Stability and asymptotic interactions of chiral magnetic skyrmions in a tilted magnetic field

TL;DR

This paper analytically calculates the interaction potentials between chiral magnetic skyrmions in a tilted magnetic field, revealing oscillating behaviors and stability predictions that align with numerical results, advancing understanding of skyrmion interactions.

Contribution

It introduces an analytical framework for skyrmion interactions in tilted fields, interpreting Dzyaloshinskii-Moriya interaction as a gauge field, and predicts stability features matching numerical data.

Findings

Interaction potentials exhibit oscillations in tilted fields.

Analytical predictions closely match numerical stability observations.

DMI interpreted as a background gauge field influences skyrmion interactions.

Abstract

Using a general framework, interaction potentials between chiral magnetic solitons in a planar system with a tilted external magnetic field are calculated analytically in the limit of large separation. The results are compared to previous numerical results for solitons with topological charge $\pm 1$. A key feature of the calculation is the interpretation of Dzyaloshinskii-Moriya interaction (DMI) as a background $SO(3)$ gauge field. In a tilted field, this leads to a $U(1)$-gauged version of the usual equation for spin excitations, leading to a distinctive oscillating interaction profile. We also obtain predictions for skyrmion stability in a tilted field which closely match numerical observations.