A theory on skyrmion size

Abstract A magnetic skyrmion is a topological object consisting of a skyrmion core, an outer domain, and a wall that separates the skyrmion core from the outer domain. The skyrmion size and wall width are two fundamental quantities of a skyrmion that depend sensitively on material parameters such as exchange energy, magnetic anisotropy, Dzyaloshinskii–Moriya interaction, and magnetic field. However, quantitative understanding of the two quantities is still very poor. Here we present a general theory on skyrmion size and wall width. The two formulas we obtained agree almost perfectly with simulations and experiments for a wide range of parameters, including most of the existing materials that support skyrmions.