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

## Abstract

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.

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## 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.

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## Acknowledgements

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

Authors

### Contributions

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.

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## 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

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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). https://doi.org/10.1038/s41567-020-0792-1

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• DOI: https://doi.org/10.1038/s41567-020-0792-1

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