Magnetic skyrmion interactions in the micromagnetic framework

Magnetic skyrmions are localized swirls of magnetization with a nontrivial 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 that can generate arbitrary repulsive interaction potentials from the micromagnetic Hamiltonian, using it to provide a correction to the interaction between a skyrmion and the boundary of its material. We also discuss a toy model of the radial profile of a skyrmion, which is accurate for a wide range of material parameters.