In the class of materials called spin liquids^1,2,3, a magnetically ordered state cannot be attained even at millikelvin temperatures because of conflicting constraints on each spin; for example, from geometric or exchange frustration. The resulting quantum spin-liquid state is currently of intense interest because it exhibits unusual excitations as well as wave-function entanglement. The layered insulator α-RuCl₃ orders as a zigzag antiferromagnet at low temperature in zero magnetic field⁴. The zigzag order is destroyed when a magnetic field is applied parallel to the zigzag axis. At moderate magnetic field strength, there is growing evidence that a quantum spin-liquid state exists. Here we report the observation of oscillations in its thermal conductivity in that field range. The oscillations, whose amplitude is very large within this field range and strongly suppressed on either side, are periodic. This is analogous to quantum oscillations in metals, even though α-RuCl₃ is an excellent insulator with a large gap. As the temperature is raised above 0.5 K, the oscillation amplitude decreases exponentially, anticorrelating with the emergence of an anomalous planar thermal Hall conductivity above approximately 2 K.

在称为自旋液体^1,2,3的材料类别中，即使在毫开尔文温度下也无法获得磁性有序状态，因为每次自旋的约束相互冲突；例如，来自几何或交换挫折。由此产生的量子自旋液态目前引起了极大的兴趣，因为它表现出不寻常的激发以及波函数纠缠。层状绝缘体 α-RuCl _{3在零磁场}⁴的低温下呈锯齿形反铁磁体. 当平行于之字形轴施加磁场时，之字形顺序被破坏。在中等磁场强度下，越来越多的证据表明存在量子自旋液态。在这里，我们报告了在该场范围内观察到其热导率的振荡。振荡，其幅度在该场范围内非常大并且在任一侧都被强烈抑制，是周期性的。这类似于金属中的量子振荡，尽管 α-RuCl ₃是具有大间隙的优良绝缘体。随着温度升高到 0.5 K 以上，振荡幅度呈指数下降，与大约 2 K 以上的异常平面热霍尔电导率的出现反相关。