Spin and thermal transport and critical phenomena in three-dimensional antiferromagnets

Abstract

We investigate spin and thermal transport near the N\'eel transition temperature ${T}_{N}$ in three dimensions by numerically analyzing the classical antiferromagnetic $XXZ$ model on the cubic lattice, where in the model, the anisotropy of the exchange interaction $\mathrm{\ensuremath{\Delta}}={J}_{z}/{J}_{x}$ plays a role to control the universality class of the transition. It is found by means of the hybrid Monte Carlo and spin-dynamics simulations that in the $XY$ and Heisenberg cases of $\mathrm{\ensuremath{\Delta}}\ensuremath{\le}1$, the longitudinal spin conductivity ${\ensuremath{\sigma}}_{\ensuremath{\mu}\ensuremath{\mu}}^{s}$ exhibits a divergent enhancement on cooling toward ${T}_{N}$ while not in the Ising case of $\mathrm{\ensuremath{\Delta}}>1$. In all three cases, the temperature dependence of the thermal conductivity ${\ensuremath{\kappa}}_{\ensuremath{\mu}\ensuremath{\mu}}$ is featureless at ${T}_{N}$, being consistent with experimental results. The divergent enhancement of ${\ensuremath{\sigma}}_{\ensuremath{\mu}\ensuremath{\mu}}^{s}$ toward ${T}_{N}$ is attributed to the spin-current relaxation time which gets longer toward ${T}_{N}$, showing a power-law divergence characteristic of critical phenomena. It is also found that in contrast to the $XY$ case where the divergence in ${\ensuremath{\sigma}}_{\ensuremath{\mu}\ensuremath{\mu}}^{s}$ is rapidly suppressed below ${T}_{N}, {\ensuremath{\sigma}}_{\ensuremath{\mu}\ensuremath{\mu}}^{s}$ likely remains divergent even below ${T}_{N}$ in the Heisenberg case, which might experimentally be observed in the ideally isotropic antiferromagnet ${\mathrm{RbMnF}}_{3}$.