Dynamical correlations from mobile vortices in two-dimensional easy-plane ferromagnets

Abstract

Assuming an ideal gas of unbound vortices above the Kosterlitz-Thouless transition temperature, we calculate the dynamic form factors for both the in-plane and out-of-plane correlations. In both cases central peaks are predicted which are, however, produced by quite different mechanisms, depending on whether the correlations are globally or locally sensitive to the presence of the vortices. For the in-plane correlations the wave-vector dependencies of the width and intensity of the peaks are very well supported by the central peaks, which are observed in a combined Monte Carlo molecular-dynamics simulation of the XY model. Therefore the parameters of the theory (root-mean-square vortex velocity and mean vortex-vortex separation) can be fitted and turn out to agree rather well with independent theoretical estimates. Recent inelastic neutron-scattering experiments on the in-plane correlations for ${\mathrm{BaCo}}_2$(${\mathrm{AsO}}_4$ ${)}_2$ and ${\mathrm{Rb}}_2$ ${\mathrm{CrCl}}_4$ also show central peaks. Their temperature and wave-vector dependencies are consistent with our results, but their widths are larger than the theoretical estimates. Therefore, these peaks are interpreted to result, at least partially, from a gas of vortices. For the out-of-plane correlations our simulations also show a central peak. However so far it cannot be identified unequivocally as a vortex contribution.