Topological magnons for thermal Hall transport in frustrated magnets with bond-dependent interactions

Thermal transport in topologically-ordered phases of matter provides valuable insights as it can detect the charge-neutral quasiparticles that would not directly couple to electromagnetic probes. An important example is the edge heat transport of the Majorana fermions in a chiral spin liquid, which leads to a half-quantized thermal Hall conductivity. This signature is precisely what has recently been measured in alpha-RuCl3 under external magnetic fields. The plateau-like behavior of the half-quantized thermal Hall conductivity as a function of external magnetic field, and the peculiar sign change depending on the magnetic field orientations, have been proposed to be strong evidence for the non-Abelian Kitaev spin liquid. On the other hand, for in-plane magnetic fields, it has been theoretically shown that such a sign structure can also arise from topological magnons in the field-polarized state. In this paper, we investigate the full implications of topological magnons as heat carriers on thermal transport measurements. We first prove analytically that for any commensurate order with a finite magnetic unit cell, reversing the field direction leads to a sign change in the magnon thermal Hall conductivity in two-dimensional systems. We corroborate this proof numerically with nontrivial magnetic orders as well as the field-polarized state in Kitaev magnets subjected to an in-plane field. In the case of the tilted magnetic field, in which there exists both finite in-plane and out-of-plane field components, we find that the plateau-like behavior of the thermal Hall conductivity and the sign change upon the reversal of the in-plane component of the magnetic field arises in the partially polarized state, as long as the in-plane field contribution to the Zeeman energy is significant. While these results are consistent with the experimental observations, we comment on other aspects that require further investigation in future studies.

Automated summary

Thermal transport in topologically-ordered phases provides valuable insights by detecting charge-neutral quasiparticles that do not couple directly to electromagnetic probes. The half-quantized thermal Hall conductivity observed in alpha-RuCl3 under external magnetic fields is evidence of the presence of the non-Abelian Kitaev spin liquid. In the case of tilted magnetic fields, the plateau-like behavior and sign change of the thermal Hall conductivity arise in the partially polarized state.