Dynamics of vortex-antivortex pairs in ferromagnets

We study the dynamics of vortex-antivortex (VA) pairs in an infinitely thin ferromagnetic film with easy-plane anisotropy. These are localized excitations with finite energy that are characterized by a topological (skyrmion) number N = 0,+1,-1. Topologically trivial (N=0) VA pairs undergo Kelvin motion analogous to that encountered in fluid dynamics. In contrast, topologically nontrivial (N = +1,-1) VA pairs perform rotational motion around a fixed guiding center. We present the results of a detailed study in both cases and further demonstrate that in the presence of dissipation a rotating N = +1,-1 VA pair shrinks to a point and is annihilated, due to the discreteness of the lattice, thus leading to a "topologically forbidden" (Delta N = 1) process. We argue that the latter process underlies the experimentally observed vortex core switching whereby the polarity of a single vortex is reversed after collision with an N = 0 VA pair created by a burst of an applied alternating magnetic field.