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Mathematics > Analysis of PDEs

arXiv:2210.00892 (math)
[Submitted on 3 Oct 2022]

Title:Phase transition threshold and stability of magnetic skyrmions

Authors:Slim Ibrahim, Ikkei Shimizu
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Abstract:We examine the stability of vortex-like configuration of magnetization in magnetic materials, so-called the magnetic skyrmion. These correspond to critical points of the Landau-Lifshitz energy with the Dzyaloshinskii-Moriya (DM) interactions. In an earlier work of the Döring and Melcher, it is known that the skyrmion is a ground state when the coefficient of the DM term is small. In this paper, we prove that there is an explicit critical value of the coefficient above which the skyrmion is unstable, while stable below this threshold. Moreover, we show that in the unstable regime, the infimum of energy is not bounded below, by giving an explicit counterexample with a sort of helical configuration. This mathematically explains the occurrence of phase transition observed in some experiments.
Comments: 12 pages
Subjects: Analysis of PDEs (math.AP); Mathematical Physics (math-ph)
MSC classes: 35B38, 35Q60, 35J61
Cite as: arXiv:2210.00892 [math.AP]
  (or arXiv:2210.00892v1 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.2210.00892
Related DOI: https://doi.org/10.1007/s00220-023-04779-6

Submission history

From: Ikkei Shimizu [view email]
[v1] Mon, 3 Oct 2022 12:58:01 UTC (16 KB)
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