The profile of chiral skyrmions of small radius

Chiral skyrmions are stable particle-like solutions of the Landau–Lifshitz equation for ferromagnets with the Dzyaloshinskii–Moriya (DM) interaction, characterized by a topological number. We study the profile of an axially symmetric skyrmion and give exact formulae for the solution of the corresponding far-field and near-field equations, in the asymptotic limit of small DM parameter (alternatively large anisotropy). The matching of these two fields leads to a formula for the skyrmion radius as a function of the DM parameter. The derived solutions show the different length scales which are present in the skyrmion profiles. The picture is thus created of a chiral skyrmion that is born out of a Belavin–Polyakov solution with an infinitesimally small radius, as the DM parameter is increased from zero. The skyrmion retains the Belavin–Polyakov profile over and well-beyond the core before it assumes an exponential decay; the profile of an axially-symmetric Belavin–Polyakov solution of unit degree plays the role of the universal core profile of chiral skyrmions.