Evidence of a Phonon Hall Effect in the Kitaev Spin Liquid Candidate $\alpha$-RuCl${}_3$

Abstract

The material $\alpha$-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, $\alpha$-RuCl${}_3$ undergoes a transition to a state with antiferromagnetic order below a temperature $T_{\mathrm{N}}$ $\approx$ 7 K, but this order can be suppressed by applying an external in-plane magnetic field of $H_{\parallel }$ = 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 $H_{\parallel }$ $>$ 7 T by Kasahara and co-workers $[$Kasahara $etal$., Nature $559$, 227 (2018)$]$ has been interpreted as evidence of itinerant Majorana fermions in the Kitaev quantum spin liquid state. In this study, we re-examine the origin of the thermal Hall conductivity ${\kappa }_{\mathrm{xy}}$ in $\alpha$-RuCl${}_3$. Our measurements of ${\kappa }_{\mathrm{xy}}$($T$) on several different crystals yield a temperature dependence very similar to that of the phonon-dominated longitudinal thermal conductivity ${\kappa }_{\mathrm{xx}}$($T$), for which the natural explanation is that ${\kappa }_{\mathrm{xy}}$ is also mostly carried by phonons. Upon cooling, ${\kappa }_{\mathrm{xx}}$ peaks at $T\simeq$ 20 K, then drops until $T_{\mathrm{N}}$, whereupon it suddenly increases again. The abrupt increase below $T_{\mathrm{N}}$ 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 ${\kappa }_{\mathrm{xy}}$ also increases suddenly below $T_{\mathrm{N}}$ is strong evidence that the thermal Hall effect in $\alpha$-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.

6 pages, 3 figures

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• $\alpha$-RuCl3: a Spin-Orbit Assisted Mott Insulator on a Honeycomb Lattice
• Robustness of the thermal Hall effect close to half-quantization in a field-induced spin liquid state
• Giant thermal Hall conductivity from neutral excitations in the pseudogap phase of cuprates

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