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

To confirm that the antisymmetric signal we measure is not an artifact of the experimental technique, we show the antisymmetric in field amplitude of transmitted longitudinal sound and reflected transverse sound. Compressional sound does not exhibit a Faraday rotation and therefore should have no antisymmetric in field component. Reflected transverse sound can exhibit a Faraday rotation, but the effect disappears on antisymmetrization because when the same transducer is used to excited and detect the sound wave the transducer cannot distinguish between clockwise and counterclockwise rotations. a, shows the null signal for sample 1 in a tilted magnetic field and b, shows the null signal for sample 2 with the magnetic field along the crystal c axis. In both cases, the antisymmetric signal for transmitted transverse sound exceeds the null signal by an order of magnitude. Symmetry constrains the Faraday rotation to occur only when the applied magnetic field has a component along the crystal c axis. Here we show the antisymmetric signal for magnetic field applied entirely in the plane (θ = 90°, where we expect no Faraday rotation) versus with an out-of-plane component of the magnetic field. c, shows the result for sample 1 along with the 55° data presented in the main text. d, shows the same for sample 2 with the 0° data from the main text. In both cases, we find no evidence of Faraday rotation with the magnetic field applied entirely in the honeycomb plane. Note that this does not imply that there is no thermal Hall effect for this magnetic field orientation; only that the Hall viscosity component we measure, η xzyz , is zero.