The 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.

Tomassetti, G. (2007). Dynamics of domain walls in ferromagnets.

Dynamics of domain walls in ferromagnets

TOMASSETTI, GIUSEPPE
2007-04-13

Abstract

The 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.
13-apr-2007
19 giugno 2002
micromagnetics
ferromagnetic materials
Settore ICAR/08 - SCIENZA DELLE COSTRUZIONI
en
Tesi di dottorato
Tomassetti, G. (2007). Dynamics of domain walls in ferromagnets.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/325
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