We report ${}^{29}\mathrm{Si}$ and ${}^{101}\mathrm{Ru}$ NMR measurements on high-quality, single-crystal ${\mathrm{URu}}_2{\mathrm{Si}}_2$ samples with a residual resistivity ratio $\mathrm{RRR}\sim 70$. Our results show that the Si and Ru sites exhibit fourfold electronic symmetry around the $c$ axis in the hidden-order state. A previously observed twofold contribution of Si NMR linewidth is concluded to be due to extrinsic magnetic centers. Since the U and Si sites are aligned along the $c$ axis, we conclude further that the electronic state shows fourfold symmetry around the U site below the hidden-order transition. From this observed local symmetry, possible space groups for the hidden-order state are $P4/nnc$ or $I4/m$, based on group theoretical considerations. Since the order vector is considered to be $Q=\left(001\right)$, the hidden-order state is then found to be $P4/nnc$ with rank 5 odd parity, i.e., electric dotriacontapolar order.

• Received 5 March 2018
• Revised 30 May 2018

DOI:https://doi.org/10.1103/PhysRevB.97.235142