Magnetoelastic Interactions
Published on 1. January 1966
Book
Hardback
VIII, 156 pages
978-3-540-03674-6 (ISBN)
Description
The modern theory of ferromagnetic magnetization processes has from the beginning recognized the importance of magnetoelastic inter actions. Most of the magnetoelastic calculations, however, have been basecl on the theory developed by R. BECKER and others in the early 1930's. That theory has several defects; how to remedy them is the subject of this monograph. I first became aware of the shortcomings of the traditional theory thru a critical study of electric and magnetic forces, which I undcrtook as a member of the COULOMB'S Law Committee of the American Asso ciation of Physics Teachers. My conclusions were published in 1951 in the American 10Z/rnal of Physics; an application of them to a problem in magnetostriction was published in 1953 in Reviews oflvlodern Physics. With the development, in 1956, of the "nucleation field" theory of micromagnetics, the need for a systematic and self-consistent theory of magnetoelastic interactions became more pressing. The traditional theory predicted that the nucleation field should differ negligibly from that of a rigid body; but my 1953 magnetostriction calculation suggested that terms omitted in that theory might be important. In the academic year 1963/64, 1 was finally able - thanks to a sabbatical furlough - to find the time needed for systematic development of a basic theory of magnetoelastic interactions in a ferromagnet.
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Content
I Fundamental Concepts and Definitions.- 1. Introduction.- 1.1. Statement of the problem.- 1.2. The conventional theory of magnetostriction.- 1.3. The rigorous formal theory.- 1.4. The aim of this treatment.- 1.5. Units and notation.- 2. Magnetostatic Fundamentals.- 2.1. Methods of approach; poles and currents.- 2.2. Current-current forces.- 2.3. Magnetized bodies.- 2.4. The field vectors B and H.- 2.5. The force and torque on a complete body.- 2.6. Energy relations for a rigid magnetic body.- 2.7. Ferromagnetic materials.- 3. Concepts of Elasticity Theory.- 3.1. The analysis of stress.- 3.2. Finite strains.- 3.3. Energy and stress-strain relations.- 3.4. Infinitesimal strains.- 4. Thermodynamic Principles.- 4.1. Introductory remarks.- 4.2. The first and second laws.- 4.3. Equilibrium and stability conditions.- 4.4. Application to rigid magnetic bodies.- 4.5. Application to elastic nonmagnetic bodies.- II Force and Stress Relations in a Deformable Magnetic Material.- 5. The Forces in General.- 5.1. Prolog.- 5.2. Sketch of the procedure.- 5.3. The forces on a whole body.- 5.4. The long-range force on part of a body.- 5.5. The stresses.- 5.6. Alternative definitions of the "stresses".- 6. Equilibrium in a Magnetizable Elastic Solid.- 6.1. Energy relations.- 6.2. The rate of change of the magnetic self-energy.- 6.3. Relations of magnetizing force and stress to magnetization and deformation.- III The Energy Method.- 7. Formal Theory.- 7.1. The minimization principle.- 7.2. The magnetic equilibrium conditions.- 7.3. The mechanical equilibrium conditions.- 7.4. Disembodied fields.- 7.5. Invariance to rotation.- 7.6. Comparison with the stress method.- 7.7. The asymmetry of the stresses.- 7.8. Dynamic modifications.- 7.9. Permissible equilibrium specifications of applied forces.- 8. Terms in the Free Energy.- 8.1. Relevance of microscopic concepts.- 8.2. The exchange energy.- 8.3. The anisotropy, magnetostrictive, and elastic energies.- 8.4. A microscopic model for magnetostriction.- 8.5. The magnetic self-energy.- 9. The Small-Displacement Approximation.- 9.1. A first-order approximation.- 9.2. A more drastic approximation.- 9.3. Verification by a variational method.- 9.4. Comparison with conventional magnetostriction theory.- 9.5. Uniqueness of the strains.- IV Applications.- 10. The Magnetostriction of a Uniformly Magnetized Ellipsoid.- 10.1. Finite-strain formulas.- 10.2. The small-displacement approximation.- 10.3. The average strains.- 10.4. The strains in a sphere.- 11. Problems of Micromagnetics.- 11.1. The distribution problem in general.- 11.2. Cubic crystals.- 11.3. Linear approximations.- 11.4. The nucleation-field problem.- Appendix A.- The Variation of the Magnetic Self-Energy.- Appendix B.- Proof of the Magnetic Reciprocity Theorem (11.32).- Appendix C.- On Angular Velocity.- References.- Author Index.