Spin dynamics simulations of two-dimensional clusters with Heisenberg and dipole-dipole interactions

Spin dynamics with the Landau-Lifshitz equation has provided topics for a wealth of research endeavors. We introduce here a numerical integration method which explicitly uses the precession motion of a spin about the local field, thus intrinsically conserving spin lengths, and therefore allowing for relatively quick results for a large number of situations with varying temperatures and couplings. This method is applied to the effect of long-range dipole-dipole interactions in two-dimensional clusters of spins with nearest-neighbor XY-Heisenberg exchange interactions on a square lattice at finite temperature. The structures thus obtained are analyzed through orientational correlations functions. Magnon dispersion curves, different from those of the standard Heisenberg model, are obtained and discussed. The number of vortices in the system is discussed as a function of temperature and typical examples of vortex dynamics are shown.