Dynamics of spin vortices in two-dimensional planar magnets

We investigate the dynamics of a dilute gas of free spin vortices in a two-dimensional planar magnet. An equation of motion for the spin vortex is presented and compared with the corresponding equation for a vortex in a superfluid film. Exploiting a similar analogy with the dynamics of a two-dimensional plasma in a perpendicular magnetic field we calculate the mean-square vortex velocity and the vortex self-diffusion constant in the critical region above the phase transition. When combined with equations obtained previously for the spin-autocorrelation functions, our results provide an approximate description of the vortex contribution to the critical dynamics outside of the hydrodynamic regime.