Spin Current as a Probe of the ${\mathbb{Z}}_{2}$-Vortex Topological Transition in the Classical Heisenberg Antiferromagnet on the Triangular Lattice

Spin Current as a Probe of the $Z_{2}$ -Vortex Topological Transition in the Classical Heisenberg Antiferromagnet on the Triangular Lattice

K. Aoyama and H. Kawamura

Phys. Rev. Lett. 124, 047202 – Published 29 January 2020

Abstract

We have theoretically investigated transport properties of the classical Heisenberg antiferromagnet on the triangular lattice, in which a binding-unbinding topological transition of $Z_{2}$ 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 $Z_{2}$ vortex whose lifetime gets longer toward $T_{v}$ . The result suggests that the spin-current measurement is a promising probe to detect the $Z_{2}$ -vortex topological transition, which has remained elusive in experiments.