ARTICLES Spin gap in Tl 2 Ru 2 O 7 and the possible formation of Haldane chains in three-dimensional crystals SEONGSU LEE 1 , J.-G. PARK 1,2 *, D. T. ADROJA 3 , D. KHOMSKII 4 , S. STRELTSOV 5 , K. A. McEWEN 6 , H. SAKAI 7 , K. YOSHIMURA 7 , V. I. ANISIMOV 5 , D. MORI 8 , R. KANNO 8 AND R. IBBERSON 3 1 Department of Physics and Institute of Basic Science, SungKyunKwan University, Suwon 440-746, Korea 2 Center for Strongly Correlated Materials Research, Seoul National University, Seoul 151-742, Korea 3 ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, UK 4 Physikalisches Institut, University of K ¨ oln, 50937 K ¨ oln, Germany 5 Institute of Metal Physics, Ekaterinburg 620219, Russia 6 Department of Physics and Astronomy, University College London, London WC1E 6BT, UK 7 Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan 8 Department of Electronic Chemistry, Tokyo Institute of Technology, Yokohama 226-8502, Japan *e-mail: jgpark@skku.edu Published online: 14 May 2006; doi:10.1038/nmat1605 Dimensionality is one of the most important parameters of physical phenomena. Only two things determine the universality class of a phase transition: the dimensionality of a given system and the symmetry of the order parameter. In most cases, the dimensionality of a substance is predetermined by its crystal structure. Examples in which the effective dimensionality is reduced are quite rare. Here we show that the three-dimensional cubic system of Tl 2 Ru 2 O 7 most probably evolves into a one-dimensional spin-one Haldane system with a spin gap below 120 K, accompanied by anomalies in the structure, resistivity and susceptibility. We argue that these anomalies are due to an orbital ordering of Ru 4d electrons, with a strong coupling among three degrees of freedom: orbital, spin and lattice. Our work provides a unique example of the spontaneous formation of Haldane system with an insight into the intriguing interplay of different degrees of freedom. W hen any physical entity in nature self-organizes itself to reduce its entropy through a phase transition, the detailed features of such a phase transition are governed by the dimensionality of a given system and the symmetry of the order parameter 1 . In most cases, materials have physical dimensions that are predetermined by the crystal structure, except for a few cases such as KCuF 3 . For example, the one-dimensional (1D) nature of transport properties found in some organic conductors arises from their strongly anisotropic crystal structures 2 , whereas the 2D physical properties of high-temperature superconductors are predominantly due to the strong 2D nature of the Cu–O plane ever present in their structures 3 . Strikingly, even a small anisotropy seems to become important when it comes to deciding the dimensionality of the physical properties. For example, one of the best known 1D Haldane gap systems, CsNiCl 3 , has a quasi-1D structure along the c axis with the c axis being shorter by 20% than the a axis 4 , which then determines the 1D nature of the spin interaction 5 . Tl 2 Ru 2 O 7 forms in a cubic pyrochlore structure with the space group of Fd ¯ 3m and a = 10.17936 ˚ A as shown in Supplementary Information, Fig. S1. In this cubic structure, Ru is located at the centre of the O 6 octahedron with a Ru–O bond distance of 1.9577 ˚ A. These Ru ions form an edge-sharing tetrahedral network with the equal Ru–Ru distance of 3.5989 ˚ A. Low-spin Ru 4+ ions of Tl 2 Ru 2 O 7 with the total spin S = 1 have four 4d electrons, which occupy the low-lying triplet t 2g states. This high-temperature phase has metallic behaviour. However, on cooling, resistivity increases markedly below the metal–insulator-transition temperature T MI ∼ = 120 K, by as much nature materials VOL 5 JUNE 2006 www.nature.com/naturematerials 471 Nature Publishing Group ©2006