  Chiral magnetic skyrmions are topological solitons, of significant physical
interest, arising in ferromagnets described by a micromagnetic energy including
a chiral (Dzyaloshinskii-Moriya) interaction term. We show that for small
chiral interaction, the skyrmions on $\mathbb{R}^2$ with co-rotational symmetry
are close to harmonic maps, and prove precise bounds on the differences. One
application of these bounds is precise energy asymptotics. Another (pursued in
a separate work) is an alternate, quantitative proof of the recent skyrmion
stability result of Li-Melcher.
