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

TL;DR

This study numerically analyzes spin and thermal transport near the Néel transition in 3D antiferromagnets, revealing divergent spin conductivity in certain cases and featureless thermal conductivity at the transition.

Contribution

It demonstrates how exchange anisotropy affects spin conductivity divergence and provides numerical evidence for critical phenomena in 3D antiferromagnetic models.

Findings

Longitudinal spin conductivity diverges near T_N in XY and Heisenberg cases.

Thermal conductivity remains featureless at T_N across all cases.

Spin-current relaxation time diverges as a power law approaching T_N.

Abstract

We investigate spin and thermal transport near the N\'{e}el 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 $\Delta=J_z/J_x$ 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 $\Delta \leq 1$, the longitudinal spin conductivity $\sigma^s_{\mu\mu}$ exhibits a divergent enhancement on cooling toward $T_N$, while not in the Ising case of $\Delta>1$. In all the three cases, the temperature dependence of the thermal conductivity $\kappa_{\mu\mu}$ is featureless at $T_N$, being consistent with experimental results. The divergent enhancement of $\sigma^s_{\mu\mu}$ 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 $\sigma^s_{\mu\mu}$ is rapidly suppressed below $T_N$, $\sigma^s_{\mu\mu}$ likely remains divergent even below $T_N$ in the Heisenberg case, which might experimentally be observed in the ideally isotropic antiferromagnet RbMnF$_3$.