Evidence of a Phonon Hall Effect in the Kitaev Spin Liquid Candidate α-RuCl_{3}

Abstract

The material α-RuCl_{3} has been the subject of intense scrutiny as a potential Kitaev quantum spin liquid, predicted to display Majorana fermions as low-energy excitations. In practice, α-RuCl_{3} undergoes a transition to a state with antiferromagnetic order below a temperature T_{N}≈7 K, but this order can be suppressed by applying an external in-plane magnetic field of H_{∥}=7 T. Whether a quantum spin liquid phase exists just above that field is still an open question, but the reported observation of a quantized thermal Hall conductivity at H_{∥}>7 T by Kasahara and co-workers [Nature (London) 559, 227 (2018)NATUAS0028-083610.1038/s41586-018-0274-0] has been interpreted as evidence of itinerant Majorana fermions in the Kitaev quantum spin liquid state. In this study, we reexamine the origin of the thermal Hall conductivity κ_{xy} in α-RuCl_{3}. Our measurements of κ_{xy}(T) on several different crystals yield a temperature dependence very similar to that of the phonon-dominated longitudinal thermal conductivity κ_{xx}(T), for which the natural explanation is that κ_{xy} is also mostly carried by phonons. Upon cooling, κ_{xx} peaks at T≃20 K, then drops until T_{N}, whereupon it suddenly increases again. The abrupt increase below T_{N} is attributed to a sudden reduction in the scattering of phonons by low-energy spin fluctuations as these become partially gapped when the system orders. The fact that κ_{xy} also increases suddenly below T_{N} is strong evidence that the thermal Hall effect in α-RuCl_{3} is also carried predominantly by phonons. This implies that any quantized signal from Majorana edge modes would have to come on top of a sizable—and sample-dependent—phonon background.