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Spin gap in Tl2Ru2O7 and the possible formation of Haldane chains in three-dimensional crystals

Abstract

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 Tl2Ru2O7 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.

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Figure 1: Resistivity and susceptibility as a function of temperature.
Figure 2: Temperature dependence of the structural data and the diagram of different Ru–Ru bonds at the low-temperature phase.
Figure 3: Total scattering obtained from inelastic neutron-scattering experiment from 6.8 to 200 K.
Figure 4: Orbital ordering in the low-temperature phase of Tl2Ru2O7, obtained from LDA+U calculations.

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Acknowledgements

We thank the Korea Basic Science Institute for allowing us to use their high-temperature SQUID magnetometer and J. van Duijn for providing us with his HET data on Bi2Ru2O7. J.G.P. acknowledges the financial support of the CSCMR at Seoul National University, the CNRF project, the BAERI programme and the Proton Accelerator User Program (No. M102KS010001-02K1901-01810). The work of D.K. was supported by the Deutsche Forshungsgemeinschaft through SFB 608, by the European project COMEPHS and by the Leverhulme Professorship in Loughborough University and S.S. thanks the Netherlands Organization for Scientific Research (NWO 047.016.005), Russian Foundation for Basic Research (RFFI-04-02-16096), INTAS (05-109-4727) and Ural branch of Russian Academy of Science. Experiments at ISIS were supported by the Council for the Central Laboratory of the Research Councils of the UK.

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Correspondence to J.-G. Park.

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Supplementary tables S1 and S2, figure S1 (PDF 516 kb)

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Lee, S., Park, JG., Adroja, D. et al. Spin gap in Tl2Ru2O7 and the possible formation of Haldane chains in three-dimensional crystals. Nature Mater 5, 471–476 (2006). https://doi.org/10.1038/nmat1605

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