Vortex Motion for the Landau-Lifshitz-Gilbert Equation with Applied Magnetic Field

Kurzke, Matthias; Melcher, Christof; Moser, Roger

doi:10.1007/978-3-319-00786-1_6

Cited by 2 publications

(1 citation statement)

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“…The idea is to determine the solution ψ in (5. Remark 23 It is possible to also encode the effect of a small applied field or anisotropy in the renormalized energy, as has been done by Kurzke-Melcher-Moser [34] for interior vortices. In this case, the optimal phase is no longer harmonic, but satisfies a nonlinear elliptic equation instead.…”

Section: Remark 22mentioning

confidence: 99%

An effective model for boundary vortices in thin-film micromagnetics

Ignat¹,

Kurzke²

2022

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Ferromagnetic materials are governed by a variational principle which is nonlocal, nonconvex and multiscale. The main object is given by a unit-length three-dimensional vector field, the magnetization, that corresponds to the stable states of the micromagnetic energy. Our aim is to analyze a thin film regime that captures the asymptotic behavior of boundary vortices generated by the magnetization and their interaction energy. This study is based on the notion of "global Jacobian" detecting the topological defects that a priori could be located in the interior and at the boundary of the film. A major difficulty consists in estimating the nonlocal part of the micromagnetic energy in order to isolate the exact terms corresponding to the topological defects. We prove the concentration of the energy around boundary vortices via a Γ-convergence expansion at the second order. The second order term is the renormalized energy that represents the interaction between the boundary vortices and governs their optimal position. We compute the expression of the renormalized energy for which we prove the existence of minimizers having two boundary vortices of multiplicity 1. Compactness results are also shown for the magnetization and the corresponding global Jacobian.

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Section: Remark 22mentioning

confidence: 99%