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arXiv · 2401.17830

Renormalised energy between boundary vortices in thin-film micromagnetics with Dzyaloshinskii-Moriya interaction

Radu Ignat·François L'Official
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Abstract

We consider a three-dimensional micromagnetic model with Dzyaloshinskii-Moriya interaction in a thin-film regime for boundary vortices. In this regime, we prove a dimension reduction result: the nonlocal three-dimensional model reduces to a local two-dimensional Ginzburg-Landau type model in terms of the averaged magnetization in the thickness of the film. This reduced model captures the interaction between boundary vortices (so-called renormalised energy), that we determine by a $\Gamma$-convergence result at the second order and then we analyse its minimisers. They nucleate two boundary vortices whose position depends on the Dzyaloshinskii-Moriya interaction.

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Radu Ignat, François L'Official. 2024-01-31. Renormalised energy between boundary vortices in thin-film micromagnetics with Dzyaloshinskii-Moriya interaction. https://arxiv.org/abs/2401.17830

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