We study the nature of the debated thermal Hall effect in the candidate Kitaev material $\alpha \text{−}{\mathrm{RuCl}}_3$. Without assuming the existence of a gapped spin liquid, we show that a realistic minimal spin model in the canted zigzag phase suffices, at the level of linear spin-wave theory, to qualitatively explain the observed temperature and magnetic field dependence of the nonquantized thermal Hall conductivity ${\kappa }_{xy}$, with its origin lying in the Berry curvature of the magnon bands. The magnitude of the effect is, however, too small compared to the measurement by Czajka et al. [Nat. Mater. 22, 36 (2023)]—after scanning a broad range of model parameters ($6\times {10}^5$ different sets), we find an empirical upper bound on ${\kappa }_{xy}/T$ to be $\sim 0.2\pi k_B^2/6\hslash$ or about $40\%$ of the value expected from Majorana edge modes. Recent experiments suggest that phonon contribution to the thermal Hall effect cannot be neglected. We show that even by including magnetoelastic coupling of phonons to spins, the resulting intrinsic contribution, from both magnons and phonons, is, however, still insufficient to explain the observed magnitude of the Hall signal. After careful analysis of the extrinsic phonon mechanisms, we use the recent experimental data on thermal transport in $\alpha \text{−}{\mathrm{RuCl}}_3$ by Lefrançois et al. [Phys. Rev. X 12, 021025 (2022)] to determine the phenomenological ratio of the extrinsic and intrinsic contributions, $\eta \equiv {\kappa }_{xy}^E/{\kappa }_{xy}^I$. We find $\eta =1.2\pm 0.5$, i.e., the extrinsic contribution, most likely due to side-jump scattering of phonons off of defects, contributes about half of the observed thermal Hall. When combined with our computed intrinsic value, this quantitatively explains both the magnitude and detailed temperature dependence of the experimental thermal Hall effect in $\alpha \text{−}{\mathrm{RuCl}}_3$.

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• Frustrated magnetism
• Magnetism
• Magnetoelastic effect
• Thermal Hall effect
• Thermal conductivity