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Magnetic and non-magnetic phases of a quantum spin liquid

Nature volume 471, pages 612–616 (2011)Cite this article

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Abstract

A quantum spin-liquid phase is an intriguing possibility for a system of strongly interacting magnetic units in which the usual magnetically ordered ground state is avoided owing to strong quantum fluctuations. It was first predicted theoretically for a triangular-lattice model with antiferromagnetically coupled S = 1/2 spins1. Recently, materials have become available showing persuasive experimental evidence for such a state2. Although many studies show that the ideal triangular lattice of S = 1/2 Heisenberg spins actually orders magnetically into a three-sublattice, non-collinear 120° arrangement, quantum fluctuations significantly reduce the size of the ordered moment3. This residual ordering can be completely suppressed when higher-order ring-exchange magnetic interactions are significant, as found in nearly metallic Mott insulators4. The layered molecular system κ-(BEDT-TTF)2Cu2(CN)3 is a Mott insulator with an almost isotropic, triangular magnetic lattice of spin-1/2 BEDT-TTF dimers5 that provides a prime example of a spin liquid formed in this way6,7,8,9,10,11. Despite a high-temperature exchange coupling, J, of 250 K (ref. 6), no obvious signature of conventional magnetic ordering is seen down to 20 mK (refs 7, 8). Here we show, using muon spin rotation, that applying a small magnetic field to this system produces a quantum phase transition between the spin-liquid phase and an antiferromagnetic phase with a strongly suppressed moment. This can be described as Bose–Einstein condensation of spin excitations with an extremely small spin gap. At higher fields, a second transition is found that suggests a threshold for deconfinement of the spin excitations. Our studies reveal the low-temperature magnetic phase diagram and enable us to measure characteristic critical properties. We compare our results closely with current theoretical models, and this gives some further insight into the nature of the spin-liquid phase.

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Figure 1: Phase diagram for κ-(BEDT-TTF)2Cu2(CN)3.
Figure 2: Low-field QPT and phase boundary.
Figure 3: Electronic spin fluctuation rate.
Figure 4: High-field QPT and critical exponents.

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References

  1. Anderson, P. W. Resonating valence bonds: a new kind of insulator? Mater. Res. Bull. 8, 153–160 (1973)

    Article  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  3. Zheng, W. Fjaerestad, J. O., Singh, R. R. P., McKenzie, R. H. & Coldea, R. Excitation spectra of the spin 1/2 triangular-lattice Heisenberg antiferromagnet. Phys. Rev. B 74, 224420 (2006)

    Article  ADS  Google Scholar 

  4. Motrunich, O. I. Variational study of triangular lattice spin-1/2 model with ring exchanges and spin liquid state in κ-(ET)2Cu2(CN)3 . Phys. Rev. B 72, 045105 (2005)

    Article  ADS  Google Scholar 

  5. Pratt, F. L. Using Shubnikov-de Haas data to estimate the magnetic frustration parameter t′/t in the spin-liquid system κ-ET2Cu2(CN)3 . Physica B 405, S205–S207 (2010)

    Article  ADS  CAS  Google Scholar 

  6. Shimizu, Y. et al. Spin liquid state in an organic Mott insulator with a triangular lattice. Phys. Rev. Lett. 91, 107001 (2003)

    Article  ADS  CAS  Google Scholar 

  7. Shimizu, Y. et al. Emergence of inhomogeneous moments from spin liquid in the triangular-lattice Mott insulator κ-(ET)2Cu2(CN)3 . Phys. Rev. B 73, 140407(R) (2006)

    Article  ADS  Google Scholar 

  8. Ohira, S. & Shimizu, Y. Kanoda, K. & Saito, G. Spin liquid state in κ-(BEDT-TTF)2Cu2(CN)3 studied by muon spin relaxation method. J. Low Temp. Phys. 142, 153–158 (2006)

    Article  ADS  CAS  Google Scholar 

  9. Yamashita, S. et al. Thermodynamic properties of a spin-1/2 spin-liquid state in a κ-type organic salt. Nature Phys. 4, 459–462 (2008)

    Article  ADS  CAS  Google Scholar 

  10. Yamashita, M. et al. Thermal-transport measurements in a quantum spin-liquid state of the frustrated triangular magnet κ-(BEDT-TTF)2Cu2(CN)3 . Nature Phys. 5, 44–47 (2009)

    Article  ADS  CAS  Google Scholar 

  11. Manna, R. S. et al. Lattice effects and entropy release at the low-temperature phase transition in the spin-liquid candidate κ-(BEDT-TTF)2Cu2(CN)3 . Phys. Rev. Lett. 104, 016403 (2010)

    Article  ADS  CAS  Google Scholar 

  12. Blundell, S. J. Spin-polarized muons in condensed matter physics. Contemp. Phys. 40, 175 (1999)

    Article  ADS  CAS  Google Scholar 

  13. Sebastian, S. E. et al. Dimensional reduction at a quantum critical point. Nature 441, 617–620 (2006)

    Article  ADS  CAS  Google Scholar 

  14. Schmalian, J. & Batista, C. D. Emergent symmetry and dimensional reduction at a quantum critical point. Phys. Rev. B 77, 094406 (2008)

    Article  ADS  Google Scholar 

  15. Lee, S.-S., Lee, P. A. & Senthil, T. Amperean pairing instability in the U(1) spin liquid state with Fermi surface and application to κ-(BEDT-TTF)2Cu2(CN)3 . Phys. Rev. Lett. 98, 067006 (2007)

    Article  ADS  Google Scholar 

  16. Galitski, V. & Kim, Y. B. Spin-triplet pairing instability of the spinon Fermi surface in a U(1) spin liquid. Phys. Rev. Lett. 99, 266403 (2007)

    Article  ADS  Google Scholar 

  17. Kaul, R. K. & Sachdev, S. Quantum criticality of U(1) gauge theories with fermionic and bosonic matter in two spatial dimensions. Phys. Rev. B 77, 155105 (2008)

    Article  ADS  Google Scholar 

  18. Xu, C. & Sachdev, S. Global phase diagrams of frustrated quantum antiferromagnets in two dimensions: doubled Chern-Simons theory. Phys. Rev. B 79, 064405 (2009)

    Article  ADS  Google Scholar 

  19. Qi, Y., Xu, C. & Sachdev, S. Dynamics and transport of the Z2 spin liquid: application to κ-(ET)2Cu2(CN)3 . Phys. Rev. Lett. 102, 176401 (2009)

    Article  ADS  Google Scholar 

  20. Senthil, T. & Fisher, M. P. A. Z2 gauge theory of electron fractionalization in strongly correlated systems. Phys. Rev. B 62, 7850–7881 (2000)

    Article  ADS  CAS  Google Scholar 

  21. Yamashita, M. et al. Highly mobile gapless excitations in a two-dimensional candidate quantum spin liquid. Science 328, 1246–1248 (2010)

    Article  ADS  CAS  Google Scholar 

  22. Ballasteros, H. G., Fernandez, L. A., Martin-Mayor, V. & Munoz Sudupe, A. Finite size effects on measures of critical exponents in d = 3 O(N) models. Phys. Lett. B 387, 125–131 (1996)

    Article  ADS  Google Scholar 

  23. Isakov, S. V. & Senthil, T. &. Kim, Y. B. Ordering in Cs2CuCl4: possibility of a proximate spin liquid. Phys. Rev. B 72, 174417 (2005)

    Article  ADS  Google Scholar 

  24. Motrunich, O. I. Orbital magnetic field effects in spin liquid with spinon Fermi sea: possible application to κ-(ET)2Cu2(CN)3 . Phys. Rev. B 73, 155115 (2006)

    Article  ADS  Google Scholar 

  25. Bulaevskii, L. N., Batista, C. D., Mostovoy, M. V. & Khomskii, D. I. Electronic orbital currents and polarization in Mott insulators. Phys. Rev. B 78, 024402 (2008)

    Article  ADS  Google Scholar 

  26. Al-Hassanieh, K. A., Batista, C. D., Ortiz, G. & Bulaevskii, L. N. Field-induced orbital antiferromagnetism in Mott insulators. Phys. Rev. Lett. 103, 216402 (2009)

    Article  ADS  CAS  Google Scholar 

  27. Gregor, K. & Motrunich, O. I. Nonmagnetic impurities in a S = 1/2 frustrated triangular antiferromagnet: broadening of 13C NMR lines in κ-(ET)2Cu2(CN)3 . Phys. Rev. B 79, 024421 (2009)

    Article  ADS  Google Scholar 

  28. Ghosh, S., Rosenbaum, T. F. & Aeppli, G. Macroscopic signature of protected spins in a dense frustrated magnet. Phys. Rev. Lett. 101, 157205 (2008)

    Article  ADS  CAS  Google Scholar 

  29. Schiffer, P., Ramirez, A. P., Huse, D. A. & Valentino, A. J. Investigation of the field induced antiferromagnetic phase transition in the frustrated magnet: gadolinium gallium garnet. Phys. Rev. Lett. 73, 2500–2503 (1994)

    Article  ADS  CAS  Google Scholar 

  30. Pratt, F. L. WiMDA: a muon data analysis program for the Windows PC. Physica B 289–290, 710–714 (2000)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We acknowledge discussions with S. Sachdev, J. Schmalian and T. Senthil. Part of this work was performed at the Swiss Muon Source, Paul Scherrer Institute, Villigen, Switzerland. This work is supported by EPSRC (UK).

Author information

Author notes

  1. G. Saito

    Present address: Present address: Research Institute, Meijo University, Nagoya 468-8502, Japan.,

Authors and Affiliations

  1. ISIS Facility, Rutherford Appleton Laboratory, Chilton OX11 0QX, UK,

    F. L. Pratt & P. J. Baker

  2. Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK,

    S. J. Blundell & T. Lancaster

  3. Neutron Science Section, J-PARC Center, Japan Atomic Energy Agency, 2-4 Shirane, Shirakata, Tokai, Ibaraki 319-1195, Japan,

    S. Ohira-Kawamura

  4. Paul Scherrer Institut, Laboratory for Muon-Spin Spectroscopy, CH-5232 Villigen, Switzerland,

    C. Baines

  5. Institute for Advanced Research, Nagoya University, Nagoya 464-8601, Japan,

    Y. Shimizu

  6. Department of Applied Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan,

    K. Kanoda

  7. Meson Science Laboratory, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan,

    I. Watanabe

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

    G. Saito

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Contributions

F.L.P. and S.O.-K. planned the experiments. F.L.P., P.J.B., S.J.B., T.L., S.O.-K., C.B. and I.W. contributed to the measurements. Y.S., G.S. and K.K. supplied the sample material and supporting NMR measurements. F.L.P. analysed the data and wrote the paper. All authors critically reviewed the paper.

Corresponding author

Correspondence to F. L. Pratt.

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The authors declare no competing financial interests.

Supplementary information

Supplementary Information

The file contains Supplementary Methods, Supplementary Figures 1-4 with legends, Supplementary Notes on Models and Critical Exponents, Supplementary Table 1 and additional references. (PDF 816 kb)

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Pratt, F., Baker, P., Blundell, S. et al. Magnetic and non-magnetic phases of a quantum spin liquid. Nature 471, 612–616 (2011). https://doi.org/10.1038/nature09910

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