Quantum liquids—known to be realized in 3He, 4He and electronsin metals—generally exhibit instabilities unforeseen under classical Newtonian dynamics, such as the superfluid and superconducting transitions. Recently, a new quantum liquid, now known as the quantum spin liquid, has been discovered in frustrated antiferromagnetic spin-1/2 systems1,2. In this state, quantum fluctuations of spins prevent classical antiferromagnetic ordering even at absolute zero, similar to the situation in the well-known quantum liquids. A fundamental question that has remained open is whether instabilities other than classical ordering can occur in a quantum spin liquid, as well as in the well-known quantum liquids. Here we demonstrate experimentally that a quantum spin liquid in an organic triangular-lattice antiferromagnet undergoes an instability involving symmetry breaking and/or topological ordering3, possibly giving rise to a new quantum state of matter. Our result reveals a new variety of quantum-liquid instability, which might become a comparable concept to the already-known fermion-liquid instabilities (such as Bardeen–Cooper–Schrieffer pairing and Peierls instability) and boson-liquid instability (Bose–Einstein condensation).
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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).
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).
Wen, X-G. Topological orders in rigid states. Int. J. Mod. Phys. B 4, 239–271 (1990).
Dyson, F. J., Lieb, E. H. & Simon, B. Phase-transitions in quantum spin systems with isotropic and non-isotropic interactions. J. Stat. Phys. 18, 335–383 (1978).
Kennedy, T., Lieb, E. H. & Shastry, B. S. Existence of Néel order in some spin-1/2 Heisenberg antiferromagnets. J. Stat. Phys. 53, 1019–1030 (1988).
Reger, J. D. & Young, A. P. Monte Carlo simulations of the spin-1/2 Heisenberg antiferromagnet on a square lattice. Phys. Rev. B 37, 5978–5981 (1988).
Anderson, P. W. Resonating valence bonds: A new kind of insulator? Mater. Res. Bull. 8, 153–160 (1973).
Lee, S-S. & Lee, P.A. U(1) gauge theory of the Hubbard model: Spin liquid states and possible application to κ-(BEDTTTF)2Cu2(CN)3 . Phys. Rev. Lett. 95, 036403 (2005).
Motrunich, O. I. Variational study of triangular lattice spin-1/2 model with ring exchanges and spin liquid state in κ-(ET)2Cu2CN3 . Phys. Rev. B 72, 045105 (2005).
Kyung, B. & Tremblay, A-M. S. Mott transition, antiferromagnetism, and d-wave superconductivity in two-dimensional organic conductors. Phys. Rev. Lett. 97, 046402 (2006).
Powell, B. J. & McKenzie, R. H. Strong electronic correlations in superconducting organic charge transfer salts. J. Phys. Condens. Matter 18, R827–R866 (2006).
Mizusaki, T. & Imada, M. Gapless quantum spin liquid, stripe, and antiferromagnetic phases in frustrated Hubbard models in two dimensions. Phys. Rev. B 74, 014421 (2006).
Yunoki, S. & Sorella, S. Two spin liquid phases in the spatially anisotropic triangular Heisenberg model. Phys. Rev. B 74, 014408 (2006).
Motrunich, O. I. Orbital magnetic field effects in spin liquid with spinon Fermi sea: Possible application to κ-(ET)2Cu2CN3 . Phys. Rev. B 73, 155115 (2006).
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-(BEDTTTF)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).
Senthil, T. Theory of a continuous Mott transition in two dimensions. Phys. Rev. B 78, 045109 (2008).
Qi, Y. & Sachdev, S. Insulator–metal transition on the triangular lattice. Phys. Rev. B 77, 165112 (2008).
Yoshioka, T., Koga, A. & Kawakami, N. Quantum phase transitions in the Hubbard model on a triangular lattice. Phys. Rev. Lett. 103, 036401 (2009).
Tocchio, L. F., Parola, A., Gros, C. & Becca, F. Spin-liquid and magnetic phases in the anisotropic triangular lattice: The case of κ-(ET)2X. Phys. Rev. B 80, 064419 (2009).
Heidarian, D., Sorella, S. & Becca, F. Spin-1/2 Heisenberg model on the anisotropic triangular lattice: From magnetism to a one-dimensional spin liquid. Phys. Rev. B 80, 012404 (2009).
Qi, Y., Xu, C. & Sachdev, S. Dynamics and transport of the Z2 spin liquid: Application to κ-(ET)2Cu2CN3 . Phys. Rev. Lett. 102, 176401 (2009).
Xu, C. & Sachdev, S. Global phase diagrams of frustrated quantum antiferromagnets in two dimensions: Doubled Chern–Simons theory. Phys. Rev. B 79, 064405 (2009).
Gregor, K. & Motrunich, O. I. Nonmagnetic impurities in a S=1/2 frustrated triangular antiferromagnet: Broadening of 13C NMR lines in κ-(ET)2Cu2CN3 . Phys. Rev. B 79, 024421 (2009).
Grover, T., Trivedi, N., Senthil, T. & Lee, P. A. Weak Mott insulators on the triangular lattice: possibility of a gapless nematic quantum spin liquid. Phys. Rev. B 81, 245121 (2010).
Kalmeyer, V. & Laughlin, R. B. Equivalence of the resonating-valence bond and fractional quantum Hall states. Phys. Rev. Lett. 59, 2095–2098 (1987).
Baskaran, G. Novel local symmetries and chiral-symmetry-broken phases in S=1/2 triangular-lattice Heisenberg model. Phys. Rev. Lett. 63, 2524–2527 (1989).
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).
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)2Cu2CN3 . Phys. Rev. B 73, 140407 (2006).
We acknowledge helpful discussions with K. Kanoda, M. Tamura and Y. Shimizu. We thank F. Kagawa for helpful suggestions for improving of the manuscript. This work was supported by Grant-In-Aid for Scientific Research from MEXT, Japan (numbers 16GS0219, 18740199, 19052005 and 21740255).
The authors declare no competing financial interests.
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Itou, T., Oyamada, A., Maegawa, S. et al. Instability of a quantum spin liquid in an organic triangular-lattice antiferromagnet. Nature Phys 6, 673–676 (2010) doi:10.1038/nphys1715
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