Spin-dynamics simulations of the triangular antiferromagneticXYmodel

Abstract

Using Monte Carlo and spin-dynamics methods, we have investigated the dynamic behavior of the classical, antiferromagnetic XY model on a triangular lattice with linear sizes $L<~300.$ The temporal evolutions of spin configurations were obtained by solving numerically the coupled equations of motion for each spin using fourth-order Suzuki-Trotter decompositions of exponential operators. From space- and time-displaced spin-spin correlation functions and their space-time Fourier transforms we obtained the dynamic structure factor $S(\mathbf{q},w)$ for momentum $\mathbf{q}$ and frequency $\ensuremath{\omega}.$ Below ${T}_{\mathrm{KT}}$ (Kosterlitz-Thouless transition), both the in-plane ${(S}^{\mathrm{xx}})$ and out-of-plane ${(S}^{\mathrm{zz}})$ components of $S(\mathbf{q},\ensuremath{\omega})$ exhibit very strong and sharp spin-wave peaks. Well above ${T}_{\mathrm{KT}},$ ${S}^{\mathrm{xx}}$ and ${S}^{\mathrm{zz}}$ apparently display a central peak, and spin-wave signatures are still seen in ${S}^{\mathrm{zz}}.$ In addition, we also observed an almost dispersionless domain-wall peak at high $\ensuremath{\omega}$ below ${T}_{c}$ (Ising transition), where long-range order appears in the staggered chirality. Above ${T}_{c},$ the domain-wall peak disappears for all q. The line shape of these peaks is captured reasonably well by a Lorentzian form. Using a dynamic finite-size scaling theory, we determined the dynamic critical exponent $z=1.002(3).$ We found that our results demonstrate the consistency of the dynamic finite-size scaling theory for the characteristic frequency ${\ensuremath{\omega}}_{m}$ and the dynamic structure factor $S(\mathbf{q},\ensuremath{\omega})$ itself.