Spin current as a probe of the $\mathbb{Z}_2$-vortex topological transition in the classical Heisenberg antiferromagnet on the triangular lattice

TL;DR

This study shows that spin-current conductivity diverges at the $ ext{Z}_2$-vortex transition temperature in a classical Heisenberg antiferromagnet, proposing spin-current measurements as a way to detect this elusive topological transition.

Contribution

It demonstrates the divergence of spin-current conductivity at the $ ext{Z}_2$-vortex transition, linking topological vortex dynamics to measurable transport properties.

Findings

Spin-current conductivity diverges at $T_v$.

Thermal conductivity shows no anomaly at $T_v$.

Spin-current relaxation time increases rapidly near $T_v$.

Abstract

We have theoretically investigated transport properties of the classical Heisenberg antiferromagnet on the triangular lattice in which a binding-unbinding topological transition of $\mathbb{Z}_2$ vortices is predicted to occur at a finite temperature $T_v$. It is shown by means of the hybrid Monte-Carlo and spin-dynamics simulations that the longitudinal spin-current conductivity exhibits a divergence at $T_v$, while the thermal conductivity only shows a monotonic temperature dependence with no clear anomaly at $T_v$. The significant enhancement of the spin-current conductivity is found to be due to the rapid growth of the spin-current-relaxation time toward $T_v$, which can be understood as a manifestation of the topological nature of the free $\mathbb{Z}_2$ vortex whose lifetime gets longer toward $T_v$. The result suggests that the spin-current measurement is a promising probe to detect the $\mathbb{Z}_2$-vortex topological transition which has remained elusive in experiments.