Li0.5Fe2.5O4) doped with Al2O3 121–122 London’s penetration depth 259–261 loop rotation 30 Lorentz’s law 28, 81, 252 lowering operator 268 magnetic anisotropy energy 153, 160, 164–165, 166, 192–196, 223, 225, 226, 296, 360, 369, 423, 430 cubic symmetry 164–165, 166 uniaxial symmetry 165–166 magnetic current 42, 43 magnetic damping 227–228 magnetic dipole moment 15, 244, 369 angular momentum 44–46 Bohr magneton 32, 46 classical motion 46–49 current-carrying wire loop 28, 29 current density 31, 42 definition 28–32, 44–46 graphic representation 45 loop rotation 30 potential energy 30, 31 torque 29, 30, 46 Zeeman magnetizing energy 31 magnetic domain 187, 224, 355 magnetic field effects, on free atom 80–85 equation of motion 82 Hamiltonian 80, 81 kinetic energy 81–83 Lenz law 84 Lorentz’s law 81 magnetic moment 83–85, 84 magnetic field excitation 208–211 magnetic fluctuation 152 magnetic flux density 2, 6, 15, 283 magnetic hysteresis loops 2–6 magnetic ions 85–99, 121, 122, 124, 126, 131, 136, 150, 153, 154, 348, 352, 353, 358, 369 crystal-field effects on 85–89 superexchange coupling between 89–99 magnetic metals 86, 101–105, 312, 314, 364, 426, 435, 441 dispersion of 314–315 ferromagnetism in 101–106 magnetic moment 8, 15, 30, 32, 36 classical motion 46–49 general definition 28–32, 44–46 magnetic order 354 magnetic polarization 250, 250 magnetic potential energy 31, 38, 77, 80, 81, 83, 140, 150, 152, 262, 263 magnetic relaxation 218–223, 227, 357 Gilbert damping 218, 220, 222 Landau–Lifshitz damping 218–221 permeability tensor element 222, 223 relaxation mechanism 221, 222 magnetic resonance 27–28, 28, 49 magnetic sublattice 85, 86, 121, 126, 160, 161, 292 magnetic surface energy 369–370 magnetic susceptibility 2, 3, 9, 259, 260Index 471 magnetic tunnel junction (MTJ) 364, 364 magnetism 27–49, 59–110, 126, 127, 131, 133, 139, 152, 162, 348, 369, 438 B and H fields 41–44 crystal-field effects 85–89 double superexchange coupling 99–101 electric dipole moment 39–41, 40 energy levels and wave functions of atoms 61–64 ferromagnetism 101–105 Heisenberg representation 72 Hund rules 75–76 intra-exchange interactions 67–72 Lande gJ-factor 78–80 magnetic dipole moment 28–32 magnetic field effects on free atom 80–85 magnetic moment 44–49 magnetic resonance 27–28, 28 magnetostatics 33–39 multiplet states 72–75 spin motion 64–67 spin–orbit interaction 77–78 superexchange coupling 89–99 magnetization 3, 41 magnetization vector 41, 157, 292, 359 magnetized bodies, magnetostatics of 3–39 magneto-dielectric films 244–272 electric dipole moment 244–247 Feynman equations, isotopic spin representation of 268–272 free energy of electrical materials 247–249 London’s penetration depth 259–261 magnetic dipole moment 244 magneto-elastic coupling 249–252 microwave properties of perfect conductors 252–253 microwave surface impedance 264–265 non-superconducting constriction 265, 265–267 type I superconductivity principles 253–258 type I superconductors 259, 260 type II superconductors 261–263, 262 magneto-elastic coupling 249–252 elastic equations of motion 252 strain 249–251, 250 magnetoelectric hexaferrite 346–365 electromagnetic wave dispersion 362–363 free energy 360–362 single-crystal films 351–353 magnetoelectric measurements 354–359, 355 magneto-impedance 383 magnetometry 354–359 magnetostatic backward volume wave (MSBW) 331 magnetostatics 33–39, 40, 323, 324, 325, 329, 330, 331, 423 circular coil 33, 33 earth’s magnetic field generation model 37, 38 Lorentz condition 34 of magnetized bodies 3–39 Zeeman interaction energy 38 magnetostatic surface wave (MSSW) 333 magnetostatic wave excitation 323–333 approximate spin wave dispersion 326, 327, 331 delay line device 324 ferromagnetic resonance 323, 324, 326, 329–330 higher mode excitations 329 magnetostatic surface wave 333 magnetostatic waves 323, 327 microwave signal propagation 325 pure spin wave 323–325, 324, 332 slope 327 spin wave resonance 325 standing spin wave mode 325 static magnetization 323–325, 324, 330, 331 surface demagnetizing field 324–327, 330–333 YIG propagation loss 328 magnetostatic waves (MSW) 323, 327, 327, 328, 332 magnetostriction 346 major magnetic hysteresis loop 2–6, 3 manganese ferrite (MnFe2O4) 122, 123, 124, 125 ATLAD film deposition 122–124 magnetic inversion factor 124 single crystal film deposition of 122–124 mathematical poles 284, 284 mathematical singularity 194, 195 MATLAB program 286, 288, 323, 340, 379, 383, 442 matrix elements 10, 11, 92, 94, 102, 103, 109, 350, 358, 416, 422 matrix representation of wave propagation FMR in composite structures 423–438 MATLAB program 438, 442–453 microwave response to microwave cavity 453–458 reflection and transmission coefficient 416, 453 transmission line parameters 440–453 wave propagation in single layers 414–423 Maxwell boundary condition 212 Maxwell’s equation 33, 43, 156, 260 equation of motion and 306–314 in Gaussian system of units 10–11 in MKS system of units 1–2 Meissner effect 259, 261 microwave cavity 337, 340, 453–458 microwave permeability 202, 211–214 microwave surface impedance 264–265 microwave susceptibility 235, 237, 240, 242, 243 minor magnetic hysteresis loop 2–6, 3472 Index MKS system of units 1–2 molecular field 103, 105, 140, 144, 145, 292, 293 molecular polarizability 23 monolithic microwave integrated circuit (MMIC) 119 multi-domains, free energy of 223–226 magnetic bubble domains configuration 223–225, 224 magnetic domain configuration 223, 224 magnetic stripe domains 223–225, 225 multiferroics 346 multiplet energy splittings 74, 74 multiplet splittings 88, 88–89 nearest neighbor 89, 103, 140, 149, 155, 369, 370, 410, 411 Neel temperature 124, 145, 358 Newton’s second law 58 nickel 146 noninteracting spins, thermodynamics of 137–139 Brillouin function 138 Curie’s law 139 magnetization 139, 139 total magnetic moment 137 nonlinear analysis 206 non-resonant mode 216, 314, 316 non-superconducting constriction 265, 265–267 nuclear magnetic resonance 27, 28 octahedral 86, 86–89, 121 off resonance 337, 464 Ohm’s law 19, 24, 253, 383 orbital 64, 68 orbital angular momentum 75, 77, 82, 83 orbital quantum number 64 orbital wave function 68 ordered ferroic materials 346 pair model 155–156 parallel FMR 300–302 parallelism 204 parallel plates, ferrite bounded by 333–336, 334 paramagnetics 141, 142, 221 partition function 170 Pauli’s exclusion principle 66, 71–73, 101 permalloy 143, 222, 323, 364 permeability 1 permeability tensor 7–9, 14, 222, 223, 306–308 permittivity 1 permittivity tensor 15, 307 perpendicular FMR 192, 300, 304 perturbation method 322 phenomenological theory 182–227 dynamic equations of motion 205–211 ferromagnetic resonance 184–196 free energy and internal fields connection 203–204 free energy of multi-domains 223–226 general formulation 201–203 hysteresis model 196–201 magnetic damping parameter 227–228, 228 magnetic relaxation 218–223 microwave permeability 211–214 normal modes 214–217 Smit and Beljers formulation 182–184 static field equations 204–205 physical constants 17 piezoelectric coupling energy 361 piezoelectricity 346 piezomagnetics 346 piezomagnetic tensor 349 Planck’s constant 59 polarization fields 11 polarization vector 23 polyvinyl alcohol (PVA) 352 potential energy 30, 31, 51, 52 potential magnetic energy 80 power loss 4, 6 Poynting integral 11, 14, 379 probability function 71, 72, 109 propagation constant 228, 265, 295, 316, 329, 367, 419, 421, 432, 463 proton 46 pulse laser deposition (PLD) 123 quantum fluxoid 257 quantum mechanics 32, 59, 77, 108–110, 148, 256, 268 matrix representation 108–110 Racah parameters 73, 74 radial wave function 74 reflection coefficient 339, 340, 453, 454 repulsive electrostatic energy 88 resonance condition 187, 188, 214, 300 ring resonator 59 saturating fields 191 scalar permeability 6 scalar potential 157, 233, 234 scattering S parameters 414, 416 Schrodinger’s equation 60–62, 68, 114, 170, 303 semiconductors 363–365 semi-infinite medium 7, 184–187, 220, 296–299, 305–306, 323 pure electromagnetic modes of propagation 305–306 spin wave dispersion for 296, 297 simple cubic (SC) symmetry 137 single ion model, for magnetic anisotropy 153–155 single-loop Cooper carrier 257 skin depth 14, 20, 25 Slater determinant 73, 101Index 473 Slater function 63 Smit and Beljers formulation 182–184, 202, 207 spherical magnetic sample 186–187 spin angular momentum 70, 77, 83 spinel ferrite films deposition, by ATLAD technique 121–126 CuFe2O4, single crystal film of 124–126 lithium ferrite (Li0.5Fe2.5O4) doped with Al2O3 121–122 MnFe 2O4, single crystal film of 122–124 spin matrix 269 spin motion 32, 47, 64–67 degeneracy 65 degrees of freedom 64, 65 magnetic moment 64 Pauli exclusion principle 66 wave function 65, 66, 67 spin–orbit interaction 77–78 spin–phonon interactions 227 spin-pinning boundary condition 424 spin spiral configuration 359–360, 360 spin surface boundary conditions 367–405 applications 367, 375–380 dynamic field 373, 373–375 magnetic surface energy 369–370 static field 372–373 surface magnetic energy 370–372, 371 spin wave dispersion 292 at high k-values 297–298, 298 for semi-infinite medium 296, 297 spin wave energy 147–150 spin wave excitation 292 FMR condition 295 isotropic case 319 in magnetic cylinders 301, 302 normal modes 318–323 resonant spin wave mode 318 surface or localized 302–305 spin wave limit k = 0 298 needle 301–302, 302 parallel FMR configuration 300–301, 301 sphere 298–299, 299 thin films 300, 300 spin wave motion 147, 148 spin wave resonance (SWR) 325 SrCo2Ti2Fe8O19 353, 356, 357 magnetoelectricity in 351–352 site occupancy of transition metal cations in 357, 357 static field boundary condition 372–373 static field equations 204–205 static magnetic field 8, 270, 281, 295, 325, 372, 423, 428 Stokes theorem 31 stripe domains 225, 225 strontium hexaferrite 127 superconductivity 253–259 superconductors 253–256, 258, 259–263, 265, 273, 279, 280, 463 type I 259, 260 type II 261–263, 262 supercurrent 252, 257, 259, 261 superexchange coupling, magnetic ions 89–99 surface boundary condition 372, 407, 431 surface demagnetizing field 330–333 surface energy 332, 369–370, 409 surface impedance 264–265, 378, 379, 385, 426–428, 434, 435, 441 surface magnetic energy 370–372, 371 surface magnetism 369 surface spin wave excitation 302–305 surface torque 369 susceptibility tensor 213 Taylor series expansion 42, 148, 183 tensor quantities 6–10 tetrahedral symmetry 86, 88, 89, 121, 124, 126, 146 thermal magnetization 141 thermal spin wave excitations 151, 151–152 thermodynamics 137–139 3d electron 72, 89 three-terminal network 363–365 time dependence 7, 8, 108, 109, 183, 282, 318, 328 time response 2, 3 titanium 100 torque 29, 30, 46, 51, 52 transfer function matrix 418, 434, 459, 459, 461, 463, 464 transition temperature 179, 256 transverse electromagnetic (TEM) wave of propagation 306 tunnel magnetoresistance ratio (TMR) 365 type I superconductivity principles 253–259 Fermi energy 254, 256 hypothetical motion of Cooper pair 253, 257 internal supercurrents 259 magnetization vs. external field 258, 258 single-loop Cooper carrier 257 superconducting carriers motion 254, 254 type I superconductors, magnetic susceptibility of 259, 260 type II superconductors 261–263, 262 uniaxial symmetry 156, 160, 192, 193 uniaxial magnetic anisotropy energy 165–166, 192, 192–196, 194–196, 223 units 1–26 conversion of 15, 16, 17 Gaussian system 10–11 MKS system 1–2 vector electric potential 39 vector magnetic potential 31474 Index vibrating sample magnetometer (VSM) 7, 354, 355 volume demagnetizing field 292, 294, 298, 312, 319, 326, 330–333 wave function 60, 61, 63, 65, 70, 71, 73, 74, 86–88, 90–92, 99, 101, 102, 107–109, 115–118, 255, 257, 265, 266, 268 orbital 68 radial 74 spin motion 65, 66, 67 3d electron 88, 99 waveguide 418–420, 454, 464 wavelength 59, 129, 131, 292, 296, 297, 326, 332, 333 wave propagation, in single layers 414–423 boundary condition equations 414 field excitations 414, 419 FMR in composite structures 423–438 incident electric field 420 incident field 420–423 incident voltage 420, 454 Kramer’s rule 417 mathematical procedure 416 2×2 matrices 415, 418, 434 matrix element calculation 422 reflected signal 421 transmission scattering S-parameters 416 transmitted signal 421 X-ray absorption spectroscopy (XAS) 355–356 X-ray magnetic dichroism 356 yttrium iron garnet (YIG) 146 deposition by laser ablation 119–120 dispersions 316, 317, 323 magnetization 146 MSSW velocity 333 Zeeman energy 140, 153, 186, 224 Zeeman interaction energy 38 Zeeman magnetizing energy 31 #ماتلاب,#متلاب,#Matlab,#مات_لاب,#مت_لاب,
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