Energy minimization for skyrmions on planar thin films
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
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| _version_ | 1866908562887802880 |
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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 |