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# Two-dimensional spin liquid behaviour in the triangular-honeycomb antiferromagnet TbInO3

## Abstract

Spin liquid ground states are predicted to arise within several distinct scenarios in condensed matter physics. The observation of these disordered magnetic states is particularly pervasive among a class of materials known as frustrated magnets, in which the competition between various magnetic exchange interactions prevents the system from adopting long-range magnetic order at low temperatures. Spin liquids continue to be of great interest due to their exotic nature and the possibility that they may support fractionalized excitations, such as Majorana fermions. Systems that allow for such phenomena are not only fascinating from a fundamental perspective but may also be practically significant in future technologies based on quantum computation. Here we show that the underlying antiferromagnetic sublattice in TbInO3 can undergo a crystal field-induced distortion of its buckled triangular arrangement to one based on a honeycomb. The absence of a conventional magnetic ordering transition at the lowest measurable temperatures indicates that another critical mechanism must govern in the ground-state selection of TbInO3. We suggest that anisotropic exchange interactions—mediated through strong spin–orbit coupling on the emergent honeycomb lattice of TbInO3—give rise to a highly frustrated spin liquid.

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## Data availability

Raw powder neutron diffraction54 and muon spin relaxation data55 were collected on the HRPD, MuSR and EMu instruments at ISIS Neutron and Muon Facility and Rutherford Appleton Laboratory, UK, respectively. Powder inelastic neutron scattering data were collected on the SEQUOIA and CNCS instruments at the Spallation Neutron Source, Oak Ridge National Laboratory, USA56. All other raw and derived data used to support the findings of this study are available from the authors on request.

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## Acknowledgements

Work at McMaster University was supported by NSERC of Canada. Research at Oak Ridge National Laboratory’s Spallation Neutron Source was supported by the Scientific User Facilities Division, Office of Basic Energy Sciences, US Department of Energy. Work at ISIS was supported by the Science and Technology Facilities Council. Work at Rutgers University was supported by the DOE under grant no. DOE: DE-FG02–07ER46382. The authors thank A. Aczel, P. Baker, G. Chen and M. Gingras for helpful and insightful discussions during preparation of this manuscript.

## Author information

Authors

### Contributions

B.D.G. and S.-W.C. conceived and supervised the project. X.W., X.X. and Y.L. prepared samples and J.K. performed single-crystal magnetic susceptibility measurements. L.C. performed and analysed powder magnetic susceptibility measurements. L.C. and K.S.K. performed high-resolution powder neutron diffraction measurements and L.C. carried out Rietveld analysis of the data. L.C. and M.T.F.T. performed muon spectroscopy measurements and L.C. analysed the data. G.S., D.D.M. and M.B.S. performed the inelastic neutron scattering measurements and G.S. and L.C. analysed the data with guidance from B.D.G. G.S. performed the crystal field calculations and analysis with guidance from B.D.G. L.C. and B.D.G. prepared figures and wrote the paper.

### Corresponding authors

Correspondence to Lucy Clark or Bruce D. Gaulin.

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### Competing interests

The authors declare no competing interests.

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## Supplementary information

### Supplementary Information

Supplementary Text, Supplementary Tables 1–2 and Supplementary Figures 1–4.

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Clark, L., Sala, G., Maharaj, D.D. et al. Two-dimensional spin liquid behaviour in the triangular-honeycomb antiferromagnet TbInO3. Nat. Phys. 15, 262–268 (2019). https://doi.org/10.1038/s41567-018-0407-2

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