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A spin–orbital-entangled quantum liquid on a honeycomb lattice

Nature volume 554, pages 341345 (15 February 2018) | Download Citation


The honeycomb lattice is one of the simplest lattice structures. Electrons and spins on this simple lattice, however, often form exotic phases with non-trivial excitations. Massless Dirac fermions can emerge out of itinerant electrons, as demonstrated experimentally in graphene1, and a topological quantum spin liquid with exotic quasiparticles can be realized in spin-1/2 magnets, as proposed theoretically in the Kitaev model2. The quantum spin liquid is a long-sought exotic state of matter, in which interacting spins remain quantum-disordered without spontaneous symmetry breaking3. The Kitaev model describes one example of a quantum spin liquid, and can be solved exactly by introducing two types of Majorana fermion2. Realizing a Kitaev model in the laboratory, however, remains a challenge in materials science. Mott insulators with a honeycomb lattice of spin–orbital-entangled pseudospin-1/2 moments have been proposed4, including the 5d-electron systems α-Na2IrO3 (ref. 5) and α-Li2IrO3 (ref. 6) and the 4d-electron system α-RuCl3 (ref. 7). However, these candidates were found to magnetically order rather than form a liquid at sufficiently low temperatures8,9,10, owing to non-Kitaev interactions6,11,12,13. Here we report a quantum-liquid state of pseudospin-1/2 moments in the 5d-electron honeycomb compound H3LiIr2O6. This iridate does not display magnetic ordering down to 0.05 kelvin, despite an interaction energy of about 100 kelvin. We observe signatures of low-energy fermionic excitations that originate from a small number of spin defects in the nuclear-magnetic-resonance relaxation and the specific heat. We therefore conclude that H3LiIr2O6 is a quantum spin liquid. This result opens the door to finding exotic quasiparticles in a strongly spin–orbit-coupled 5d-electron transition-metal oxide.

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  1. 1.

    & The rise of graphene. Nat. Mater. 6, 183–191 (2007)

  2. 2.

    Anyons in an exactly solved model and beyond. Ann. Phys. 321, 2–111 (2006)

  3. 3.

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

  4. 4.

    & Mott insulators in the strong spin-orbit coupling limit: from Heisenberg to a quantum compass and Kitaev models. Phys. Rev. Lett. 102, 017205 (2009)

  5. 5.

    & Antiferromagnetic Mott insulating state in single crystals of the honeycomb lattice material Na2IrO3. Phys. Rev. B 82, 064412 (2010)

  6. 6.

    et al. Relevance of the Heisenberg-Kitaev model for the honeycomb lattice iridates A2IrO3. Phys. Rev. Lett. 108, 127203 (2012)

  7. 7.

    et al. α-RuCl3: a spin-orbit assisted Mott insulator on a honeycomb lattice. Phys. Rev. B 90, 041112(R) (2014)

  8. 8.

    et al. Direct evidence of a zigzag spin-chain structure in the honeycomb lattice: a neutron and X-ray diffraction investigation of single-crystal Na2IrO3. Phys. Rev. B 85, 180403(R) (2012)

  9. 9.

    et al. Incommensurate counterrotating magnetic order stabilized by Kitaev interactions in the layered honeycomb α-Li2IrO3. Phys. Rev. B 93, 195158 (2016)

  10. 10.

    et al. Monoclinic crystal structure of α-RuCl3 and the zigzag antiferromagnetic ground state. Phys. Rev. B 92, 235119 (2015)

  11. 11.

    , & Kitaev-Heisenberg model on a honeycomb lattice: possible exotic phases in iridium oxides A2IrO3. Phys. Rev. Lett. 105, 027204 (2010)

  12. 12.

    , & Generic spin model for the honeycomb iridates beyond the Kitaev limit. Phys. Rev. Lett. 112, 077204 (2014)

  13. 13.

    et al. Spin waves and revised crystal structure of honeycomb iridate Na2IrO3. Phys. Rev. Lett. 108, 127204 (2012)

  14. 14.

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

  15. 15.

    , , , & Spin liquid state in an organic Mott insulator with a triangular lattice. Phys. Rev. Lett. 91, 107001 (2003)

  16. 16.

    , , , & Quantum spin liquid in the spin-1/2 triangular antiferromagnet EtMe3Sb[Pd(dmit)2]2. Phys. Rev. B 77, 104413 (2008)

  17. 17.

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

  18. 18.

    et al. 17O NMR study of the intrinsic magnetic susceptibility and spin dynamics of the quantum kagome antiferromagnet ZnCu3(OH)6Cl2. Phys. Rev. Lett. 100, 087202 (2008)

  19. 19.

    et al. Fractionalized excitations in the spin-liquid state of a kagome-lattice antiferromagnet. Nature 492, 406–410 (2012)

  20. 20.

    , , & Evidence for a gapped spin-liquid ground state in a kagome Heisenberg antiferromagnet. Science 350, 655–658 (2015)

  21. 21.

    et al. Phase-sensitive observation of a spin-orbital Mott state in Sr2IrO4. Science 323, 1329–1332 (2009)

  22. 22.

    et al. Direct evidence for dominant bond-directional interactions in a honeycomb lattice iridate Na2IrO3. Nat. Phys. 11, 462–466 (2015)

  23. 23.

    et al. Proximate Kitaev quantum spin liquid behaviour in a honeycomb magnet. Nat. Mater. 15, 733–740 (2016)

  24. 24.

    , & Production and isolation of pH sensing materials by carbonate melt oxidation of iridium and platinum. J. Mater. Chem. 22, 7782–7790 (2012)

  25. 25.

    et al. Solution of the heavily stacking faulted crystal structure of the honeycomb iridate H3LiIr2O6. Dalton Trans. 46, 15216–15227 (2017)

  26. 26.

    , , & Challenges in design of Kitaev materials: magnetic interactions from competing energy scales. Phys. Rev. B 93, 214431 (2016)

  27. 27.

    , & Site dilution in the Kitaev honeycomb model. Phys. Rev. B 84, 115146 (2011)

  28. 28.

    , & Thermal fractionalization of quantum spins in a Kitaev model: temperature-linear specific heat and coherent transport of Majorana fermions. Phys. Rev. B 92, 115122 (2015)

  29. 29.

    , & Fractional spin fluctuations as a precursor of quantum spin liquids: Majorana dynamical mean-field study for the Kitaev model. Phys. Rev. Lett. 117, 157203 (2016)

  30. 30.

    . & VESTA: a three-dimensional visualization system for electronic and structural analysis. J. Appl. Cryst. 41, 653–658 (2008)

  31. 31.

    , & Structure solution and refinement of stacking faulted NiCl(OH). J. Appl. Cryst. 48, 1706–1718 (2015)

  32. 32.

    , , & Distributed τ2 effect in relaxation calorimetry. Physica B 329–333, 1552–1553 (2003)

  33. 33.

    et al. Ga NMR study of the local susceptibility in kagomé-based SrCr8Ga4O19: pseudogap and paramagnetic defects. Phys. Rev. Lett. 85, 3496–3499 (2000)

  34. 34.

    et al. Unconventional dynamics in triangular Heisenberg antiferromagnet NaCrO2. Phys. Rev. Lett. 97, 167203 (2006)

  35. 35.

    et al. Spin dynamics and spin freezing behavior in the two-dimensional antiferromagnet NiGa2S4 revealed by Ga-NMR, NQR and μSR measurements. Phys. Rev. B 77, 054429 (2008)

  36. 36.

    et al. Spin liquid state in the 3D frustrated antiferromagnet PbCuTe2O6: NMR and muon spin relaxation studies. Phys. Rev. Lett. 116, 107203 (2016)

  37. 37.

    et al. Further conventions for NMR shielding and chemical shifts (IUPAC recommendations 2008). Pure Appl. Chem. 80, 59–84 (2008)

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We thank Y. Motome, M. Udagawa, R. Valentí, A. Gibbs, Y. B. Kim, A. Smerald and N. Shannon for discussions, and U. Wedig, Y. Ishikuro, T. Nishioka and S. Nakatsuji for experimental support and discussions. This work was partly supported by the Japan Society for the Promotion of Science (JSPS) KAKAENHI (numbers 24224010, 26707018, 15K13523, JP15H05852, JP15K21717 and 17H01140) and the Alexander von Humboldt foundation.

Author information

Author notes

    • K. Kitagawa
    •  & T. Takayama

    These authors contributed equally to this work.


  1. Department of Physics, University of Tokyo, Bunkyo-ku, Hongo 7-3-1, Tokyo 113-0033, Japan

    • K. Kitagawa
    • , A. Kato
    • , R. Takano
    •  & H. Takagi
  2. Max Planck Institute for Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart, Germany

    • T. Takayama
    • , Y. Matsumoto
    • , S. Bette
    • , R. Dinnebier
    • , G. Jackeli
    •  & H. Takagi
  3. Graduate School of Integrated Arts and Sciences, Kochi University, Akebonocho 2-5-1, Kochi 780-8520, Japan

    • Y. Kishimoto
  4. Institute for Functional Matter and Quantum Technologies, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany

    • G. Jackeli
    •  & H. Takagi


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T.T. and A.K. prepared the sample and performed the bulk experiments. K.K., R.T. and Y.K. carried out the NMR measurements. Y.M. carried out the low-temperature specific heat measurements. S.B. and R.D. performed structural analysis. G.J. gave theoretical inputs. T.T., K.K., Y.M. and H.T. wrote manuscript and all authors commented on it. H.T. designed and supervised the experiments.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to H. Takagi.

Reviewer Information Nature thanks M. Mourigal and S. Todadri for their contribution to the peer review of this work.

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