Proposed effective Hamiltonians from the literature for the material $\alpha -\mathrm{RuCl}{}_3$ are used to compute the magnon thermal Hall conductivity ${\kappa }_{xy}$ using linear spin-wave theory for the magnetically ordered state. No model previously proposed that was tested explains the published experimental data. Models with Kitaev interaction $K>0$ are seen to predict ${\kappa }_{xy}\gtrsim 0$, which is inconsistent with the data. Fluctuations toward a Kitaev-type spin liquid would have the wrong sign to explain the data. However, a slight variant of a previously proposed model predicts a large ${\kappa }_{xy}$, demonstrating that the low-temperature thermal Hall effect could be generated exclusively by the Berry curvature of the magnon bands. The experimental data of ${\kappa }_{xy}$ can therefore serve as another method to constrain a proposed effective Hamiltonian.

• Received 15 July 2018
• Revised 10 August 2018

DOI:https://doi.org/10.1103/PhysRevB.98.060412