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Quantum-spin-liquid states in the two-dimensional kagome antiferromagnets ZnxCu4−x(OD)6Cl2


A three-dimensional system of interacting spins typically develops static long-range order when it is cooled. If the spins are quantum (S=1/2), however, novel quantum paramagnetic states may appear. The most highly sought state among them is the resonating-valence-bond state1,2, in which every pair of neighbouring quantum spins forms an entangled spin singlet (valence bonds) and these singlets are quantum mechanically resonating among themselves. Here we provide an experimental indication for such quantum paramagnetic states existing in frustrated antiferromagnets, ZnxCu4−x(OD)6Cl2, where the S=1/2 magnetic Cu2+ moments form layers of a two-dimensional kagome lattice. We find that in Cu4(OD)6Cl2, where distorted kagome planes are weakly coupled, a dispersionless excitation mode appears in the magnetic excitation spectrum below 20 K, whose characteristics resemble those of quantum spin singlets in a solid state, known as a valence-bond solid, that breaks translational symmetry. Doping with non-magnetic Zn2+ ions reduces the distortion of the kagome lattice, and weakens the interplane coupling but also dilutes the magnetic occupancy of the kagome lattice. The valence-bond-solid state is suppressed, and for ZnCu3(OD)6Cl2, where the kagome planes are undistorted and 90% occupied by the Cu2+ ions, the low-energy spin fluctuations become featureless.

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Figure 1: Local crystal structure and phase diagram of ZnxCu4−x(OD)6Cl2.
Figure 2: Energy and temperature dependence of the static and dynamic spin correlations in Cu4(OD)6Cl2.
Figure 3: Doping dependence of static and dynamic spin correlations.
Figure 4: Q dependence of magnetic fluctuations in ZnxCu4−x(OD)6Cl2.
Figure 5: Magnetic-field effect on magnetic excitations.


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

    Article  CAS  Google Scholar 

  2. Fazekas, P. & Anderson, P. W. Ground-state properties of anisotropic triangular antiferromagnet. Phil. Mag. 30, 423–440 (1974).

    Article  CAS  Google Scholar 

  3. Anderson, P. W. The resonating valence bond state in La2CuO4 and superconductivity. Science 235, 1196–1198 (1987).

    Article  CAS  Google Scholar 

  4. Kivelson, S. A., Rokhsar, D. S. & Sethna, J. P. Topology of the resonating valence-bond state—solitons and high-Tc superconductivity. Phys. Rev. B 35, 8865–8868 (1987).

    Article  CAS  Google Scholar 

  5. Read, N. & Sachdev, S. Large-N expansion for frustrated quantum antiferromagnets. Phys. Rev. Lett. 66, 1773–1776 (1991).

    Article  CAS  Google Scholar 

  6. Hastings, M. B. Dirac structure, RVB, and Goldstone modes in the kagomé antiferromagnet. Phys. Rev. B 63, 014413 (2001).

    Article  Google Scholar 

  7. Park, K. & Sachdev, S. Bond and Néel order and fractionalization in ground states of easy-plane antiferromagnets in two dimensions. Phys. Rev. B 65, 220405(R) (2002).

    Article  Google Scholar 

  8. Senthil, T., Balents, L., Sachdev, S., Vishwanath, A. & Fisher, M. P. A. Quantum criticality beyond the Landau–Ginzburg–Wilson paradigm. Phys. Rev. B 70, 144407 (2004).

    Article  Google Scholar 

  9. Ran, Y., Hermele, M., Lee, P. A. & Wen, X.-G. Projected wavefunction study of spin-1/2 Heisenberg model on the kagomé lattice. Phys. Rev. Lett. 98, 117205 (2007).

    Article  Google Scholar 

  10. Ryu, S., Motrunich, O. I., Alicea, J. & Fisher, M. P. A. Algebraic vortex liquid theory of a quantum antiferromagnet on the kagomé lattice. Phys. Rev. B 75, 184406 (2007).

    Article  Google Scholar 

  11. Ramirez, A. P. in Handbook on Magnetic Materials Vol. 13 (ed. Busch, K. J. H.) 423 (Elsevier Science, Amsterdam, 2001).

    Google Scholar 

  12. Lee, S.-H. et al. Emergent excitations in a geometrically frustrated magnet. Nature 418, 856–858 (2002).

    Article  CAS  Google Scholar 

  13. Shores, M. P. et al. A structurally perfect S=1/2 kagomé antiferromagnet. J. Am. Chem. Soc. 127, 13462–13463 (2005).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  15. Ofer, O. et al. Ground state and excitation properties of the quantum kagomé system ZnCu3(OH)6Cl2 investigated by local probes. Preprint at <> (2006).

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

    Article  CAS  Google Scholar 

  17. Zheng, X. G. et al. Unconventional magnetic transitions in the mineral clinoatacamite Cu2Cl(OH)3 . Phys. Rev. B 71, 052409 (2005).

    Article  Google Scholar 

  18. Zheng, X. G. et al. Coexistence of long-range order and spin fluctuation in geometrically frustrated clinoatacamite Cu2Cl(OH)3 . Phys. Rev. Lett. 95, 057201 (2005).

    Article  CAS  Google Scholar 

  19. Sato, T. J. et al. Unconventional spin fluctuations in the hexagonal antiferromagnet YMnO3 . Phys. Rev. B 68, 014432 (2003).

    Article  Google Scholar 

  20. Nishiyama, M. et al. Magnetic ordering and spin dynamics in potassium jarosite: A Heisenberg kagome lattice antiferromagnet. Phys. Rev. B 67, 224435 (2003).

    Article  Google Scholar 

  21. Matan, M. et al. Spin waves in the frustrated kagome lattice antiferromanget KFe3(OH)6(SO4)2 . Phys. Rev. Lett. 96, 247201 (2006).

    Article  CAS  Google Scholar 

  22. Furrer, A. & Gudel, H. U. Neutron inelastic-scattering from isolated clusters of magnetic ions. J. Magn. Magn. Mater. 14, 256–264 (1979).

    Article  CAS  Google Scholar 

  23. Lee, S.-H. et al. Isolated spin pairs and two-dimensional magnetism in SrCr9pGa12−9pO19 . Phys. Rev. Lett. 76, 4424–4427 (1996).

    Article  CAS  Google Scholar 

  24. Rigol, M. & Singh, R. R. P. Magnetic susceptibility of the kagomé antiferromagnet. Phys. Rev. Lett. 98, 207204 (2007).

    Article  Google Scholar 

  25. Levi, B. G. New candidate emerges for a quantum spin liquid. Phys. Today 60, 16–19 (2007).

    Article  Google Scholar 

  26. Mizuno, Y. et al. Electronic states and magnetic properties of edge-sharing Cu–O chains. Phys. Rev. B 57, 5326–5335 (1998).

    Article  CAS  Google Scholar 

  27. Tornow, S., Entin-Wohlman, O. & Aharony, A. Anisotropic superexchange for nearest and next-nearest coppers in chain, ladder, and lamellar cuprates. Phys. Rev. B 60, 10206–10215 (1999).

    Article  CAS  Google Scholar 

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We thank D. Khomskii, S. Sachdev and M. Gingras for helpful discussions. S.-H.L. is supported by US DOC through NIST-70NANB5H1152. Activities at NIST were partially supported by NSF through DMR-0454672.

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Correspondence to S.-H. Lee.

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Lee, SH., Kikuchi, H., Qiu, Y. et al. Quantum-spin-liquid states in the two-dimensional kagome antiferromagnets ZnxCu4−x(OD)6Cl2. Nature Mater 6, 853–857 (2007).

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