  We examine lower order perturbations of the harmonic map prob- lem from
$\mathbb{R}^2$ to $\mathbb{S}^2$ including chiral interaction in form of a
helicity term that prefers modulation, and a potential term that enables decay
to a uniform background state. Energy functionals of this type arise in the
context of magnetic systems without inversion symmetry. In the almost conformal
regime, where these perturbations are weighted with a small parameter, we
examine the existence of relative minimizers in a non-trivial homotopy class,
so-called chiral skyrmions, strong compactness of almost minimizers, and their
asymptotic limit. Finally we examine dynamic stability and compactness of
almost minimizers in the context of the Landau-Lifshitz-Gilbert equation
including spin-transfer torques arising from the interaction with an external
current.
