Abstract
Supersolid phases are quantum-entangled states of matter exhibiting the dual characteristics of superfluidity and solidity. Theory predicts that hard-core bosons on a triangular lattice can form such phases at half filling and near complete filling. Leveraging an exact mapping between bosons and spin-\(\frac{1}{2}\) degrees of freedom, here we show that these phases are realized in the triangular-lattice antiferromagnet K2Co(SeO3)2. At zero field, neutron diffraction reveals the development of quasi-two-dimensional \(\sqrt{3}\times \sqrt{3}\) magnetic order with Z3 translational symmetry breaking (solidity), though with reduced amplitude indicating strong quantum fluctuations. These fluctuations manifest as equidistant bands of continuum neutron scattering, where the lowest-energy mode is gapless at K \((\frac{1}{3}\frac{1}{3})\), consistent with broken U(1) spin rotational symmetry (superfluidity). For c-axis-oriented magnetic fields near saturation, we find a second phase consistent with a high-field supersolid. These two supersolids are separated by a pronounced 1/3 magnetization plateau phase that supports coherent spin waves, from which we determine the underlying spin Hamiltonian.
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The numerical data underlying the magnetization, specific heat, and elastic neutron scattering figures have been deposited in the Figshare database and can be accessed at https://figshare.com/s/9771e9a4e5a2cac62fb8. Due to the large file sizes, the raw inelastic neutron scattering datasets are hosted in the ORNL database https://analysis.sns.govunder the experiment identifier IPTS-29655. Processed inelastic neutron scattering data and all other data that support the findings of this study are available from the corresponding authors upon request.
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Acknowledgements
We gratefully acknowledge valuable discussions with Gang Chen, Cristian Batista, Yuan Gao, Andreas Läuchli, Wei Li, Changle Liu, Frédéric Mila, Roderich Moessner, Oleg Tchernyshyov, and Shu Zhang. Initial phases of this work were supported as part of the Institute for Quantum Matter, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award No. DE-SC0019331. Further neutron scattering work was supported by Department of Energy, Office of Science, Basic Energy Sciences under Award No. DE-SC0024469. C.B. was supported by the Gordon and Betty Moore Foundation EPIQS program under GBMF9456. Y.H. and H.C. were supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Early Career Research Program Award KC0402020. J.Z. acknowledges the support of the NSF CAREER grant DMR-1848349. A portion of this work was performed at the National High Magnetic Field Laboratory, which is supported by the National Science Foundation Cooperative Agreement No. DMR-2128556*, the U.S. Department of Energy, and the State of Florida. This research used resources at the High Flux Isotope Reactor and Spallation Neutron Source, DOE Office of Science User Facilities operated by Oak Ridge National Laboratory. The beam time was allocated to HYSPEC and CNCS on proposal number IPTS-29655. The beam time was allocated to HB-3A on proposal number IPTS-31928.
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T.C., R.Z., and C.B. initiated this work. A.G., X.X., and R.C. prepared the samples. T.C., Y.C., Y.H., H.C., B.L.W., A.A.P., and D.M.P. carried out neutron scattering experiments. A.G., E.C., M.J., and M.L. measured high-field magnetization. L.S., Z.T., and N.P.A. performed THz measurements. T.C., A.G., J.Z., L.C., and C.B. wrote the manuscript with input from all coauthors.
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Chen, T., Ghasemi, A., Zhang, J. et al. Phase diagram and spectroscopic signatures of a supersolid in the quantum ising magnet K2Co(SeO3)2. Nat Commun (2026). https://doi.org/10.1038/s41467-026-69661-0
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DOI: https://doi.org/10.1038/s41467-026-69661-0
