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# Physical realization of a quantum spin liquid based on a complex frustration mechanism

## Abstract

Unlike conventional magnets where the magnetic moments are partially or completely static in the ground state, in a quantum spin liquid they remain in collective motion down to the lowest temperatures. The importance of this state is that it is coherent and highly entangled without breaking local symmetries. In the case of magnets with isotropic interactions, spin-liquid behaviour is sought in simple lattices with antiferromagnetic interactions that favour antiparallel alignments of the magnetic moments and are incompatible with the lattice geometries. Despite an extensive search, experimental realizations remain very few. Here we investigate the novel, unexplored magnet Ca10Cr7O28, which has a complex Hamiltonian consisting of several different isotropic interactions and where the ferromagnetic couplings are stronger than the antiferromagnetic ones. We show both experimentally and theoretically that it displays all the features expected of a quantum spin liquid. Thus spin-liquid behaviour in isotropic magnets is not restricted to the simple idealized models currently investigated, but can be compatible with complex structures and ferromagnetic interactions.

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## Acknowledgements

We thank S. Toth for his help with the SpinW program and E. J. Bergholtz for helpful discussions. We acknowledge the Helmholtz Gemeinschaft for funding via the Helmholtz Virtual Institute (Project No. HVI-521) and DFG through Research Training Group GRK 1621 and SFB 1143. We also acknowledge the support of the HLD-HZDR, a member of the European Magnetic Field Laboratory (EMFL). This work used facilities supported in part by the National Science Foundation under Agreement No. DMR-1508249. J.R. was supported by the Freie Universität Berlin, within the Excellence Initiative of the German Research Foundation.

## Author information

Authors

### Contributions

C.B. performed or participated in all measurements, and analysed the data with help from the other authors. B.L. directed the project, participated in most measurements, and wrote the manuscript with contributions from all authors. J.R. carried out the PFFRG calculations and provided theoretical insight. Y.S. introduced the compound and made the powder, while the crystals were grown by Y.S. and A.T.M.N.I.; H.R. carried out the specific heat measurements; R.S. and T.H. performed the AC susceptibility measurements and helped with the analysis; C.B. and H.L. helped with the μSR measurements and with their analysis; E.M.W., J.A.R.-R., T.G. and G.G.S. supported the INS measurements.

### Corresponding author

Correspondence to Christian Balz.

## Ethics declarations

### Competing interests

The authors declare no competing financial interests.

## Supplementary information

### Supplementary information

Supplementary information (PDF 16502 kb)

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Balz, C., Lake, B., Reuther, J. et al. Physical realization of a quantum spin liquid based on a complex frustration mechanism. Nature Phys 12, 942–949 (2016). https://doi.org/10.1038/nphys3826

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• DOI: https://doi.org/10.1038/nphys3826

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