Chiral skyrmions of large radius

TL;DR

This paper rigorously analyzes large-radius chiral skyrmions in ferromagnets with Dzyaloshinskii-Moriya interaction, identifying the critical parameter where skyrmion radius diverges and energy vanishes, indicating a phase transition.

Contribution

It provides explicit formulas and asymptotic analysis for the skyrmion profile, energy, and critical parameters, advancing theoretical understanding of skyrmion behavior at large sizes.

Findings

Critical parameter for skyrmion radius divergence identified

Explicit asymptotic formulas for skyrmion energy derived

Skyrmion energy is an odd function of radius

Abstract

We study the structure of an axially symmetric magnetic skyrmion in a ferromagnet with the Dzyaloshinskii-Moriya interaction. We examine the regime of large skyrmions and we identify rigorously the critical value of the dimensionless parameter at which the skyrmion radius diverges to infinity, while the skyrmion energy converges to zero. This critical value coincides with the expected transition point from the uniform phase, which accommodates the skyrmion as an excited state, to the helical phase, which has negative energy. We give the profile field at the skyrmion core, its outer field, and the intermediate field at the skyrmion domain wall. Moreover, we derive an explicit formula for the leading asymptotic behavior of the energy as well as the leading term and first asymptotic correction for the value of the critical parameter. The key leading to the results is a parity theorem that utilizes exact formulae for the asymptotic behavior of the solutions of the static Landau-Lifshitz equation centered at the skyrmion domain wall. The skyrmion energy is shown to be an odd function of the radius and the dimensionless parameter to be an even function.