Compactness results for static and dynamic chiral skyrmions near the conformal limit

TL;DR

This paper investigates the existence, compactness, and stability of chiral skyrmions in magnetic systems near the conformal limit, considering perturbations like helicity and potential terms, with implications for dynamic behavior under external currents.

Contribution

It provides new results on the existence, compactness, and asymptotic behavior of chiral skyrmions in perturbed harmonic map models near the conformal limit, including their dynamic stability.

Findings

Existence of relative minimizers in a non-trivial homotopy class.

Strong compactness of almost minimizers.

Asymptotic analysis of skyrmions and their stability under external currents.

Abstract

We examine lower order perturbations of the harmonic map prob- lem from $\mathbb{R}^2$ to $\mathbb{S}^2$ including chiral interaction in form of a helicity term that prefers modulation, and a potential term that enables decay to a uniform background state. Energy functionals of this type arise in the context of magnetic systems without inversion symmetry. In the almost conformal regime, where these perturbations are weighted with a small parameter, we examine the existence of relative minimizers in a non-trivial homotopy class, so-called chiral skyrmions, strong compactness of almost minimizers, and their asymptotic limit. Finally we examine dynamic stability and compactness of almost minimizers in the context of the Landau-Lifshitz-Gilbert equation including spin-transfer torques arising from the interaction with an external current.