Co-rotational chiral magnetic skyrmions near harmonic maps

TL;DR

This paper investigates co-rotational chiral magnetic skyrmions in ferromagnets with Dzyaloshinskii-Moriya interaction, showing they approximate harmonic maps for small chiral interaction and providing precise energy bounds.

Contribution

It establishes that such skyrmions are close to harmonic maps and derives precise bounds and energy asymptotics, advancing understanding of their structure and stability.

Findings

Skyrmions are close to harmonic maps for small chiral interaction.

Provides precise bounds on the difference between skyrmions and harmonic maps.

Derives energy asymptotics for these skyrmions.

Abstract

Chiral magnetic skyrmions are topological solitons, of significant physical interest, arising in ferromagnets described by a micromagnetic energy including a chiral (Dzyaloshinskii-Moriya) interaction term. We show that for small chiral interaction, the skyrmions on $\mathbb{R}^2$ with co-rotational symmetry are close to harmonic maps, and prove precise bounds on the differences. One application of these bounds is precise energy asymptotics. Another (pursued in a separate work) is an alternate, quantitative proof of the recent skyrmion stability result of Li-Melcher.