Motivated by the recent discovery of broken four-fold symmetry in the hidden order phase of URu2Si2[R. Okazaki et al., Science 331, 439 (2011)], we examine a scenario of a spin nematic state as a possible candidate of the hidden order phase. We demonstrate that the scenario naturally explains most of experimental observations, and furthermore, reproduces successfully the temperature dependence of the spin anisotropy detected by the above-mentioned experiment in a semi-quantitative way. This result provides strong evidence for the realization of the spin nematic order.
PACS numbers:The heavy fermion compound URu 2 Si 2 exhibits a second order phase transition at T HO ≈ 17.5 K. In spite of long-standing enormous efforts in experimental and theoretical studies [1][2][3][4][5][6][7][8][9][10][11][12][13][14], the order parameter of this phase transition has not yet been identified. The enigmatic features of this so-called "hidden order(HO)" phase are described as follows: (i) Despite large anomaly in thermodynamic quantities and drastic reconstruction of the Fermi surfaces at T = T HO , there is neither conventional magnetic order nor the change of the crystal structure [1][2][3][15][16][17][18][19]. (ii) However, under applied pressure, an antiferromagnetic (AF) state with large moment appears, and more surprisingly, the Fermi surfaces in the AF ordered state are almost the same as those found in the HO phase [20][21][22][23][24].Recently, an experimental breakthrough for this issue was achieved by Okazaki et al. [25], who found spontaneous symmetry breaking in the spin space at T < T HO . They reported that the anisotropy of the spin susceptibility in the xy-plane, which is measured by the quantity χ xy = S x S y , becomes nonzero below T HO . Since URu 2 Si 2 is tetragonal with four-fold symmetry at T > T HO , and the phase transition at T = T HO does not accompany any lattice distortion, it is reasonable to expect that this symmetry breaking is an essential feature of the HO phase, which imposes a crucial constraint on possible candidates of the HO parameter. Motivated by this experimental observation, in this letter, we discuss a possibility that a spin nematic (SN) state is realized as the hidden order in URu 2 Si 2 . The SN phase is a state with circulating spin currents, but with no magnetic moment [26][27][28]. The circulating spin currents break spin rotational symmetry, leading to spin anisotropy, without breaking time-reversal symmetry. We demonstrate that the above-mentioned features of the HO phase are naturally understood within the scenario of the SN order, and furthermore, that the temperature dependence of the spin anisotropy spontaneously generated in the SN state successfully explains the above experimental observation in a semi-quantitative way, providing strong evidence for the realization of the SN state as the HO phase of URu 2 Si 2 .We, first, present a mean field analysis for basic properties of the SN state applied to the case of URu 2 Si 2 . The SN state is induced by nesting of the Fermi...