Phase transition threshold and stability of magnetic skyrmions

TL;DR

This paper analyzes the stability of magnetic skyrmions, identifying a critical threshold for their stability based on the Dzyaloshinskii-Moriya interaction coefficient, and explains phase transitions observed experimentally.

Contribution

It provides an explicit critical value for skyrmion stability and demonstrates unbounded energy behavior above this threshold, advancing understanding of magnetic phase transitions.

Findings

Skyrmions are stable below a specific DM coefficient threshold.

Above the threshold, the energy becomes unbounded, indicating instability.

The results mathematically explain experimentally observed phase transitions.

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 D\"oring 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.