Static and fluctuating zigzag order, and possible signatures of Kitaev physics, in torque measurements of ${\alpha}$-RuCl${_3}$
We have measured magnetic torque on a $T_N=7$ K single crystal of $\alpha$-RuCl$_3$, as a function of the field angle in the $ab$-plane, focusing on temperatures between 2 and 20 K and fields from 0 to 9 T. We find a number of features, many of which can be classified by their angular periodicity. The sample shows an oscillation with a period of 180$^\circ$ (i.e.\ two-fold periodicity) and within the magnetically ordered zigzag phase there is a 60$^\circ$ period (i.e.\ six-fold) sawtooth pattern, which can be explained by reorientation of the zigzag domains as the crystal rotates in the applied field. We argue that the six-fold sawtooth and the two-fold sinusoidal signals arise from distinct regions of the crystal. Suppressing the zigzag order with an applied field above $\sim8$ T at low temperature, a six-fold {\sl sinusoidal} signal remains, suggesting that there is fluctuating zigzag order in the putative field-induced quantum spin liquid state. Finally, in testing theoretical results which predict a torque response with divergent slope across C$_2$-preserving $b$-axes (B1-axis), we find no features like that predicted for Ising topological order. Instead we find features at low temperatures and fields just above the zigzag phase across the non-C$_2$-preserving $b$-axes (B2-axes). Interpretation of this feature is complicated by the development of other similar signatures nearby at slightly lower fields, and by clear enhancement with thermal cycling. Additionally, we contrast the torque response of $T_N \sim$ 7 K and 14 K samples.