Materials Science: Structure Research Frontiers 2014 46 Lattice symmetry breaking at the hidden-order transition in URu 2 Si 2 To elucidate the nature of a phase transition in materials, the most important step is to identify which symmetries are broken below the transition temperature. In 1985, a large anomaly in the specific heat was observed in the heavy-fermion metal, URu 2 Si 2 , at 17.5 K, indicating the presence of a phase transition at this temperature. Since then, tremendous efforts have been made to study the nature of this transition, but neither a symmetry change in the crystal structure nor a large magnetic moment that can account for the entropy change has been observed. This enigmatic order is thus called the “hidden order,” and understanding this hidden-order transition is a long-standing issue in condensed matter physics [1]. Recently, magnetic torque measurements in small pure crystals under an in-plane magnetic field rotation have shown that the two-fold oscillation as a function of field angle in the ab plane starts to develop below the hidden-order transition temperature ( T HO ). This two-fold oscillation indicates that the four-fold rotational symmetry associated with the body-centered tetragonal crystal structure (Fig. 1(a)) is broken in the hidden-order phase [2]. Similarly, cyclotron resonance [3] and nuclear magnetic resonance experiments [4] under an in-plane field rotation have provided evidence for four-fold rotational symmetry breaking below T HO . However, these experiments were conducted under an in-plane magnetic field, which itself can break the rotational symmetry. Thus, direct observation of symmetry breaking in the absence of a magnetic field is required to identify the ground state of the hidden order. To this end, we performed high-resolution synchrotron X-ray crystal structure analysis of URu 2 Si 2 at beamline BL02B1 [5]. We used ultraclean single crystals with very high residual resistivity ratios of ~ 670, which have become available recently [3]. First, out of more than ~ 30 crystals, we selected a high crystalline quality sample with the sharpest high-angle Bragg peak, which was measured using an imaging plate at room temperature. Then, we tuned the X-ray energy to 17.15 keV, which is just below the absorption edge of uranium so that the X-ray attenuation length is sufficient to obtain bulk information. To realize a high Fig. 1. (a) Crystal structure of URu 2 Si 2 above the hidden- order transition temperature T HO , which is I 4/ mmm body- centered tetragonal type. Schematic Bragg spots (black circles) in the ( h k 0) plane ( h , k ≥ 0) are also shown on the right. Left bottom is the origin. (b) Orthorhombic Fmmm structure in the ordered phase below T HO identified in our study. Bragg spots split due to formation of the domains. Colored circles correspond to the four different domains. (a) (b) U Ru Si ( h h 0) T ( h 0 0) T (2 h 0 0) O Research Frontiers 2014 47 resolution, we used a high-angle reflection set-up in which the four-circle diffractometer was equipped with a cryocooler. We focused on the high-angle (880) T Bragg peak at a reflection angle 2 θ above 165 degrees, which corresponds to the experimental resolution of a lattice constant as good as 3 × 10 –5 . Figure 2(a) shows the temperature dependence of the (880) T Bragg peak measured by the 2 θ / θ scattering mode. Below the hidden-order transition at T HO = 17.5 K, clear peak splitting is observed, indicating that symmetry-breaking lattice distortion sets in just below the transition. We also performed two-dimensional scans in the ( h k 0) plane as shown in Figs. 2(b) and 2(c). The single peak at 19 K (above T HO ) clearly splits at 10 K (below T HO ). The integrated intensities of these data are identical within experimental error. Our analysis indicates that the profile at 10 K is consistent with the four-fold splitting of the single Bragg peak, as expected for the orthorhombic Fmmm -type crystal structure shown in Fig. 1(b) [5]. Hence, we conclude that the space symmetry of the hidden order belongs to this orthorhombic type, which breaks four-fold rotational symmetry. Our observation is fully consistent with previous high-field measurements [2-4], and indicates that rotational symmetry breaking is not field induced but is an intrinsic property of the hidden order. To our knowledge, this is the first direct observation of a symmetry change in the hidden-order phase transition in URu 2 Si 2 by scattering experiments. The clarified space symmetry places very strong constraints on the genuine hidden order parameter. Thus, the present results can be regarded as a big step toward the full resolution of this 30-year old mystery. In addition, we believe that understanding the origin of such spontaneous rotational symmetry breaking found in URu 2 Si 2 may be important to uncover the nature of other unusual states of matter hidden in several strongly correlated electron systems. Takasada Shibauchi Department of Advanced Materials Science, The University of Tokyo E-mail: shibauchi@k.u-tokyo.ac.jp References [1] See, for a review, J.A. Mydosh and P.M. Oppeneer: Rev. Mod. Phys. 83 (2011) 1301. [2] R. Okazaki et al .: Science 331 (2011) 439. [3] S. Tonegawa et al .: Phys. Rev. Lett. 109 (2012) 036401. [4] S. Kambe et al .: Phys. Rev. Lett. 110 (2013) 246406. [5] S. Tonegawa, S. Kasahara, T. Fukuda, K. Sugimoto, N. Yasuda, Y. Tsuruhara, D. Watanabe, Y. Mizukami, Y. Haga, T.D. Matsuda, E. Yamamoto, Y. Onuki, H. Ikeda, Y. Matsuda and T. Shibauchi: Nat. Commun. 5 (2014) 4188 . Fig. 2. (a) Temperature dependence of the Bragg peak (880) T in an ultraclean single crystal of URu 2 Si 2 . Each curve is shifted vertically for clarity. Below the hidden order transition at T HO = 17.5 K, clear splitting of the Bragg peak is observed. (b) Two-dimensional intensity plot in the ( hk 0) plane near the (880) T Bragg peak at 19 K (above T HO ). (c) Similar data for 10 K (below T HO ). 8.002 8.001 8.000 7.999 7.998 7.998 7.999 8.000 8.001 8.002 8.002 8.001 8.000 7.999 7.998 7.998 7.999 8.000 8.001 8.002 k k (a) (b) (c) (880) T 19 K 19 K 10 K 18 K 17.5 K 17 K 14.5 K 11.5 K 10.5 K 9.5 K 165.2 165.4 165.6 165.8 166.0 166.2 h h 2 θ (deg) I / I max
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