Chiral phase transition and thermal Hall effect in an anisotropic spin model on the kagome lattice

TL;DR

This paper investigates how a chiral phase transition in an anisotropic kagome lattice spin model influences the thermal Hall effect, revealing a controllable switch for thermal transport via magnetic field and temperature adjustments.

Contribution

It demonstrates the link between chiral symmetry breaking and thermal Hall conductivity, including topological magnon band transitions, in an extended Heisenberg model.

Findings

Thermal Hall conductivity is zero above the chiral transition temperature.

Chiral symmetry breaking induces a non-zero thermal Hall effect at low temperatures.

The model allows control of thermal transport by magnetic field and temperature.

Abstract

We present a study of the thermal Hall effect in the extended Heisenberg model with $XXZ$ anisotropy in the kagome lattice. This model has the particularity that, in the classical case, and for a broad region in parameter space, an external magnetic field induces a chiral symmetry breaking: the ground state is a doubly degenerate $q=0$ order with either positive or negative net chirality. Here, we focus on the effect of this chiral phase transition in the thermal Hall conductivity using Linear-Spin-Waves theory. We explore the topology and calculate the Chern numbers of the magnonic bands, obtaining a variety of topological phase transitions. We also compute the magnonic effect to the critical temperature associated with the chiral phase transition ($T_c^{SW}$). Our main result is that, the thermal Hall conductivity, which is null for $T>T_c^{SW}$, becomes non-zero as a consequence of the spontaneous chiral symmetry breaking at low temperatures. Therefore, we present a simple model where it is possible to "switch" on/off the thermal transport properties introducing a magnetic field and heating or cooling the system.