Phonon Hall viscosity and the intrinsic thermal Hall effect of α-RuCl₃

The thermal Hall effect has been observed in a wide variety of magnetic insulators^1-9, yet its origins remain controversial. Although some studies attribute the effect to intrinsic mechanisms^10-14, such as heat carriers with Berry curvature, others propose extrinsic mechanisms^15-17, such as heat carriers scattering off crystal defects. Even the nature of the heat carriers is unknown: magnons, phonons and fractionalized spin excitations have all been proposed. Resolving these issues is essential for the study of quantum spin liquids, and particularly for α-RuCl₃, in which a quantized thermal Hall effect has been attributed to Majorana edge modes^18,19. Here we use ultrasonic measurements of the acoustic Faraday effect to demonstrate that the phonons in α-RuCl₃ have Hall viscosity-a non-dissipative viscosity that rotates phonon polarizations and deflects phonon heat currents. We show that phonon Hall viscosity produces an intrinsic thermal Hall effect that quantitatively accounts for a substantial fraction of the measured thermal Hall effect in α-RuCl₃: the thermal Hall effect in α-RuCl₃ is due to phonons, and it is intrinsic. More broadly, we demonstrate that the acoustic Faraday effect is a powerful tool for detecting phonon Hall viscosity and the associated phonon Berry curvature, offering a new way to uncover and study exotic states of matter that elude conventional experiments.