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.
This is a preview of subscription content, access via your institution
Access options
Subscribe to this journal
Receive 12 print issues and online access
$259.00 per year
only $21.58 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Wilson, K. G. Renormalization group and critical phenomena. I. Renormalization group and the Kadanoff scaling picture. Phys. Rev. B 4, 3174–3183 (1971).
Keller, H. J. Chemistry and Physics of One-Dimensional Metals (Plenum, New York, 1977).
Bednorz, J. G. & Müller, K. A. Possible high Tc superconductivity in the barium-lanthanum-copper-oxygen system. Z. Phys. B 64, 189–193 (1986).
Cox, D. E. & Minikiewicz, V. J. Magnetic ordering and low Ni2+ moment in CsNiCl3 . Phys. Rev. B 4, 2209–2212 (1971).
Buyers, W. J. L. et al. Experimental evidence for the Haldane gap in a spin-1 nearly isotropic, antiferromagnetic chain. Phys. Rev. Lett. 56, 371–374 (1986).
Sakai, H., Kato, M., Yoshimura, K. & Kosuge, K. Tl-NMR study of pyrochlore oxide Tl2Ru2O7: observation of spin-singlet formation. J. Phys. Soc. Jpn 71, 422–424 (2002).
Takeda, T. et al. Structure-property relationships in pyrochlores: low-temperature structures of Tl2Ru2O7−δ (δ=0.00 and 0.05). J. Mater. Chem. 9, 215–222 (1999).
Jo, Y. et al. Low-temperature anomaly of a spin-glass type in ferromagnetic R2Mo2O7 with R=Sm and Nd. J. Kor. Phys. Soc. 47, 123–129 (2005).
Khalifah, P. et al. Orbital ordering transition in La4Ru2O10 . Science 297, 2237–2240 (2002).
Adroja, D. T. et al. Spin gap formation in the heavy fermion skutterudite compound CeRu4Sb12 . Phys. Rev. B 68, 094425 (2003).
Hase, M., Terasaki, I. & Uchinokura, K. Observation of the spin-Peierls transition in linear Cu2+ (spin-1/2) chains in an inorganic compound CuGeO3 . Phys. Rev. Lett. 70, 3651–3654 (1993).
Shaz, M. et al. Spin-Peierls transition in TiOCl. Phys. Rev. B 71, 100405 (2005).
Schmidt, M. et al. Spin singlet formation in MgTi2O4: evidence of a helical dimerization pattern. Phys. Rev. Lett. 92, 056402 (2004).
Radaelli, P. G. et al. Formation of isomorphic Ir3+ and Ir4+ octamers and spin dimerization in the spinel CuIr2S4 . Nature 416, 155–158 (2002).
Khomskii, D. I. & Mizokawa, T. Orbitally induced Peierls state in spinels. Phys. Rev. Lett. 94, 156402 (2005).
Haldane, F. D. M. Nonlinear field theory of large-spin Heisenberg antiferromagnets: semiclassically quantized solitons of the one-dimensional easy-axis Néel state. Phys. Rev. Lett. 50, 1153–1156 (1983).
Lee, J. S. et al. Temperature-dependent self-doping effects on the metal-insulator transition of Tl2Ru2O7 . Phys. Rev. B 64, 165108 (2001).
Andersen, O. K., Klose, W. & Nohl, H. Electronic structure of Chevrel-phase high-critical-field superconductors. Phys. Rev. B 17, 1209–1237 (1978).
White, S. R. Density-matrix algorithms for quantum renormalization groups. Phys. Rev. B 48, 10345–10356 (1993).
Kim, Y. J. & Birgeneau, R. J. Monte Carlo study of the S=1/2 and S=1 Heisenberg antiferromagnet on a spatially anisotropic square lattice. Phys. Rev. B 62, 6378–6384 (2000).
Kolezhuk, A., Roth, R. & Schollwock, U. First order transition in the frustrated antiferromagnetic Heisenberg S=1 quantum spin chain. Phys. Rev. Lett. 77, 5142–5145 (1996).
Sleight, A. W. & Bouchard, R. J. Solid State Chemistry, Proceedings of the 5th Materials Research Symposium 227–232 (NBS Spec., Washington DC, 1972).
Takeda, T. et al. High-pressure synthesis, crystal structure, and metal–semiconductor transitions in the Tl2Ru2O7−δ pyrochlore. J. Solid State Chem. 140, 182–193 (1998).
Jarret, H. S. et al. in Valence Instabilities and Related Narrow-Band Phenomena (ed. Parks, R. D.) 545–549 (Plenum, New York, 1977).
Rodriguez-Carvajal, J. Recent advances in magnetic structure determination by neutron powder diffraction. Physica B 192, 55–69 (1993).
Anisimov, V. I., Zaanen, J. & Andersen, O. K. Band theory and Mott insulators: Hubbard U instead of Stoner I. Phys. Rev. B 44, 943–954 (1991).
Solovyev, I., Hamada, N. & Terakura, K. t2g versus all 3d localization in LaMO3 perovskite (M=Ti–Cu): First-principle study. Phys. Rev. B 53, 7158–7170 (1996).
Andersen, O. K. & Jepsen, O. Explicit, first-principles tight-binding theory. Phys. Rev. Lett. 53, 2571–2574 (1984).
Katsnelson, M. I. & Lichtenstein, A. I. First-principles calculations of magnetic interactions in correlated systems. Phys. Rev. B 61, 8906–8912 (2000).
Pavarini, E., Yamasaki, A., Nuss, J. & Andersen, O. K. How chemistry controls electron localization in 3d1 perovskites: a Wannier-function study. New J. Phys. 7, 188 (2005).
Ulrich, C. et al. Magnetic order and dynamics in an orbitally degenerate ferromagnetic insulator. Phys. Rev. Lett. 89, 167202 (2002).
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.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing financial interests.
Supplementary information
Supplementary Information
Supplementary tables S1 and S2, figure S1 (PDF 516 kb)
Rights and permissions
About this article
Cite this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/nmat1605
This article is cited by
-
Coexisting Z-type charge and bond order in metallic NaRu2O4
Communications Materials (2022)
-
Spin-1 pyrochlore antiferromagnets: Theory, model, and materials’ survey
Frontiers of Physics (2020)
-
Robust singlet dimers with fragile ordering in two-dimensional honeycomb lattice of Li2RuO3
Scientific Reports (2016)
-
Characterization of quantum conducting channels in metal/molecule/metal devices using pressure-modulated conductance microscopy
Applied Physics A (2011)
-
Travels in one dimension
Nature Materials (2006)