PREPRINT

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

Bruno Barton-Singer and Bernd J. Schroers

Submitted on 15 November 2022

## 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 $±1$. A key feature of the calculation is the interpretation of Dzyaloshinskii-Moriya interaction (DMI) as a background $SO\left(3\right)$ gauge field. In a tilted field, this leads to a $U\left(1\right)$-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.

## Preprint

Comment: 35 pages, 9 figures

Subjects: Condensed Matter - Mesoscale and Nanoscale Physics; High Energy Physics - Theory; Mathematical Physics; 70S20