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Proximate spin liquid and fractionalization in the triangular antiferromagnet KYbSe2

Nature Physics volume 20, pages 74–81 (2024)Cite this article

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Abstract

The Heisenberg triangular-lattice quantum spin liquid and its phase transitions to nearby magnetic orders have received much theoretical attention, but clear experimental manifestations of these states are rare. Here we demonstrate that a spin-half delafossite material, namely, KYbSe2, shows close proximity to the triangular-lattice Heisenberg quantum spin liquid. Using neutron scattering, we identify a diffuse continuum with a sharp lower bound within the measured spectra. Applying entanglement witnesses to the data indicates multipartite entanglement spread between its neighbours, and an analysis of its magnetic-exchange couplings reveals close proximity to the theoretical quantum spin-liquid phase. The key features of the data are reproduced by Schwinger boson theory and tensor network calculations with a substantial next-nearest-neighbour coupling. The strength of the dynamical structure factor at the Brillouin-zone K point shows a scaling collapse down to 0.3 K, indicating the existence of a second-order quantum phase transition. Comparing this with previous theoretical work suggests that the proximate phase at a larger next-nearest-neighbour coupling is a gapped \({{\mathbb{Z}}}_{2}\) spin liquid, resolving a long-debated issue.

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Fig. 1: Crystal structure and phase diagram of KYbSe2.
Fig. 2: Neutron spectrum of KYbSe2 at 0.3, 1.0 and 2.0 K.
Fig. 3: CEF spectrum of KYbSe2.
Fig. 4: KYbSe2 entanglement witnesses.
Fig. 5: Comparison between experimental KYbSe2 scattering and theoretical simulations.
Fig. 6: Critical scaling in KYbSe2.

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Data availability

All the plotted experimental data are publicly available at https://doi.org/10.14461/oncat.data.64bed7e0fd6850c0afce4da2/1995350. Source data are provided with this paper.

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Acknowledgements

This research used resources at the Spallation Neutron Source and High Flux Isotope Reactor, Department of Energy (DOE), Office of Science User Facilities, operated by the Oak Ridge National Laboratory. The work by D.A.T., C.D.B. and E.A.G. is supported by the Quantum Science Center (QSC), a National Quantum Information Science Research Center of the US DOE. The work of J.A.M.P. (magnetic diffuse scattering fits) was supported by the US DOE, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division. J.X. and A.S.S. were supported by the US DOE, Basic Energy Sciences, Materials Science and Engineering Division. L.O.M. and A.E.T. were supported by CONICET under grant no. 364 (PIP2015). This research used resources at the Missouri University Research Reactor and the Department of Chemistry at the University of Missouri. S.L., A.J.W. and R.M. were supported by the US DOE, Office of Science, National Quantum Information Science Research Centers, and Quantum Science Center. N.E.S., M.D., J.E.M., C.D.P. and T.P.D. were supported by the US DOE, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division, under contract no. DE-AC02-05CH11231 (DE-AC02-76SF00515) through the Theory Institute for Materials and Energy Spectroscopy (TIMES). J.E.M. acknowledges additional support by a Simons Investigatorship. This research used the Lawrencium computational cluster resource provided by the IT Division at the Lawrence Berkeley National Laboratory (supported by the Director, US DOE, Office of Science, Office of Basic Energy Sciences, under contract no. DE-AC02-05CH11231). This research also used resources of the National Energy Research Scientific Computing Center (NERSC), a US DOE, Office of Science User Facility, operated under contract no. DE-AC02-05CH11231. This paper has been authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US DOE. The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a non-exclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this paper, or allow others to do so, for US government purposes. The US DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (https://www.energy.gov/doe-public-access-plan).

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Authors and Affiliations

  1. Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN, USA

    A. O. Scheie, D. Abernathy, D. M. Pajerowski & T. J. Williams

  2. Department of Physics and Astronomy, University of Tennessee, Knoxville, TN, USA

    E. A. Ghioldi, C. D. Batista & D. A. Tennant

  3. Instituto de Física Rosario (CONICET) and Universidad Nacional de Rosario, Rosario, Argentina

    E. A. Ghioldi, L. O. Manuel & A. E. Trumper

  4. Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN, USA

    J. Xing, J. A. M. Paddison, A. S. Sefat & D. S. Parker

  5. Department of Physics, University of California, Berkeley, Berkeley, CA, USA

    N. E. Sherman, M. Dupont & J. E. Moore

  6. Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    N. E. Sherman, M. Dupont & J. E. Moore

  7. University of Missouri Research Reactor (MURR), Columbia, MO, USA

    L. D. Sanjeewa

  8. Department of Chemistry, University of Missouri, Columbia, MO, USA

    L. D. Sanjeewa

  9. Los Alamos National Laboratory, Los Alamos, NM, USA

    Sangyun Lee, A. J. Woods & R. Movshovich

  10. School of Physics and Astronomy and William I. Fine Theoretical Physics Institute, University of Minnesota, Minneapolis, MN, USA

    Shang-Shun Zhang

  11. Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Stanford, CA, USA

    C. D. Pemmaraju & T. P. Devereaux

  12. Department of Materials Science and Engineering, Stanford University, Stanford, CA, USA

    T. P. Devereaux

  13. Shull Wollan Center—A Joint Institute for Neutron Sciences, Oak Ridge National Laboratory, Oak Ridge, TN, USA

    C. D. Batista & D. A. Tennant

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  1. A. O. Scheie
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Contributions

A.O.S. and D.A.T. conceived and coordinated the project. J.X., L.D.S. and A.S.S. synthesized and characterized the single-crystal KYbSe2 samples for experiments. A.O.S., D.A., D.M.P. and T.J.W. performed the neutron experiments, and A.O.S. analysed the neutron data and calculated the entanglement witnesses. J.A.M.P. performed the ORF fits. E.A.G., S.-S.Z., L.O.M., A.E.T. and C.D.B. carried out the SB calculations. N.E.S., M.D. and J.E.M. carried out the tensor network calculations of the dynamical structure factors. C.D.P., T.P.D. and D.S.P. carried out the DFT calculations. S.L., A.J.W. and R.M. performed the heat capacity measurements. A.O.S., N.E.S., M.D., J.E.M., C.D.B. and D.A.T. wrote the paper with input from all co-authors.

Corresponding authors

Correspondence to A. O. Scheie or C. D. Batista.

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The authors declare no competing interests.

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Nature Physics thanks Romain Sibille and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 KYbSe2 sample mount.

KYbSe2 sample used to measure the low-energy spin excitations on CNCS. 20 crystals were coaligned and glued to two aluminum plates (top) which were then screwed to a copper rod (bottom). The different crystals are different shades of red because of their different thicknesses.

Extended Data Fig. 2 High resolution KYbSe2 scattering at (1/3,1/3,0).

Panel (a) shows a slice through the data showing the gapless dispersion. Panel (b) shows a 1D cut indicated by the faint vertical red bar in panel (a). Both plots show the dispersion to be gapless at 0.3 K to within 0.04 meV. Error bars indicate one standard deviation uncertainty.

Source data

Extended Data Fig. 3 KYbSe2 background subtraction for CNCS data.

The top row shows the raw data at 0.3 K. The middle row shows the phenomenological background generated from the 12 K scattering data. The bottom row shows the data with the background subtracted, eliminating artifacts near Q = 0 and ℏω = 0.

Source data

Extended Data Fig. 4 Illustration of the geometry used and corresponding Brillouin zone for the tensor network simulations.

Panel a is a 6x6 lattice that we make a cylinder by identifying the top and bottom rows shown in red. Panel b is the Brillouin zone for this geometry, with the blue shaded region showing the allowed momenta, and the arrows show the path we take to generate Fig. (5e).

Extended Data Fig. 5 DFT electronic density of states in KYbSe2.

DFT electronic density of states in KYbSe2 calculated using the SCAN functional with an additional Hubbard-U correction of U = 8 eV on the Yb 5f states. The Fermi energy is set to 0 eV.

Source data

Supplementary information

Supplementary Information

Supplementary Sections I–VII and Figs. 1–11.

Supplementary Data 1

Source data for Supplementary Fig. 1.

Supplementary Data 2

Source data for Supplementary Fig. 2.

Source data

Source Data Fig. 2

Source data for Fig. 2.

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Source data for Fig. 6.

Source Data Extended Data Fig. 2

Source data for Extended Data Fig. 2.

Source Data Extended Data Fig. 3

Source data for Extended Data Fig. 3.

Source Data Extended Data Fig. 5

Source data for Extended Data Fig. 5.

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Scheie, A.O., Ghioldi, E.A., Xing, J. et al. Proximate spin liquid and fractionalization in the triangular antiferromagnet KYbSe2. Nat. Phys. 20, 74–81 (2024). https://doi.org/10.1038/s41567-023-02259-1

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