Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Spin-disordered quantum phases in a quasi-one-dimensional triangular lattice

Nature Physics volume 11, pages 679–683 (2015)Cite this article

Subjects

Abstract

Large quantum fluctuations drive the spins in solids into magnetically disordered phases that are not simply paramagnetic. This class of system includes the valence bond crystals and quantum spin liquids, in which spin singlets—the basic unit of entangled pairs of spins—form solids and liquids, respectively. In both phases, geometrical frustration is expected to play a role. So far, very few candidate quantum-spin-liquid materials have been found, including an organic Mott insulator, κ-(ET)2Cu2(CN)3, which is based on a regular triangular lattice. Here, we report a material, κ-(ET)2B(CN)4, with different geometry—a highly distorted quasi-one-dimensional triangular lattice. The magnetic susceptibility follows that of the spin-1/2 Heisenberg model on this distorted lattice. The material sustains a magnetically disordered Mott insulating state with enhanced quantum fluctuations over a wide temperature range, and undergoes a transition into a spin-gapped phase at 5 K.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Crystal structure of κ-(ET)2B(CN)4.
Figure 2: Magnetic properties of κ-(ET)2B(CN)4.
Figure 3: Transport properties of κ-(ET)2B(CN)4.
Figure 4: Band structures of κ-(ET)2X.

Similar content being viewed by others

References

  1. Balents, L. Spin liquids in frustrated magnets. Nature 464, 199–208 (2010).

    Article  ADS  Google Scholar 

  2. Wen, X-G. Quantum orders and symmetric spin liquids. Phys. Rev. B 65, 165113 (2002).

    Article  ADS  Google Scholar 

  3. Senthil, T., Vishwanath, A., Balents, L., Sachdev, S. & Fisher, M. P. A. Deconfined quantum critical points. Science 303, 1490–1494 (2004).

    Article  ADS  Google Scholar 

  4. Sandvik, A. W. Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions. Phys. Rev. Lett. 98, 227202 (2007).

    Article  ADS  Google Scholar 

  5. Jiang, H-C., Yao, H. & Balents, L. Spin liquid ground state of the spin-1/2 square J1–J2 Heisenberg model. Phys. Rev. B 86, 024424 (2012).

    Article  ADS  Google Scholar 

  6. Ishiguro, T., Yamaji, K. & Saito, G. Organic Superconductors (Springer-Verlag, 1990).

    Book  Google Scholar 

  7. Shimizu, Y., Miyagawa, K., Kanoda, K., Maesato, M. & Saito, G. Spin liquid state in an organic Mott insulator with a triangular lattice. Phys. Rev. Lett. 91, 107001 (2003).

    Article  ADS  Google Scholar 

  8. Itou, T., Oyamada, A., Maegawa, S., Tamura, M. & Kato, R. Quantum spin liquid in the spin-1/2 triangular antiferromagnet EtMe3Sb[Pd(dmit)2]2 . Phys. Rev. B 77, 104413 (2008).

    Article  ADS  Google Scholar 

  9. Isono, T. et al. Gapless quantum spin liquid in an organic spin-1/2 triangular-lattice κ-H3(Cat-EDT-TTF)2 . Phys. Rev. Lett. 112, 177201 (2014).

    Article  ADS  Google Scholar 

  10. Mendels, P. et al. Quantum magnetism in the paratacamite family: Towards an ideal kagomé lattice. Phys. Rev. Lett. 98, 077204 (2007).

    Article  ADS  Google Scholar 

  11. Helton, J. S. et al. Spin dynamics of the spin-1/2 kagome lattice antiferromagnet ZnCu3(OH)6Cl2 . Phys. Rev. Lett. 98, 107204 (2007).

    Article  ADS  Google Scholar 

  12. Okamoto, Y. et al. Spin-liquid state in the S = 1/2 hyperkagome antiferromagnet Na4Ir3O8 . Phys. Rev. Lett. 99, 137207 (2007).

    Article  ADS  Google Scholar 

  13. Koretsune, T. & Hotta, C. Evaluating model parameters of the κ- and β-type Mott insulating organic solids. Phys. Rev. B 89, 045102 (2014).

    Article  ADS  Google Scholar 

  14. Komatsu, T., Matsukawa, N., Inoue, T. & Saito, G. Realization of superconductivity at ambient pressure by band-filling control in κ-(BEDT-TTF)2Cu2(CN)3 . J. Phys. Soc. Jpn 65, 1340–1354 (1996).

    Article  ADS  Google Scholar 

  15. Zheng, W., Singh, R. R. P., McKenzie, R. H. & Coldea, R. Temperature dependence of the magnetic susceptibility for triangular-lattice antiferromagnets with spatially anisotropic exchange constants. Phys. Rev. B 71, 134422 (2005).

    Article  ADS  Google Scholar 

  16. Elstner, N., Singh, R. R. P. & Young, A. P. Finite temperature properties of the spin-1/2 Heisenberg antiferromagnet on the triangular lattice. Phys. Rev. Lett. 71, 1629–1632 (1993).

    Article  ADS  Google Scholar 

  17. Bonner, J. C. & Fisher, M. E. Linear magnetic chains with anisotropic coupling. Phys. Rev. 135, A640–A658 (1964).

    Article  ADS  Google Scholar 

  18. Miyagawa, K., Kawamoto, A., Nakazawa, Y. & Kanoda, K. Antiferromagnetic ordering and spin structure in the organic conductor, κ-(BEDT-TTF)2Cu[N(CN)2]Cl. Phys. Rev. Lett. 75, 1174–1177 (1995).

    Article  ADS  Google Scholar 

  19. Sachdev, S. NMR relaxation in half-integer antiferromagnetic spin chains. Phys. Rev. B 50, 13006–13008 (1994).

    Article  ADS  Google Scholar 

  20. Chakravarty, S., Halperin, B. I. & Nelson, D. R. Two-dimensional quantum Heisenberg antiferromagnet at low temperatures. Phys. Rev. B 39, 2344–2371 (1989).

    Article  ADS  Google Scholar 

  21. Shimizu, Y., Miyagawa, K., Kanoda, K., Maesato, M. & Saito, G. Emergence of inhomogeneous moments from spin liquid in the triangular-lattice Mott insulator κ-(ET)2Cu2(CN)3 . Phys. Rev. B 73, 140407 (2006).

    Article  ADS  Google Scholar 

  22. Ito, H., Ishiguro, T., Kubota, M. & Saito, G. Metal–nonmetal transition and superconductivity localization in the two-dimensional conductor κ-(BEDT-TTF)2Cu[N(CN)2]Cl under pressure. J. Phys. Soc. Jpn 65, 2987–2993 (1996).

    Article  ADS  Google Scholar 

  23. Kagawa, F., Miyagawa, K. & Kanoda, K. Unconventional critical behaviour in a quasi-two-dimensional organic conductor. Nature 436, 534–537 (2005).

    Article  ADS  Google Scholar 

  24. Bray, J. W. et al. Observation of a spin-Peierls transition in a Heisenberg antiferromagnetic linear-chain system. Phys. Rev. Lett. 35, 744–747 (1975).

    Article  ADS  Google Scholar 

  25. Tamura, M., Nakao, A. & Kato, R. Frustration-induced valence-bond ordering in a new quantum triangular antiferromagnet based on [Pd(dmit)2]. J. Phys. Soc. Jpn 75, 093701 (2006).

    Article  ADS  Google Scholar 

  26. Bulaevskii, L. N. Magnetic susceptibility of a chain of spins with antiferromagnetic interaction. Sov. Phys. Solid State 11, 921–924 (1969).

    Google Scholar 

  27. Pytte, E. Peierls instability in Heisenberg chains. Phys. Rev. B 10, 4637–4642 (1974).

    Article  ADS  Google Scholar 

  28. Huizinga, S. et al. Spin-Peierls transition in N-methyl-N-ethyl-morpholinium-ditetracyanoquinodimethanide [MEM-(TCNQ)2]. Phys. Rev. B 19, 4723–4732 (1979).

    Article  ADS  Google Scholar 

  29. Dumm, M. et al. Electron spin resonance studies on the organic linear-chain compounds (TMTCF)2X (C = S, Se; X = PF6, AsF6, ClO4, Br). Phys. Rev. B 61, 511–521 (2000).

    Article  ADS  Google Scholar 

  30. 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).

    Article  ADS  Google Scholar 

  31. Kohno, M., Starykh, O. A. & Balents, L. Spinons and triplons in spatially anisotropic frustrated antiferromagnets. Nature Phys. 3, 790–795 (2007).

    Article  ADS  Google Scholar 

  32. Pratt, F. L. et al. Magnetic and non-magnetic phases of a quantum spin liquid. Nature 471, 612–616 (2011).

    Article  ADS  Google Scholar 

  33. Morita, H., Watanabe, S. & Imada, M. Nonmagnetic insulating states near the Mott transitions on lattices with geometrical frustration and implications for κ-(ET)2Cu2(CN)3 . J. Phys. Soc. Jpn 71, 2109–2112 (2002).

    Article  ADS  Google Scholar 

  34. Kyung, B. & Tremblay, A-M. S. Mott transition, antiferromagnetism, and d-wave superconductivity in two-dimensional organic conductors. Phys. Rev. Lett. 97, 046402 (2006).

    Article  ADS  Google Scholar 

  35. Shinaoka, H., Misawa, T., Nakamura, K. & Imada, M. Mott transition and phase diagram of κ-(BEDT-TTF)2Cu(NCS)2 studied by two-dimensional model derived from ab initio method. J. Phys. Soc. Jpn 81, 034701 (2012).

    Article  ADS  Google Scholar 

  36. Starykh, O. A. & Balents, L. Ordering in spatially anisotropic triangular antiferromagnets. Phys. Rev. Lett. 98, 077205 (2007).

    Article  ADS  Google Scholar 

  37. Pardini, T. & Singh, R. R. P. Magnetic order in coupled spin-half and spin-one Heisenberg chains in an anisotropic triangular-lattice geometry. Phys. Rev. B 77, 214433 (2008).

    Article  ADS  Google Scholar 

  38. Hauke, P., Roscilde, T., Murg, V., Cirac, J. I. & Schmied, R. Modified spin-wave theory with ordering vector optimization: Spatially anisotropic triangular lattice and J1J2J3 model with Heisenberg interactions. New J. Phys. 13, 075017 (2011).

    Article  ADS  Google Scholar 

  39. Yunoki, S. & Sorella, S. Two spin liquid phases in the spatially anisotropic triangular Heisenberg model. Phys. Rev. B 74, 014408 (2006).

    Article  ADS  Google Scholar 

  40. Coldea, R. et al. Direct measurement of the spin Hamiltonian and observation of condensation of magnons in the 2D frustrated quantum magnet Cs2CuCl4 . Phys. Rev. Lett. 88, 137203 (2002).

    Article  ADS  Google Scholar 

  41. Yang, H-Y., Läuchli, A. M., Mila, F. & Schmidt, K. P. Effective spin model for the spin-liquid phase of the Hubbard model on the triangular lattice. Phys. Rev. Lett. 105, 267204 (2010).

    Article  ADS  Google Scholar 

  42. Fettouhi, M. et al. Structural and physical properties of κ-(BEDT-TTF)2(CF3SO3). Synth. Met. 70, 1131–1132 (1995).

    Article  Google Scholar 

  43. Burla, M. C. et al. SIR2004: An improved tool for crystal structure determination and refinement. J. Appl. Crystallogr. 38, 381–388 (2005).

    Article  Google Scholar 

  44. Sheldrick, G. M. SHELXL-97: Program for Crystal Structure Refinement (University of Göttingen, 1997).

    Google Scholar 

  45. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).

    Article  ADS  Google Scholar 

  46. Giannozzi, P. et al. QUANTUM ESPRESSO: A modular and open-source software project for quantum simulations of materials. J. Phys. Condens. Matter 21, 395502 (2009).

    Article  Google Scholar 

  47. Vanderbilt, D. Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Phys. Rev. B 41, 7892–7895 (1990).

    Article  ADS  Google Scholar 

  48. Marzari, N. & Vanderbilt, D. Maximally localized generalized Wannier functions for composite energy bands. Phys. Rev. B 56, 12847–12865 (1997).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work was supported by JSPS KAKENHI Grant Number 23225005 and 25800204. We thank H. Kageyama for his comments.

Author information

Authors and Affiliations

  1. Faculty of Agriculture, Meijo University, Shiogamaguchi 1-501 Tempaku-ku, Nagoya 468-8502, Japan

    Yukihiro Yoshida, Hiromi Hayama, Takaaki Hiramatsu & Gunzi Saito

  2. Department of Applied Physics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan

    Hiroshi Ito, Yuto Nakamura & Hideo Kishida

  3. Division of Chemistry, Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan

    Mitsuhiko Maesato

  4. Department of Physics, Graduate School of Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8602, Japan

    Yasuhiro Shimizu

  5. Center for Emergent Matter Science, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan

    Takashi Koretsune

  6. Department of Basic Science, University of Tokyo, Komaba, Meguro-ku, Tokyo 153-8902, Japan

    Chisa Hotta

  7. Toyota Physical and Chemical Research Institute, 41-1 Yokomichi, Nagakute, Aichi 480-1192, Japan

    Gunzi Saito

Authors
  1. Yukihiro Yoshida
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hiroshi Ito
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mitsuhiko Maesato
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yasuhiro Shimizu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Hiromi Hayama
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Takaaki Hiramatsu
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Yuto Nakamura
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Hideo Kishida
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Takashi Koretsune
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Chisa Hotta
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. Gunzi Saito
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Y.Y. designed the project and carried out the synthesis and X-ray diffraction measurements. H.I. carried out the resistivity measurements, M.M. the magnetic susceptibility and the high-pressure resistivity measurements, Y.S. the 1H NMR measurements, and Y.N. and H.K. the Raman measurements. H.H. supported the synthesis. T.H. collected crystallographic data of some reference salts. T.K. carried out the DFT calculations. The manuscript was written by Y.Y. and C.H. with contributions from Y.S., M.M. and G.S. All authors commented on the manuscript.

Corresponding author

Correspondence to Yukihiro Yoshida.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 3336 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yoshida, Y., Ito, H., Maesato, M. et al. Spin-disordered quantum phases in a quasi-one-dimensional triangular lattice. Nature Phys 11, 679–683 (2015). https://doi.org/10.1038/nphys3359

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphys3359

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing