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.

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

## Preprint

Comment: 35 pages, 9 figures

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