Oscillations of the thermal conductivity in the spin-liquid state of α-RuCl<sub>3</sub>

Abstract

In the class of materials called spin liquids, a magnetically ordered state\ncannot be attained even at milliKelvin temperatures because of conflicting\nconstraints on each spin (for e.g. from geometric or exchange frustration). The\nresulting quantum spin-liquid (QSL) state is currently of intense interest\nbecause it exhibits novel excitations as well as wave-function entanglement.\nThe layered insulator $\\alpha$-RuCl$_3$ orders as a zigzag antiferromagnet\nbelow $\\sim$7 K in zero magnetic field. The zigzag order is destroyed when a\nmagnetic field $\\bf H$ is applied parallel to the zigzag axis a. Within the\nfield interval (7.3, 11) Tesla, there is growing evidence that a QSL state\nexists. Here we report the observation of oscillations in its thermal\nconductivity below 4 K. The oscillation amplitude is very large within the\ninterval (7.3, 11) T and strongly suppressed on either side. Paradoxically, the\noscillations are periodic in 1/\\emph{H}, analogous to quantum oscillations in\nmetals, even though $\\alpha$-RuCl$_3$ is an excellent insulator with a gap of\n1.9 eV. By tilting $\\bf H$ out of the plane, we find that the oscillation\nperiod is determined by the in-plane component $H_a$. As the temperature is\nraised above 0.5 K, the oscillation amplitude decreases exponentially. The\ndecrease anticorrelates with the emergence above $\\sim$2 K of an anomalous\nplanar thermal Hall conductivity measured with $\\bf H\\parallel a$. To exclude\nextrinsic artifacts, we carried out several tests. The implications of the\noscillations are discussed.\n