Symmetry of the Hidden Order in URu2Si2 from Nuclear Magnetic Resonance Studies

The hidden order (HO) in URu2Si2 has been investigated by both Si-29 and Ru-99 NMR on a single crystal. Tiny, but finite additional broadening of the spectrum in the HO phase in both Si-29 and Ru-99 NMR with external magnetic field applied along the crystallographic [100] or [110] direction, and its persistence as H-ext -> 0 in Si-29 NMR clearly indicate the existence of internal hyperfine field, and the breaking of the time-reversal symmetry in the HO phase can therefore be concluded. We discuss which symmetry of the D-4h symmetry group of the URu2Si2 crystal structure is compatible with the observed dependence on the crystal-axis direction of the existence or nonexistence of the internal hyperfine field. Then, by imposing a strong constraint that the wave-vector of the HO is also Q(0) = [0, 0, 1], the wave-vector of the pressure-induced antiferromagnetism, we show that the two-dimensional representation E-remains as the only possible candidate for the HO symmetry. Since dipoles are obviously excluded from the major HO parameter, we conclude the E-multipole (octupole or triakontadipole) to be the HO parameter. We further discuss that the E- multipole, but with no associated dipoles, seems to be a key feature of the HO in URu2Si2.