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Spectral evidence for Dirac spinons in a kagome lattice antiferromagnet

Nature Physics (2024)Cite this article

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Abstract

Emergent quasiparticles with a Dirac dispersion in condensed matter systems can be described by the Dirac equation for relativistic electrons, in analogy with Dirac particles in high-energy physics. For example, electrons with a Dirac dispersion have been intensively studied in electronic systems such as graphene and topological insulators. However, charge is not a prerequisite for Dirac fermions, and the emergence of Dirac fermions without a charge degree of freedom has been theoretically predicted to be realized in Dirac quantum spin liquids. These quasiparticles carry a spin of 1/2 but are charge-neutral and so are called spinons. Here we show that the spin excitations of a kagome antiferromagnet, YCu3(OD)6Br2[Br0.33(OD)0.67], are conical with a spin continuum inside, which is consistent with the convolution of two Dirac spinons. The predictions of a Dirac spin liquid model with a spinon velocity obtained from spectral measurements are in agreement with the low-temperature specific heat of the sample. Our results, thus, provide spectral evidence for a Dirac quantum spin liquid state emerging in this kagome lattice antiferromagnet. However, the locations of the conical spin excitations differ from those calculated by the nearest-neighbour Heisenberg model, suggesting the Dirac spinons have an unexpected origin.

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Fig. 1: Schematics of low-energy conical spin excitations and reciprocal space for YCu3-Br.
Fig. 2: INS results at low energies with the incident energy of neutrons (Ei) = 2.566 meV.
Fig. 3: Quantitative analysis of the low-energy data at 0.3 K.
Fig. 4: High-energy spin excitations at Ei = 9.986 meV and static susceptibility \({\chi }^{{\prime} }(Q,0)\) in YCu3-Br.

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All relevant data supporting the findings of this study are available from the corresponding authors on reasonable request. Source data are provided with this paper.

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Acknowledgements

We thank Y. Zhou, Y. Li and P. Lee for discussions. This work is supported by the National Key Research and Development Program of China (Grant Nos. 2022YFA1403400 and 2021YFA1400401), the K. C. Wong Education Foundation (Grant No. GJTD-2020-01), the Strategic Priority Research Program (B) of the Chinese Academy of Sciences (Grant No. XDB33000000) and the Research Grants Council of Hong Kong Special Administrative Region of China (Project Nos. 17301721, AoE/P701/20, 17309822, C7037-22GF, A_HKU703/22 and 17302223). Measurements on AMATERAS were performed based on the approved proposal (Grant No. 2022B0048). The measurement on CAMEA was carried out under the proposal number 20220991. We thank HPC2021 system under the Information Technology Services and the Blackbody HPC system at the Department of Physics, University of Hong Kong, as well as the Beijng PARATERA Tech CO., Ltd. (https://cloud.paratera.com).

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Authors and Affiliations

  1. Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, China

    Zhenyuan Zeng, Honglin Zhou, Lankun Han, Runze Chi & Shiliang Li

  2. School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, China

    Zhenyuan Zeng, Honglin Zhou, Lankun Han, Runze Chi & Shiliang Li

  3. Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Hong Kong SAR, China

    Chengkang Zhou & Zi Yang Meng

  4. Center for High Pressure Science and Technology Advanced Research, Beijing, China

    Kuo Li

  5. J-PARC Center, Japan Atomic Energy Agency, Tokai, Japan

    Maiko Kofu & Kenji Nakajima

  6. Photon Science Division, Paul Scherrer Institut, Villigen, Switzerland

    Yuan Wei & Wenliang Zhang

  7. Laboratory for Neutron Scattering and Imaging, Paul Scherrer Institut, Villigen, Switzerland

    Daniel G. Mazzone

  8. Songshan Lake Materials Laboratory, Dongguan, China

    Shiliang Li

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Contributions

Z.Z. grew the samples and analysed the INS data. C.Z., R.C. and Z.Y.M. performed the theoretical analysis and calculations. H.Z. and L.H. helped in co-aligning the crystals. K.L. helped in preparing the deuterated samples. M.K., K.N., Y.W., W.Z. and D.G.M. carried out the neutron scattering experiments. Z.Y.M. and S.L. drafted the paper with input from all authors. S.L. designed and supervised the project.

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Correspondence to Kenji Nakajima, Zi Yang Meng or Shiliang Li.

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Supplementary Information

Supplementary Figs .1–11 and Discussion.

Source data

Source Data for Fig. 2

ASCII data for colour maps of the low-energy INS results.

Source Data for Fig. 3

ASCII data for constant energy cuts along [H, 0] and FWHM versus energy.

Source Data for Fig. 4

ASCII data for high-energy INS colour maps and calculated Kramers–Kronig relation.

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Zeng, Z., Zhou, C., Zhou, H. et al. Spectral evidence for Dirac spinons in a kagome lattice antiferromagnet. Nat. Phys. (2024). https://doi.org/10.1038/s41567-024-02495-z

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