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

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.