Effects of magnetic anisotropy on spin and thermal transport in classical antiferromagnets on the square lattice

Abstract

Transport properties of the classical antiferromagnetic XXZ model on the square lattice have been theoretically investigated, putting emphasis on how the occurrence of a phase transition is reflected in spin and thermal transports. As is well known, the anisotropy of the exchange interaction $\mathrm{\ensuremath{\Delta}}\ensuremath{\equiv}{J}_{z}/{J}_{x}$ plays a role to control the universality class of the transition of the model, i.e., either a second-order transition at ${T}_{N}$ into a magnetically ordered state or the Kosterlitz-Thouless (KT) transition at ${T}_{\text{KT}}$, which respectively occur for the Ising-type ($\mathrm{\ensuremath{\Delta}}>1$) and XY-type ($\mathrm{\ensuremath{\Delta}}<1$) anisotropies, while for the isotropic Heisenberg case of $\mathrm{\ensuremath{\Delta}}=1$, a phase transition does not occur at any finite temperature. It is found by means of the hybrid Monte Carlo and spin-dynamics simulations that the spin current probes the difference in the ordering properties, while the thermal current does not. For the XY-type anisotropy, the longitudinal spin-current conductivity ${\ensuremath{\sigma}}_{xx}^{s}$ ($={\ensuremath{\sigma}}_{yy}^{s}$) exhibits a divergence at ${T}_{\text{KT}}$ of the exponential form ${\ensuremath{\sigma}}_{xx}^{s}\ensuremath{\propto}exp\left[B/\sqrt{T/{T}_{\text{KT}}\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}\right]$ with $B=O(1)$, while for the Ising-type anisotropy, the temperature dependence of ${\ensuremath{\sigma}}_{xx}^{s}$ is almost monotonic without showing a clear anomaly at ${T}_{N}$ and such a monotonic behavior is also the case in the Heisenberg-type spin system. The significant enhancement of ${\ensuremath{\sigma}}_{xx}^{s}$ at ${T}_{\text{KT}}$ is found to be due to the exponential rapid growth of the spin-current relaxation time toward ${T}_{\text{KT}}$, which can be understood as a manifestation of the topological nature of a vortex whose lifetime is expected to get longer toward ${T}_{\text{KT}}$. Possible experimental platforms for the spin-transport phenomena associated with the KT topological transition are discussed.