Rotating vortex dipoles in ferromagnets.

Vortex-antivortex pairs are spontaneously created in magnetic elements. In the case of opposite vortex polarities the pair has a nonzero topological charge, and it behaves as a rotating vortex dipole. We find theoretically and confirm numerically its energy as a function of angular momentum and the associated rotation frequencies. The annihilation process of the pair changes the topological charge while the energy is monotonically decreasing. The change of topological charge affects the dynamics profoundly. We finally discuss the implications of our results for Bloch point dynamics.