Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Gapless ground state in the archetypal quantum kagome antiferromagnet ZnCu3(OH)6Cl2


Spin liquids are exotic phases of quantum matter that challenge Landau’s paradigm of symmetry-breaking phase transitions. Despite strong exchange interactions, spins do not order or freeze down to zero temperature. Although well established for one-dimensional quantum antiferromagnets, in higher dimensions where quantum fluctuations are less acute, realizing and understanding such states is a major issue, both theoretically and experimentally. In this regard, the simplest nearest-neighbour Heisenberg antiferromagnet Hamiltonian on the highly frustrated kagome lattice has proven to be a fascinating and inspiring model. The exact nature of its ground state remains elusive and the existence of a spin-gap is the first key issue to be addressed to discriminate between the various classes of proposed spin liquids. Here, through low-temperature NMR contrast experiments on high-quality single crystals, we single out the kagome susceptibility and the corresponding dynamics in the kagome archetype, the mineral herbertsmithite, ZnCu3(OH)6Cl2. We firmly conclude that this material does not harbour any spin-gap, which restores a convergence with recent numerical results promoting a gapless Dirac spin liquid as the ground state of the Heisenberg kagome antiferromagnet.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Herbertsmithite structure.
Fig. 2: Low-T NMR spectra measured for Ba*.
Fig. 3: Gapless ground state from shift and T1 measurements.
Fig. 4: Defect lines and local configurations.

Data availability

The data represented in Figs. 2a–c, 3a(left, right), b–d and 4a,c,d are available as Source Data. All other data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.


  1. 1.

    Knolle, J. & Moessner, R. A field guide to spin liquids. Annu. Rev. Condens. Matter Phys. 10, 451–472 (2019).

    ADS  Google Scholar 

  2. 2.

    Wen, X. G. Quantum orders and symmetric spin liquids. Phys. Rev. B 65, 165113 (2002).

    ADS  Google Scholar 

  3. 3.

    Savary, L. & Balents, L. Quantum spin liquids: a review. Rep. Prog. Phys. 80, 016502 (2017).

    ADS  Google Scholar 

  4. 4.

    Lacroix, C. et al. (eds) Introduction to Frustrated Magnetism (Springer, 2010).

  5. 5.

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

    ADS  Google Scholar 

  6. 6.

    Mendels, P. & Bert, F. Quantum kagome antiferromagnet ZnCu3(OH)6Cl2. J. Phys. Soc. Jpn 79, 011001 (2010).

    ADS  Google Scholar 

  7. 7.

    Mendels, P. & Bert, F. Quantum kagome frustrated antiferromagnets: one route to quantum spin liquids. C. R. Phys. 17, 455–470 (2016).

    ADS  Google Scholar 

  8. 8.

    Zhou, Y., Kanoda, K. & Ng, T. K. Quantum spin liquid states. Rev. Mod. Phys. 89, 025003 (2017).

    ADS  MathSciNet  Google Scholar 

  9. 9.

    Shores, M. P., Nytko, E. A., Bartlett, B. M. & Nocera, D. G. A structurally perfect S = 1/2 kagome antiferromagnet. J. Am. Chem. Soc. 127, 13462–13463 (2005).

    Google Scholar 

  10. 10.

    Jeschke, H. O., Pujol, F. S. & Roser Valenti, R. First-principles determination of Heisenberg Hamiltonian parameters for the spin-1/2 kagome antiferromagnet ZnCu3(OH)6Cl2. Phys. Rev. B 88, 075106 (2013).

    ADS  Google Scholar 

  11. 11.

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

    ADS  Google Scholar 

  12. 12.

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

    ADS  Google Scholar 

  13. 13.

    Norman, M. R. Herbertsmithite and the search for the quantum spin liquid. Rev. Mod. Phys. 88, 041002 (2016).

    ADS  MathSciNet  Google Scholar 

  14. 14.

    Han, T. H. et al. Barlowite: a spin-1/2 antiferromagnet with a geometrically perfect kagome motif. Phys. Rev. Lett. 113, 227203 (2014).

    ADS  Google Scholar 

  15. 15.

    Feng, Z. et al. Gapped spin-1/2 spinon excitations in a new kagome quantum spin liquid compound Cu3 Zn(OH)6 FBr. Chin. Phys. Lett. 34, 077502 (2017).

    ADS  Google Scholar 

  16. 16.

    Li, Y. Gapless quantum spin liquid in the S = 1/2 anisotropic kagome antiferromagnet ZnCu3(OH)6SO4. New J. Phys. 16, 093011 (2014).

    Google Scholar 

  17. 17.

    Puphal, P. et al. Tuning of a kagome magnet: insulating ground state in Ga-substituted Cu4(OH)6Cl2. Phys. Status Solidi B 256, 1800663 (2019).

    ADS  Google Scholar 

  18. 18.

    Puphal, P. et al. Strong magnetic frustration in Y3Cu9(OH)19Cl18: a distorted kagome antiferromagnet. J. Mater. Chem. C 5, 2629–2635 (2017).

    Google Scholar 

  19. 19.

    Sun, W. et al. Perfect kagomé lattices in YCu3(OH)6Cl3: a new candidate for the quantum spin liquid state. J. Mater. Chem. C 4, 8772–8777 (2016).

    Google Scholar 

  20. 20.

    Barthélemy, Q. et al. Local study of the insulating quantum kagome antiferromagnets YCu3(OH)6OxCl3 − x (x = 0, 1/3). Phys. Rev. Mater. 3, 074401 (2019).

    Google Scholar 

  21. 21.

    Kelly, Z. A., Gallagher, M. J. & McQueen, T. M. Electron doping a kagome spin liquid. Phys. Rev. X 6, 041007 (2016).

    Google Scholar 

  22. 22.

    Clark, L. et al. Gapless spin liquid ground state in the S = 1/2 vanadium oxyfluoride kagome antiferromagnet [NH4]2[C7H14N][V7O6F18]. Phys. Rev. Lett. 110, 207208 (2013).

    ADS  Google Scholar 

  23. 23.

    Orain, J. C. et al. Nature of the spin liquid ground state in a breathing kagome compound studied by NMR and series expansion. Phys. Rev. Lett. 118, 237203 (2017).

    ADS  Google Scholar 

  24. 24.

    Singh, R. R. P. & Huse, D. A. Ground state of the spin-1/2 kagome-lattice Heisenberg antiferromagnet. Phys. Rev. B 76, 180407(R) (2007).

    ADS  Google Scholar 

  25. 25.

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

    ADS  Google Scholar 

  26. 26.

    Hermele, M., Ran, Y., Lee, P. A. & Wen, X.-G. Properties of an algebraic spin liquid on the kagome lattice. Phys. Rev. B 77, 224–413 (2008).

    Google Scholar 

  27. 27.

    Ran, Y., Ko, W.-H., Lee, P. A. & Wen, X.-G. Spontaneous spin ordering of a Dirac spin liquid in a magnetic field. Phys. Rev. Lett. 102, 047205 (2009).

    ADS  Google Scholar 

  28. 28.

    Sindzingre, P. & Lhuillier, C. Low-energy excitations of the kagome antiferromagnet and the spin-gap issue. Europhys. Lett. 88, 27009 (2009).

    ADS  Google Scholar 

  29. 29.

    Yan, S., Huse, D. A. & White, S. R. Spin liquid ground state of the S = 1/2 kagomé Heisenberg model. Science 332, 1173–1176 (2011).

    ADS  Google Scholar 

  30. 30.

    Depenbrock, S., McCulloch, I. P. & Schollwöck, U. Nature of the spin–liquid ground state of the S = 1/2 Heisenberg model on the kagome lattice. Phys. Rev. Lett. 109, 067201 (2012).

    ADS  Google Scholar 

  31. 31.

    Iqbal, Y., Becca, F., Sorella, S. & Poilblanc, D. Gapless spin-liquid phase in the kagome spin-1/2 Heisenberg antiferromagnet. Phys. Rev. B 87, 060405(R) (2013).

    ADS  Google Scholar 

  32. 32.

    Läuchli, A. M., Sudan, J. & Moessner, R. The S = 1/2 kagome Heisenberg antiferromagnet revisited. Phys. Rev. B 100, 155142 (2019).

    ADS  Google Scholar 

  33. 33.

    Hotta, C. & Asano, K. Magnetic susceptibility of quantum spin systems calculated by sine square deformation: one-dimensional, square lattice, and kagome lattice Heisenberg antiferromagnet. Phys. Rev. B 98, 140405(R) (2018).

    ADS  Google Scholar 

  34. 34.

    He, Y.-C., Zaletel, M. P., Oshikawa, M. & Pollmann, F. Signatures of Dirac cones in a DMRG study of the kagome Heisenberg model. Phys. Rev. X 7, 031020 (2017).

    Google Scholar 

  35. 35.

    Liao, H. J. et al. Gapless spin–liquid ground state in the S = 1/2 kagome antiferromagnet. Phys. Rev. Lett. 118, 137202 (2017).

    ADS  Google Scholar 

  36. 36.

    M. A. de Vries, M. Ade et al. Magnetic ground state of an experimental S = 1/2 kagome antiferromagnet. Phys. Rev. Lett. 100, 157205 (2008).

    ADS  Google Scholar 

  37. 37.

    Han, T. H. et al. Thermodynamic properties of the quantum spin liquid candidate ZnCu3(OH)6Cl2 in high magnetic fields. Preprint at (2014).

  38. 38.

    Bert, F. et al. Low temperature magnetization of the S = 1/2 kagome antiferromagnet ZnCu3(OH)6Cl2. Phys. Rev. B 76, 132411 (2007).

    ADS  Google Scholar 

  39. 39.

    Han, T. H. et al. Synthesis and characterization of single crystals of the spin-1/2 kagome-lattice antiferromagnets ZnxCu4 − x (OH)6Cl2. Phys. Rev. B 83, 100402(R) (2011).

    ADS  Google Scholar 

  40. 40.

    Olariu, A. 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).

    ADS  Google Scholar 

  41. 41.

    Fu, M., Imai, T., Han, T. H. & Lee, Y. S. Evidence for a gapped spin–liquid ground state in a kagome heisenberg antiferromagnet. Science 350, 655–658 (2015).

    ADS  Google Scholar 

  42. 42.

    Bernu, B. & Lhuillier, C. Spin susceptibility of quantum magnets from high to low temperatures. Phys. Rev. Lett. 114, 057201 (2015).

    ADS  Google Scholar 

  43. 43.

    Kawamura, H., Watanabe, K. & Shimokawa, T. Quantum spin–liquid behavior in the spin-1/2 random-bond heisenberg antiferromagnet on the kagome lattice. J. Phys. Soc. Jpn 83, 103704 (2014).

    ADS  Google Scholar 

  44. 44.

    Zhu, L. & Wang, X. Singularity of density of states induced by random bond disorder in graphene. Phys. Lett. A 380, 2233–2236 (2016).

    ADS  Google Scholar 

  45. 45.

    Schnack, J., Schulenburg, J. & Richter, J. Magnetism of the N = 42 kagome lattice antiferromagnet. Phys. Rev. B 98, 094423 (2018).

    ADS  Google Scholar 

  46. 46.

    Lee, C.-Y., B.Normand, B. & Kao, Y. J. Gapless spin liquid in the kagome heisenberg antiferromagnet with Dzyaloshinskii–Moriya interactions. Phys. Rev. B 98, 224414 (2018).

    ADS  Google Scholar 

  47. 47.

    Zorko, A. et al. Dzyaloshinsky–Moriya anisotropy in the spin-1/2 kagome compound ZnCu3(OH)6Cl2. Phys. Rev. Lett. 101, 026405 (2008).

    ADS  Google Scholar 

  48. 48.

    El Shawish, S., Cepas, O. & Miyashita, S. Electron spin resonance in S = 1/2 antiferromagnets at high temperature. Phys. Rev. B 81, 224421 (2010).

    ADS  Google Scholar 

  49. 49.

    Zorko, A. et al. Dzyaloshinsky–Moriya interaction in vesignieite: a route to freezing in a quantum kagome antiferromagnet. Phys. Rev. B 88, 144419 (2013).

    ADS  Google Scholar 

  50. 50.

    Tedoldi, F., Santachiara, R. & Horvatic, M. 89NMR imaging of the staggered magnetization in the doped haldane chain Y2BaNi1 − xMgxO5. Phys. Rev. Lett. 83, 412–415 (1999).

    ADS  Google Scholar 

  51. 51.

    Alloul, H., Bobroff, J., Gabay, M. & Hirschfeld, P. J. Defects in correlated metals and superconductors. Rev. Mod. Phys. 81, 45–108 (2009).

    ADS  Google Scholar 

  52. 52.

    Zorko, A. et al. Symmetry reduction in the quantum kagome antiferromagnet herbertsmithite. Phys. Rev. Lett. 118, 017202 (2017).

    ADS  Google Scholar 

  53. 53.

    Freedman, D. E. et al. Site specific X-ray anomalous dispersion of the geometrically frustrated kagome magnet, herbertsmithite, ZnCu3(OH)6Cl2. J. Am. Chem. Soc. 132, 16185–16190 (2010).

    Google Scholar 

  54. 54.

    Rousochatzakis, I., Manmana, S. R., Lauchli, A. M., Normand, B. & Mila, F. Dzyaloshinskii–Moriya anistropy and nonmagnetic impurities in the kagome system ZnCu3(OH)6Cl2. Phys. Rev. B 79, 214415 (2009).

    ADS  Google Scholar 

  55. 55.

    Gomilšek, M. et al. Kondo screening in a charge-insulating spinon metal. Nat. Phys. 15, 754–758 (2019).

    Google Scholar 

Download references


This work was supported by the French Agence Nationale de la Recherche under grants ANR-12-BS04-0021 ‘SPINLIQ’ and ANR-18-CE30-0022-04 ‘LINK’, and by Université Paris-Sud grant MRM PMP. P.K. acknowledges support from the European Commission through a Marie Curie International Incoming Fellowship (PIIF-GA-2013-627322). A.Z. acknowledges the support of the Slovenian Research Agency (project no. BI-US/18-20-064 and programme no. P1-0125). We thank J. Quilliam and G. Simutis for a critical reading of the manuscript.

Author information




P.M. and F.B. conceived, designed and led the project. M.V. grew and characterized the single crystal. P.K., P.M., A.L. and Q.B. carried out the NMR measurements and analysis. A.Z. carried out the ESR experiments. L.M. and B.B. performed the calculations of series. E.K., F.B. and P.M. supervised part of the experimental work and discussed the results. P.M. wrote the manuscript, with feedback from all the authors.

Corresponding author

Correspondence to P. Mendels.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Figs. 1–11 and Discussion (8 sections).

Source Data Fig. 2

Spectra with contrast and without contrast versus temperature.

Source Data Fig. 3

Scaling of (M) spectra and T-variation of shift and T1.

Source Data Fig. 4

(D) spectra and shifts.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Khuntia, P., Velazquez, M., Barthélemy, Q. et al. Gapless ground state in the archetypal quantum kagome antiferromagnet ZnCu3(OH)6Cl2. Nat. Phys. 16, 469–474 (2020).

Download citation

Further reading


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing