Annihilation of Vortex-Antivortex Pairs in Thin Ferromagnetic Films

We study theoretically the annihilation of a vortex-antivortex pair in a two-dimensional easy-plane ferromagnet. The motion is governed by the interplay of three types of forces: attraction between the vortices mediated by exchange interaction, a gyroscopic force proportional to the vortex's velocity and orthogonal to it, and viscous forces. For opposite out-of-plane orientations of the vortex cores, the two solitons orbit each other. In the presence of finite damping, the radius of the orbit gradually decreases until the cores overlap. We show that the viscous forces involve several components. In addition to the expected viscous force proportional to the vortex's velocity and opposing it, there is mutual drag exerted by vortices on each other. In addition, image vortices, created by the sample edge, also generate appreciable drag on the real ones. We compare predictions of analytical theory to results of micromagnetic simulations.