Dynamic correlations in the classical two-dimensional antiferromagnetic Heisenberg model with easy-plane symmetry

We investigate the dynamics of the two-dimensional antiferromagnetic Heisenberg model with easy-plane exchange symmetry. We develop a phenomenology of spin-wave and vortex excitations and calculate their contributions to the dynamical correlation functions ${\mathit{S}}^{\mathrm{\alpha }\mathrm{\alpha }}$(q,ω), α=x,y,z. The vortex shape depends explicitly on an exchange anisotropy parameter λ and changes from a mainly in-plane structure below a critical ${\lambda }_{\mathit{c}}$ to a shape with well-established z components around the vortex center above ${\lambda }_{\mathit{c}}$. In this paper we will discuss only the case λ<${\lambda }_{\mathit{c}}$, where the system behaves almost like the pure XY model. The general properties of the dynamical behavior of the spin waves and vortices below the Kosterlitz-Thouless transition temperature ${\mathit{T}}_{\mathrm{KT}}$ have been widely examined for the ferromagnetic XY model, and do not change much in the antiferromagnet (although here we have two magnon branches according to the two different spin sublattices). Our main interest is focused on the unbound vortices just above ${\mathit{T}}_{\mathrm{KT}}$. Assuming a dilute gas of ballistically moving vortices, we obtain central peaks in ${\mathit{S}}^{\mathrm{\alpha }\mathrm{\alpha }}$(q,ω) similar to the ferromagnetic case, but in some cases at different positions in q space depending on whether the static vortex structure or the deviation from it due to a finite velocity dominates the correlations. These results are compared with a combined Monte Carlo–molecular-dynamics simulation on a 100×100 square lattice. The phenomenological predictions for the correlation functions and the integrated intensities describe the numerical results quite well and, by comparing both methods, we obtain values for the vortex correlation length, which are in good agreement with the Kosterlitz-Thouless theory.