Axial symmetry of DMI-stabilised Skyrmions on the disk

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• Leon Happ (Technische Universität Wien)
• Friday 22 August 2025, 11:00-11:45
• Seminar Room 1, Newton Institute.

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DNMW06 - Recent challenges in the mathematical design of new materials

Magnetic Skyrmions – two-dimensional, topologically nontrivial, localised magnetisation configurations – are know to arise in ferromagnetic thin films from the competition between symmetric exchange, magnetic anisotropy, and the chiral Dzyaloshinskii-Moriya interaction (DMI). Although experiment and simulation often reveal nearly circular Skyrmion profiles, the mathematical justification for axial symmetry is subtle: while exchange and anistropy energies are invariant under in-plane rotations, the DMI term breaks rotational symmetry, a fact that the priori permits nonsymmetric minimisers. In this talk, I will present a joint work in progress with Giovanni Di Fratta and Valeriy Slastikov establishing that, under a standard micromagnetic energy on the unit disk and for sufficiently small anisotropy and DMI strengths, there indeed exists a unique, axially symmetric local minimiser of topological degree one. One result rigourously corroborates the empirical observation of circular Skyrmion shapes in confined geometries and complements earlier work by Li and Melcher (2017), who obtained an analogous existence and stability result for the unbounded plane.

This talk is part of the Isaac Newton Institute Seminar Series series.

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