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# Emergence of spin singlets with inhomogeneous gaps in the kagome lattice Heisenberg antiferromagnets Zn-barlowite and herbertsmithite

## Abstract

The kagome Heisenberg antiferromagnet formed by frustrated spins arranged in a lattice of corner-sharing triangles is a prime candidate for hosting a quantum spin liquid (QSL) ground state consisting of entangled spin singlets1. However, the existence of various competing states makes a convincing theoretical prediction of the QSL ground state difficult2, calling for experimental clues from model materials. The kagome lattice materials Zn-barlowite (ZnCu3(OD)6FBr)3,4,5 and herbertsmithite (ZnCu3(OD)6Cl2)6,7,8,9,10 do not exhibit long-range order and are considered the best realizations of the kagome Heisenberg antiferromagnet known so far. Here we use 63Cu nuclear quadrupole resonance combined with the inverse Laplace transform11,12,13 to locally probe the inhomogeneity of delicate quantum ground states affected by disorder14,15,16,17. We present direct evidence for the gradual emergence of spin singlets with spatially varying excitation gaps, but even at temperatures far below the super-exchange energy scale their fraction is limited to ~60% of the total spins. Theoretical models18,19 need to incorporate the role of disorder to account for the observed inhomogeneously gapped behaviour.

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## Data availability

The datasets generated during the current study are available from the corresponding author on reasonable request.

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## Acknowledgements

T.I. thanks T. Sakai, K. Uematsu, R. R. P. Singh, I. Kimchi, P. A. Lee and S. Sachdev for helpful communications, and P. Dube and R. Giannetta for technical assistance. The work at McMaster was supported by NSERC (T.I.). P.M.S. was supported by the Rice University Consortium for Processes in Porous Media. The work at Stanford and SLAC (sample synthesis and characterization) was supported by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under contract no. DE-AC02-76SF00515 (Y.S.L. and J. Wen). R.W.S. was supported by the US Department of Defense (DoD) through the National Defense Science and Engineering Graduate Fellowship (NDSEG) Program as well as an NSF Graduate Research Fellowship (DGE-1656518).

## Author information

Authors

### Contributions

T.I. and Y.S.L. conceived the project. R.W.S., W.H., J. Wen and Y.S.L. synthesized and characterized the samples. J. Wang, W.Y., P.M.S. and T.I. carried out the NMR measurements and data analysis. All authors contributed to the writing and editing of the manuscript.

### Corresponding author

Correspondence to Takashi Imai.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature Physics thanks Martin Klanjsek and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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## Supplementary information

### Supplementary information

Supplementary Discussion and Figs. 1–9.

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Reprints and Permissions

Wang, J., Yuan, W., Singer, P.M. et al. Emergence of spin singlets with inhomogeneous gaps in the kagome lattice Heisenberg antiferromagnets Zn-barlowite and herbertsmithite. Nat. Phys. 17, 1109–1113 (2021). https://doi.org/10.1038/s41567-021-01310-3

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