Phonon Hall viscosity of and the thermal Hall effect of RuCl₃

The origin of the thermal Hall effect in RuCl₃ remains controversial. In particular, a sizable phonon contribution complicates the interpretation of a quantized thermal Hall conductivity [1,2]. An intriguing possibility is that phonons contribute to the thermal Hall effect through intrinsic coupling to low-energy spin excitations, acquiring Berry curvature and Hall viscosity [3]. We use pulse echo ultrasound to measure the Hall viscosity of RuCl₃ through its field-induced magnetic phase transition and find nonzero Hall viscosity near the transition, where the thermal Hall conductivity peaks. Our measurement suggests that phonons coupled to spin excitations contribute to the thermal Hall effect in RuCl₃.

[1] Yokoi et al. Science 373, 568 (2021).

[2] E Lefrancois et al. PRX 12, 021025 (2022).

[3] T. Qin et al. PRB 86, 104305 (2012).