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.File | Dimensione | Formato | |
---|---|---|---|
chapter1.pdf
accesso aperto
Descrizione: chapter1
Dimensione
183.73 kB
Formato
Adobe PDF
|
183.73 kB | Adobe PDF | Visualizza/Apri |
chapter2.pdf
accesso aperto
Descrizione: chapter2
Dimensione
94.57 kB
Formato
Adobe PDF
|
94.57 kB | Adobe PDF | Visualizza/Apri |
chapter3.pdf
accesso aperto
Descrizione: chapter3
Dimensione
237.14 kB
Formato
Adobe PDF
|
237.14 kB | Adobe PDF | Visualizza/Apri |
appendix.pdf
accesso aperto
Descrizione: appendix
Dimensione
67.11 kB
Formato
Adobe PDF
|
67.11 kB | Adobe PDF | Visualizza/Apri |
bibliography.pdf
accesso aperto
Descrizione: bibliography
Dimensione
68.39 kB
Formato
Adobe PDF
|
68.39 kB | Adobe PDF | Visualizza/Apri |
introduction.pdf
accesso aperto
Descrizione: introduction
Dimensione
88.67 kB
Formato
Adobe PDF
|
88.67 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.