Energy minimization for skyrmions on planar thin films

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arXiv. 2025 Sep 27;. doi: 10.48550/arXiv.2509.23495
Energy minimization for skyrmions on planar thin films Scientific Computing
Di Fratta Giovanni, Innerberger Michael, Praetorius Dirk, Slastikov Valeriy
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Abstract

We consider an energy functional that arises in micromagnetic and liquid crystal theory on thin films. In particular, our energy comprises a non-convex term that models anti-symmetric exchange as well as an anisotropy term. We devise an algorithm for energy minimization in the continuous case and show weak convergence of a subsequence towards a solution of the corresponding Euler--Lagrange equation. Furthermore, an algorithm for numerical energy minimization is presented. We show empirically that this numerical algorithm converges to the correct solutions for a benchmark problem without the need for user-supplied parameters, and present a rigorous convergence analysis for important special cases.

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Janelia Authors

Michael Innerberger
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