Di Fratta, G., Innerberger, M., Praetorius, D., & Slastikov, V. (2025). Energy minimization for skyrmions on planar thin films. arXiv. https://doi.org/10.48550/arXiv.2509.23495
E101-02-2 - Forschungsgruppe Numerik von PDEs E129-02 - Fachbereich TUForMath
-
ArXiv ID:
2509.23495
-
Date (published):
27-Sep-2025
-
Number of Pages:
22
-
Preprint Server:
arXiv
-
Keywords:
Micromagnetic energy minimization; Antisymmetric exchange interactions; Thin-film liquid crystals
en
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.
