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Please use this identifier to cite or link to this item: http://hdl.handle.net/2108/325

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contributor.advisorDavini, Cesare-
contributor.advisorLuciano, Raimondo-
contributor.advisorAuricchio, Ferdinando-
contributor.advisorMaceri, Franco-
contributor.advisorDe Simone, Antonio-
contributor.authorTomassetti, Giuseppe-
description14. cicloen
description.abstractThe Gilbert equation summarizes the standard model for the evolution of the magnetization m in rigid ferromagnetic bodies. Under common constitutive assumptions, it has the form of a parabolic PDE: γ−1m˙ + μm×m˙ = m× (αΔm+ β(m· e)e + hs + he) . Here m˙ and Δm denote, respectively, the time derivative and the Laplacian of m, and the symbol × denotes the cross product; γ is the gyromagnetic ratio, a negative constant; α, β, μ are positive constants; e is a unimodular vector (the easy axis); he is the external magnetic field and hs is the stray field, the magnetic field generated by the body.1 In ferromagnetic bodies, it is possible to observe magnetic domains, i.e., regions where the orientation is nearly constant, separated by narrow transitions layers, the domain walls. The application of an external magnetic field induces re-orientation and growth of some domains at the expense of others. Our intention is to picture the resulting domain-boundary displacement, accompanied by re-orientation changes in the magnetization, as a process in which domain walls are regarded as surfaces endowed with a mechanical structure, whose motion is ruled by dynamical laws deduced from the Gilbert equation.en
description.tableofcontentsIntroduction 1 1 Micromagnetics 3 1.1 Ferromagnetic Materials 3 1.2 Micromagnetics 3 1.2.1 Euler-Lagrange equations 4 1.2.2 Internal and external energy 4 1.2.3 Standard constitutive assumptions 5 1.3 Magnetic Domains and Domain Walls 7 1.3.1 Small and large bodies 7 1.3.2 Exchange vs. stray-field energy: size effects 8 1.3.3 Shape anisotropy 9 1.3.4 Hard and softmaterials 11 1.3.5 Anisotropy vs. exchange: the internal structure of a domain wall 12 1.4 Domain Theory as a Sharp-Interface Theory 15 2 Dynamical Micromagnetics 17 2.1 The Generalized Gilbert Equation 17 2.2 Standard Form of the Gilbert Equation 18 2.3 The Gilbert Equation as a Balance Law 19 3 Dynamics of Domain Walls 23 3.1 Flat Walls 27 3.1.1 Preliminaries 28 3.1.2 Walker processes 29 3.1.3 Satisfying theWalker condition 30 3.1.4 Solving the Gilbert equation 32 3.1.5 High-order exchange energy and exchange dissipation 34 3.1.6 Dry-friction dissipation 36 3.2 Curved Walls 38 3.2.1 Dimensionless equations 38 3.2.2 Normal coordinates with respect to an evolving surface 40 3.2.3 Matched asymptotic expansions 42 3.2.4 Magnetic domains 43 3.2.5 Estimates 43 3.2.6 Motion by curvature of domain walls 46 Appendix 51 Bibliography 53en
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subjectferromagnetic materialsen
subject.classificationICAR 08; Scienza delle costruzionien
titleDynamics of domain walls in ferromagnetsen
typeDoctoral thesisen
degree.nameDottorato in ingegneria delle struttureen
degree.disciplineFacoltà di Ingegneriaen
degree.grantorUniversità degli Studi di Roma Tor Vergataen
date.dateofdefense19 giugno 2002en
Appears in Collections:Tesi di dottorato in ingegneria

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