Symmetry of the Hidden Order in URu₂Si₂from Nuclear Magnetic Resonance Studies

Abstract

The hidden order (HO) in URu 2 Si 2 has been investigated by both 29 Si and 99 Ru NMR on a single crystal. Tiny, but finite additional broadening of the spectrum in the HO phase in both 29 Si and 99 Ru NMR with external magnetic field applied along the crystallographic [100] or [110] direction, and its persistence as H ext →0 in 29 Si 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 4 h symmetry group of the URu 2 Si 2 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 URu 2 Si 2 .