Magnetic skyrmion interactions in the micromagnetic framework

Magnetic skyrmions are localized swirls of magnetization with a non-trivial
topological winding number. This winding increases their robustness to
superparamagnetism and gives rise to a myriad of novel dynamical properties,
making them attractive as next-generation information carriers. Recently the
equation of motion for a skyrmion was derived using the approach pioneered by
Thiele, allowing for macroscopic skyrmion systems to be modeled efficiently.
This powerful technique suffers from the prerequisite that one must have a
priori knowledge of the functional form of the interaction between a skyrmion
and all other magnetic structures in its environment. Here we attempt to
alleviate this problem by providing a simple analytic expression which can
generate arbitrary repulsive interaction potentials from the micromagnetic
Hamiltonian. We also discuss a toy model of the radial profile of a skyrmion
which is accurate for a wide range of material parameters.