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arXiv · 2509.23495

Energy minimization for skyrmions on planar thin films

Giovanni Di Fratta·Michael Innerberger·Dirk Praetorius·Valeriy Slastikov
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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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Giovanni Di Fratta, Michael Innerberger, Dirk Praetorius, Valeriy Slastikov. 2025-09-27. Energy minimization for skyrmions on planar thin films. https://arxiv.org/abs/2509.23495

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