The Annihilation of Vortex Anti-Vortex Pairs

We study theoretically the annihilation of a vortex-antivortex pair in a two-dimensional easy-plane ferromagnet. 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 compare predictions of analytical theory to results of micromagnetic simulations.