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

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(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.