Energy minimization for skyrmions on planar thin films

Fuente: arXiv
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Autori principali: Di Fratta, Giovanni, Innerberger, Michael, Praetorius, Dirk, Slastikov, Valeriy
Natura: Preprint
Pubblicazione: 2025
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author Di Fratta, Giovanni
Innerberger, Michael
Praetorius, Dirk
Slastikov, Valeriy
author_facet Di Fratta, Giovanni
Innerberger, Michael
Praetorius, Dirk
Slastikov, Valeriy
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2509_23495
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Energy minimization for skyrmions on planar thin films
Di Fratta, Giovanni
Innerberger, Michael
Praetorius, Dirk
Slastikov, Valeriy
Numerical Analysis
Analysis of PDEs
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.
title Energy minimization for skyrmions on planar thin films
topic Numerical Analysis
Analysis of PDEs
url https://arxiv.org/abs/2509.23495