Thermal Hall conductivity with sign change in the Heisenberg-Kitaev kagome magnet

TL;DR

This paper investigates the topological magnon excitations and thermal Hall conductivity in the Heisenberg-Kitaev model on kagome lattices, revealing a sign change in the thermal Hall effect linked to scalar spin chirality and Chern number variations.

Contribution

It demonstrates how the scalar spin chirality and magnon band topology change across the Klein duality boundary, causing a sign reversal in thermal Hall conductivity in the kagome lattice HK model.

Findings

Sign change in scalar spin chirality across the KFM point.

Opposite Chern numbers of magnon bands in two regions.

Reversal of magnon thermal Hall conductivity sign.

Abstract

The Heisenberg-Kitaev (HK) model on various lattices have attracted a lot of attention because they may lead to exotic states such as quantum spin liquid and topological orders. The rare-earth-based kagome lattice (KL) compounds $\rm{Mg_2RE_3Sb_3O_{14}}$ $\rm{(RE=Gd, Er)}$ and $\rm{(RE=Nd)}$ have ${\bf q=0}$, $120^\circ$ order and canted ferromagnetic (CFM) order, respectively. Interestingly, the HK model on the KL has the same ground state long-range orders. In the theoretical phase diagram, the CFM phase resides in a continuous parameter region and there is no phase change across special parameter points, such as the Kitaev ferromagnetic (KFM) point, the ferromagnetic (FM) point and its dual FM point. However, a ground state property cannot distinguish a system with or without topological nontrivial excitations and related phase transitions. Here, we study the topological magnon excitations and related thermal Hall conductivity in the HK model on the KL with CFM order. The CFM phase can be divided into two regions related by the Klein duality, with the self dual KFM point as their boundary. We find that the scalar spin chirality which is intrinsic in the CFM order changes sign across the KFM point. This leads to the opposite Chern numbers of corresponding magnon bands in the two regions, and also the sign change of the magnon thermal Hall conductivity.