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.
This is a preview of subscription content, access via your institution
Open Access articles citing this article.
npj Quantum Materials Open Access 21 July 2021
Nature Communications Open Access 12 June 2019
Nature Communications Open Access 17 April 2018
Subscribe to Journal
Get full journal access for 1 year
only $3.90 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Get time limited or full article access on ReadCube.
All prices are NET prices.
Anderson, P. W. Resonating valence bonds: a new kind of insulator? Mater. Res. Bull. 8, 153–160 (1973)
Balents, L. Spin liquids in frustrated magnets. Nature 464, 199–208 (2010)
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)
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)
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)
Shimizu, Y. et al. Spin liquid state in an organic Mott insulator with a triangular lattice. Phys. Rev. Lett. 91, 107001 (2003)
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)
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)
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)
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)
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)
Blundell, S. J. Spin-polarized muons in condensed matter physics. Contemp. Phys. 40, 175 (1999)
Sebastian, S. E. et al. Dimensional reduction at a quantum critical point. Nature 441, 617–620 (2006)
Schmalian, J. & Batista, C. D. Emergent symmetry and dimensional reduction at a quantum critical point. Phys. Rev. B 77, 094406 (2008)
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)
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)
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)
Xu, C. & Sachdev, S. Global phase diagrams of frustrated quantum antiferromagnets in two dimensions: doubled Chern-Simons theory. Phys. Rev. B 79, 064405 (2009)
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)
Senthil, T. & Fisher, M. P. A. Z2 gauge theory of electron fractionalization in strongly correlated systems. Phys. Rev. B 62, 7850–7881 (2000)
Yamashita, M. et al. Highly mobile gapless excitations in a two-dimensional candidate quantum spin liquid. Science 328, 1246–1248 (2010)
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)
Isakov, S. V. & Senthil, T. &. Kim, Y. B. Ordering in Cs2CuCl4: possibility of a proximate spin liquid. Phys. Rev. B 72, 174417 (2005)
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)
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)
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)
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)
Ghosh, S., Rosenbaum, T. F. & Aeppli, G. Macroscopic signature of protected spins in a dense frustrated magnet. Phys. Rev. Lett. 101, 157205 (2008)
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)
Pratt, F. L. WiMDA: a muon data analysis program for the Windows PC. Physica B 289–290, 710–714 (2000)
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).
The authors declare no competing financial interests.
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)
About this article
Cite this article
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
This article is cited by
Nature Reviews Methods Primers (2022)
npj Quantum Materials (2021)
Nature Communications (2019)
Nature Communications (2018)
Nature Physics (2017)