MICROMAGNETISM AND THE MICROSTRUCTURE OF FERROMAGNETIC SOLIDS

Transcription

1 MICROMAGNETISM AND THE MICROSTRUCTURE OF FERROMAGNETIC SOLIDS HELMUT KRONMULLER MANFRED FÄHNLE Max-Planck-lnstitut fiir Metallforschung, Stuttgart, Germany CAMBRIDGE UNIVERSITY PRESS

2 Acknowledgements page xi Introduction 1 References 8 Appendix: Units of magnetic properties 9 Magnetic Gibbs free energy Introductionary remarks Magnetic energy terms Exchange energy Short-range exchange interactions Long-range exchange interactions Magnetocrystalline anisotropy energy Magnetostatic energies Elastic potential of a ferromagnet Strain tensor in ferromagnetic materials Determination of strain tensors Derivation of the magnetoelastic potential Summary 35 References 37 Basic micromagnetic equilibrium conditions Static micromagnetic equations Micromagnetic equations in polar coordinates Micromagnetic equations in terms of swirls and magnetic charges Linearized micromagnetic equations 45 References 50 Domain walls in crystalline and amorphous solids General remarks Bloch walls 51 v

3 4.3 Effect of magnetostrictive deformations Effect of internal stresses Bloch walls in cubic crystals Neel walls in bulk materials and thin films General remarks Neel walls in bulk crystals Neel walls in thin films Phase diagrams of Neel and Bloch walls in thin films 69 References 70 Interaction of domain walls with defects Introductionary remarks Interaction energy of domain walls with point defects wall in amorphous alloys with uniaxial anisotropy wallina-fe Interaction forces of domain walls with point defects Interaction of Bloch walls with dislocations Straight dislocation lines Dislocations of length I parallel to the domain wall plane (x, y) Dislocations intersecting the domain walls Straight dislocation dipoles Dislocation loops Interaction of domain walls with planar defects Pinning by thin planar defects Pinning by extended planar defects Pinning by phase boundaries 86 References 88 Coercivity of modern magnetic materials Introduction Micromagnetism of hard magnetic materials Homogeneous rotation Inhomogeneous rotation by the curling mode Inhomogeneous rotation by the buckling mode Critical diameters of single domain particles Thermal stability limit Crossover diameter for nucleation processes Critical diameter for domain formation Comparison with experiment 107

4 Vll 6.3 Nucleation under oblique magnetic fields Homogeneous rotation Curling mode Nucleation in magnetically soft regions Nucleation in inhomogeneous misaligned grains Micromagnetic analysis of the coercive field of modern permanent magnets Nucleation versus pinning Analysis of the temperature dependence of the coercive field Nanocrystalline and composite nanocrystalline magnets Nanostructured, nanocrystalline Sn^Con-based Permanentmagnets Alternative coercivity models - the nucleus expansion model 141 References 144 Statistical theory of domain wall pinning Statistical pinning potential Applications of the statistical pinning theory Dislocations in crystalline metals Dislocation dipoles Point defects Amorphous alloys Intrinsic fluctuations of exchange and local anisotropy energy Internal stress sources Coercive field due to surface irregularities Nanocrystalline alloys 164 References 172 Law of approach to ferromagnetic saturation and high-field susceptibility Introduction Approach to saturation in uniaxial crystals Approach to saturation in cubic crystals Approach to saturation in the presence of stress sources Introduction Isotropic spherical defects Dislocation loops Straight dislocation lines Dislocation groups Dislocation dipoles 191

5 Vlll Contents Anisotropy of the high-field susceptibility Amorphous alloys General remarks Magnetostatic fluctuations Magnetocrystalline fluctuations Magnetoelastic fluctuations Analysis of experimental results Nonmagnetic holes and nonferromagnetic precipitations 217 References Microstructure and domain patterns Origin of domain patterns Laminar domain patterns Landau structure Kittel structure Partial Landau-Kittel structure Kittel-type structure for in-plane easy direction The ß*-correction Branching of domains in hard magnetic materials Domain patterns in amorphous alloys As-quenched amorphous alloys Magnetic annealing of amorphous alloys Domain structure and magnetization processes Stress-induced magnetic anisotropy Stripe domains in thin ferromagnetic films Dislocations and domain patterns Introduction Domain patterns in plastically deformed Ni-single crystals Domain patterns in plastically deformed Fe-single crystals Micromagnetic background of the magnetoelastic coupling energy due to dislocations Ripple structures 269 References Magnetic after-effects in amorphous alloys Introduction Double-well model of magnetic after-effects in amorphous alloys Stabilization energy of domain walls Formation of induced anisotropy 283

6 ix 10.5 Basic experimental results Concluding remarks 292 References Magnetostriction in amorphous and polycrystalline ferromagnets Outline of the problems Polycrystalline model of amorphous ferromagnets Basic computational ideas Mathematical formalism Balance-of-force method Incompatibility method Zeroth-and first-order terms Results for the saturation magnetostriction of ferromagnets Field dependence of magnetostriction 313 References 316 Appendix Micromagnetic theory of phase transitions in spatially disordered spin systems Classification of disordered spin systems Phase transition in random exchange ferromagnets Critical behaviour Crossover regime to mean field behaviour Molecular field theory and Landau-Ginzburg theory Extended Landau-Ginzburg theory Correlated molecular field theory Physical motivation Calculation of the paramagnetic zero-field susceptibility Random ferrimagnets, spin glasses and random anisotropy magnets Dynamic correlated molecular field theory 350 References Computational micromagnetism of thin platelets and small particles Introduction Applications of the finite difference method Applications of the finite element method Discretization and adaptive mesh refinement Discretization of the Gibbs free energy used for computational micromagnetism Magnetic structures and magnetization processes in thin platelets 371

7 X Contents Magnetic structures and magnetization processes in small particles Soft magnetic particles in a hard magnetic matrix Assemblies of nanocrystalline grains 385 References Computational micromagnetism of dynamic magnetization processes Landau-Lifshitz and Gilbert equations Characteristic time ranges Magnetization reversal in thin films Discretization of the Landau-Lifshitz-Gilbert equation Dynamic nucleation field Dynamics of thermally activated reversal processes Thermal fluctuations Thermally activated relaxation 420 References 422 Appendix Scaling laws of the statistical pinning theory 423 Index 428