Odd-parity electronic multipolar ordering in URu2Si2 : Conclusions from Si and Ru NMR measurements

Abstract

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 $\mathrm{RRR}\ensuremath{\sim}70$. 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 $Q=(001)$, the hidden-order state is then found to be $P4/nnc$ with rank 5 odd parity, i.e., electric dotriacontapolar order.