Thermal Hall effect in the Kitaev-Heisenberg system with spin-phonon coupling

Motivated by the giant phonon anomalies in alpha-RuCl3 reported by H. Li et al. [Nat. Commun. 12, 3513 (2021)], we investigate the thermal Hall effect in a Kitaev-Heisenberg system in the presence of the coupling between spins and phonons arising from chlorine atoms' vibration. We observe that the coupling modifies the relative stability between different magnetic states under a magnetic field, especially stabilizing a canted zigzag antiferromagnetic state. Remarkably, the spin-phonon interaction has distinct effects on the thermal Hall conductivity in different magnetically ordered states. For a canted zigzag state, which is relevant to alpha-RuCl3, the spin-phonon interaction enhances the magnon excitation gap induced by a magnetic field and suppresses the thermal Hall conductivity at low temperatures. For the Kitaev spin liquid state, we find that the spin-phonon interaction reduces the excitation gap of Majorana fermions and destabilizes the quantized thermal Hall effect. Our results demonstrate a crucial role of phonon degrees of freedom in the thermal Hall effect in Kitaev materials.

Automated summary

Motivated by the giant phonon anomalies in alpha-RuCl3, this study investigates the thermal Hall effect in a Kitaev-Heisenberg system with spin-phonon coupling. The results show that the coupling has different effects on the thermal Hall conductivity in different magnetically ordered states. For alpha-RuCl3, it enhances the magnon excitation gap and suppresses the thermal Hall conductivity, while for the Kitaev spin liquid state, it reduces the excitation gap of Majorana fermions and destabilizes the quantized thermal Hall effect.