Geometry and Dynamics of Magnetic Skyrmions

This talk is about vortex-like structures in planar ferromagnetic materials which are stabilised by the so-called Dzyaloshinski-Moryia (DM) interaction. The vortex structures, called magnetic skyrmions in this context, are widely studied in physics because of their potential role in future magnetic information storage devices. The DM term is linear in the gradient of the magnetisation field and can be interpreted in terms of a non-abelian gauge field. The applicability of techniques from complex geometry and gauge theory is rather surprising in this model, and leads to an infinite family of exact solutions for special values of coupling constants. I will discuss the solutions and their relation to the variational equations at generic values of couplings, and also comment on the dynamics of magnetic skyrmions in response to an applied current.