Micromagnetism and the microstructure of ferromagnetic solids / Helmut Kronmüller, Manfred Fähnle.

Format:

Book

Author/Creator:

Kronmüller, Helmut.

Contributor:

Fähnle, Manfred, 1951-

Language:

English

Subjects (All):

Magnetic structure.

Ferromagnetic materials--Structure.

Ferromagnetic materials.

Microstructure.

Physical Description:

xv, 432 pages : illustrations ; 26 cm

Place of Publication:

Cambridge ; New York : Cambridge University Press, 2003.

Summary:

The main topic of this book is micromagnetism and microstructure as well as the analysis of the relations between characteristic properties of the hysteresis loop and microstructure. Also presented is an analysis of the role of microstructure in the fundamental magnetic properties (for example magnetostriction or critical behaviour) of crystalline and amorphous alloys. The authors apply the theory of micromagnetism to all aspects of advanced magnetic materials including domain patterns and magnetization processes under the influence of defect structures. Coverage includes modern developments in computational micromagnetism and its application to spin structures of small particles and platelets.

Based on the continuum theory of micromagnetism, the physical principles of modern permanent and soft magnetic materials are covered comprehensively. Magnetization processes in small particles are outlined on the basis of the Landau-Lifshitz-Gilbert equation including the effects of thermal fluctuations. Magnetic aspects of intermetallic compounds, nanocrystalline and amorphous alloys are considered in detail within the framework of nucleation and pinning phenomena. Measurements of high-field susceptibility in the approach to ferromagnetic saturation are shown to be an appropriate method for the analysis of magnetically active microstructures in ferromagnets. To demonstrate the power of the theory of micromagnetism, the authors present many examples showing that theoretical predictions are supported by experimental results.

This book will be of interest to researchers and graduate students in condensed matter physics, electrical engineering and materials science, and to industrial researchers working in the electrotechnical and recording industries.

Contents:

Appendix Units of magnetic properties 9

2 Magnetic Gibbs free energy 11

2.1 Introductionary remarks 11

2.2 Magnetic energy terms 13

2.2.1 Exchange energy 14

2.2.1.1 Short-range exchange interactions 14

2.2.1.2 Long-range exchange interactions 17

2.2.2 Magnetocrystalline anisotropy energy 20

2.2.3 Magnetostatic energies 25

2.2.4 Elastic potential of a ferromagnet 28

2.2.4.1 Strain tensor in ferromagnetic materials 28

2.2.4.2 Determination of strain tensors 28

2.2.4.3 Derivation of the magnetoelastic potential 31

3 Basic micromagnetic equilibrium conditions 40

3.1 Static micromagnetic equations 40

3.2 Micromagnetic equations in polar coordinates 44

3.3 Micromagnetic equations in terms of swirls and magnetic chares 44

3.4 Linearized micromagnetic equations 45

4 Domain walls in crystalline and amorphous solids 51

4.2 Bloch walls 51

4.3 Effect of magnetostrictive deformations 55

4.4 Effect of internal stresses 57

4.5 Bloch walls in cubic crystals 57

4.6 Neel walls in bulk materials and thin films 64

4.6.2 Neel walls in bulk crystals 65

4.6.3 Neel walls in thin films 66

4.6.4 Phase diagrams of Neel and Bloch walls in thin films 69

5 Interaction of domain walls with defects 71

5.2 Interaction energy of domain walls with point defects 71

5.3 180[degree]-wall in amorphous alloys with uniaxial anisotropy 74

5.4 180[degree]-wall in [alpha]-Fe 75

5.5 Interaction forces of domain walls with point defects 75

5.6 Interaction of Bloch walls with dislocations 75

5.6.1 Straight dislocation lines 77

5.6.1.1 Dislocations of length l parallel to the domain wall plane (x, y) 78

5.6.1.2 Dislocations intersecting the domain walls 79

5.6.2 Straight dislocation dipoles 80

5.6.3 Dislocation loops 81

5.7 Interaction of domain walls with planar defects 81

5.7.1 Pinning by thin planar defects 81

5.7.2 Pinning by extended planar defects 85

5.7.3 Pinning by phase boundaries 86

6 Coercivity of modern magnetic materials 90

6.2 Micromagnetism of hard magnetic materials 95

6.2.1 Homogeneous rotation 96

6.2.2 Inhomogeneous rotation by the curling mode 99

6.2.3 Inhomogeneous rotation by the buckling mode 101

6.2.4 Critical diameters of single domain particles 103

6.2.4.1 Thermal stability limit 103

6.2.4.2 Crossover diameter for nucleation processes 104

6.2.4.3 Critical diameter for domain formation 104

6.2.5 Comparison with experiment 107

6.3 Nucleation under oblique magnetic fields 108

6.3.1 Homogeneous rotation 108

6.3.2 Curling mode 113

6.4 Nucleation in magnetically soft regions 114

6.5 Nucleation in inhomogeneous misaligned grains 117

6.6 Micromagnetic analysis of the coercive field of modern permanent magnets 119

6.6.1 Nucleation versus pinning 119

6.6.2 Analysis of the temperature dependence of the coercive field 122

6.6.3 Nanocrystalline and composite nanocrystalline magnets 126

6.6.4 Nanostructured, nanocrystalline Sm[subscript 2]Co[subscript 17]-based permanent magnets 131

6.7 Alternative coercivity models - the nucleus expansion model 141

7 Statistical theory of domain wall pinning 148

7.1 Statistical pinning potential 148

7.2 Applications of the statistical pinning theory 151

7.2.1 Dislocations in crystalline metals 151

7.2.2 Dislocation dipoles 153

7.2.3 Point defects 155

7.2.4 Amorphous alloys 155

7.2.4.1 Intrinsic fluctuations of exchange and local anisotropy energy 156

7.2.4.2 Internal stress sources 158

7.2.4.3 Coercive field due to surface irregularities 161

7.2.5 Nanocrystalline alloys 164

8 Law of approach to ferromagnetic saturation and high-field susceptibility 174

8.2 Approach to saturation in uniaxial crystals 176

8.3 Approach to saturation in cubic crystals 177

8.4 Approach to saturation in the presence of stress sources 177

8.4.2 Isotropic spherical defects 179

8.4.3 Dislocation loops 183

8.4.4 Straight dislocation lines 184

8.4.5 Dislocation groups 187

8.4.6 Dislocation dipoles 191

8.4.7 Anisotropy of the high-field susceptibility 193

8.4.8 Amorphous alloys 196

8.4.8.2 Magnetostatic fluctuations 198

8.4.8.3 Magnetocrystalline fluctuations 200

8.4.8.4 Magnetoelastic fluctuations 201

8.4.8.5 Analysis of experimental results 207

8.4.9 Nonmagnetic holes and nonferromagnetic precipitations 217

9 Microstructure and domain patterns 225

9.1 Origin of domain patterns 225

9.2 Laminar domain patterns 227

9.2.1 Landau structure 227

9.2.2 Kittel structure 228

9.2.3 Partial Landau-Kittel structure 229

9.2.4 Kittel-type structure for in-plane easy direction 231

9.2.5 The [mu]* -correction 232

9.2.6 Branching of domains in hard magnetic materials 233

9.3 Domain patterns in amorphous alloys 237

9.3.1 As-quenched amorphous alloys 238

9.3.2 Magnetic annealing of amorphous alloys 243

9.3.3 Domain structure and magnetization processes 243

9.3.4 Stress-induced magnetic anisotropy 247

9.4 Stripe domains in thin ferromagnetic films 249

9.5 Dislocations and domain patterns 255

9.5.2 Domain patterns in plastically deformed Ni-single crystals 255

9.5.3 Domain patterns in plastically deformed Fe-single crystals 261

9.5.4 Micromagnetic background of the magnetoelastic coupling energy due to dislocations 263

9.5.5 Ripple structures 269

10 Magnetic after-effects in amorphous alloys 274

10.2 Double-well model of magnetic after-effects in amorphous alloys 275

10.3 Stabilization energy of domain walls 278

10.4 Formation of induced anisotropy 283

10.5 Basic experimental results 284

11 Magnetostriction in amorphous and polycrystalline ferromagnets 295

11.2 Polycrystalline model of amorphous ferromagnets 297

11.3 Basic computational ideas 299

11.4 Mathematical formalism 302

11.4.1 Balance-of-force method 302

11.4.2 Incompatibility method 306

11.4.3 Zeroth- and first-order terms 308

11.5 Results for the saturation magnetostriction of ferromagnets 310

11.6 Field dependence of magnetostriction 313

12 Micromagnetic theory of phase transitions in spatially disordered spin systems 320

12.1 Classification of disordered spin systems 321

12.2 Phase transition in random exchange ferromagnets 323

12.2.1 Critical behaviour 323

12.2.2 Crossover regime to mean field behaviour 325

12.3 Molecular field theory and Landau-Ginzburg theory 327

12.4 Extended Landau-Ginzburg theory 332

12.5 Correlated molecular field theory 334

12.5.1 Physical motivation 334

12.5.2 Calculation of the paramagnetic zero-field susceptibility 339

12.6 Random ferrimagnets, spin glasses and random anisotropy magnets 347

12.7 Dynamic correlated molecular field theory 350

13 Computational micromagnetism of thin platelets and small particles 356

13.2 Applications of the finite difference method 357

13.3 Applications of the finite element method 364

13.3.1 Discretization and adaptive mesh refinement 364

13.3.2 Discretization of the Gibbs free energy used for computational micromagnetism 366

13.3.3 Magnetic structures and magnetization processes in thin platelets 371

13.3.4 Magnetic structures and magnetization processes in small particles 380

13.3.5 Soft magnetic particles in a hard magnetic matrix 384

13.3.6 Assemblies of nanocrystalline grains 385

14 Computational micromagnetism of dynamic magnetization processes 402

14.1 Landau-Lifshitz and Gilbert equations 402

14.2 Characteristic time ranges 405

14.3 Magnetization reversal in thin films 408

14.4 Discretization of the Landau-Lifshitz-Gilbert equation 409

14.5 Dynamic nucleation field 410

14.6 Dynamics of thermally activated reversal processes 416

14.6.1 Thermal fluctuations 416

14.6.2 Thermally activated relaxation 420

Appendix Scaling laws of the statistical pinning theory 423.

Notes:

Includes bibliographical references and index.

ISBN:

0521331358

OCLC:

50906524

Online:

Publisher description