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Evidence for a spinon Fermi surface in a triangular-lattice quantum-spin-liquid candidate

Nature volume 540, pages 559–562 (2016)Cite this article

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Abstract

A quantum spin liquid is an exotic quantum state of matter in which spins are highly entangled and remain disordered down to zero temperature. Such a state of matter is potentially relevant to high-temperature superconductivity and quantum-information applications, and experimental identification of a quantum spin liquid state is of fundamental importance for our understanding of quantum matter. Theoretical studies have proposed various quantum-spin-liquid ground states1,2,3,4, most of which are characterized by exotic spin excitations with fractional quantum numbers (termed ‘spinons’). Here we report neutron scattering measurements of the triangular-lattice antiferromagnet YbMgGaO4 that reveal broad spin excitations covering a wide region of the Brillouin zone. The observed diffusive spin excitation persists at the lowest measured energy and shows a clear upper excitation edge, consistent with the particle–hole excitation of a spinon Fermi surface. Our results therefore point to the existence of a quantum spin liquid state with a spinon Fermi surface in YbMgGaO4, which has a perfect spin-1/2 triangular lattice as in the original proposal4 of quantum spin liquids.

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Figure 1: Crystal structure and magnetic susceptibility of a single crystal of YbMgGaO4.
Figure 2: Measured and calculated momentum dependence of the spin excitations, and calculated spinon Fermi surface of YbMgGaO4.
Figure 3: Intensity of the spin-excitation spectrum along the high-symmetry momentum directions.
Figure 4: Constant-energy scans along the symmetry directions and constant-Q scans at the high-symmetry points.

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Acknowledgements

We thank D. Lee, S. Li, Y. Lu, X. Wang and, especially, J.-W. Mei for discussions, and F. Song for assistance with magnetic susceptibility measurements. This work was supported by the National Key R&D Program of the MOST of China (grant number 2016YFA0300203), the Ministry of Science and Technology of China (Program 973: 2015CB921302), and the National Natural Science Foundation of China (grant number 91421106). Y.-D.L. and G.C. were supported by the Thousand Youth Talent Program of China. Q.M.Z. was supported by the NSF of China and the Ministry of Science and Technology of China (grant number 2016YFA0300504). A portion of this research used resources at the High Flux Isotope Reactor, a DOE Office of Science User Facility operated by the Oak Ridge National Laboratory.

Author information

Authors and Affiliations

  1. State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai, 200433, China

    Yao Shen, Hongliang Wo, Shoudong Shen, Bingying Pan, Qisi Wang, Yiqing Hao, Gang Chen & Jun Zhao

  2. School of Computer Science, Fudan University, Shanghai, 200433, China

    Yao-Dong Li

  3. Department of Physics, Beijing Key Laboratory of Opto-electronic Functional Materials and Micro-nano Devices, Renmin University of China, Beijing, 100872, China

    Yuesheng Li & Qingming Zhang

  4. ISIS Facility, Rutherford Appleton Laboratory, STFC, Chilton, OX11 0QX, Didcot, UK

    H. C. Walker

  5. Institut Laue-Langevin, 71 Avenue des Martyrs, Grenoble, 38042, Cedex 9, France

    P. Steffens & M. Boehm

  6. Helmholtz-Zentrum Berlin für Materialien und Energie, Berlin, D-14109, Germany

    D. L. Quintero-Castro

  7. NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, 20899, Maryland, USA

    L. W. Harriger

  8. Quantum Condensed Matter Division, Oak Ridge National Laboratory, Oak Ridge, 37831-6393, Tennessee, USA

    M. D. Frontzek

  9. Neutron Scattering Laboratory, China Institute of Atomic Energy, Beijing, 102413, China

    Lijie Hao & Siqin Meng

  10. Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China

    Qingming Zhang

  11. Collaborative Innovation Center of Advanced Microstructures, Nanjing, 210093, China

    Qingming Zhang, Gang Chen & Jun Zhao

  12. Center for Field Theory and Particle Physics, Fudan University, Shanghai, 200433, China

    Gang Chen

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  1. Yao Shen
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Contributions

J.Z. and G.C. planned the project. Y.S., H.W. and S.S. synthesized the sample. Y.S. and Y.H. characterized the sample with the help of Y.L. and Q.Z. Y.S., H.W., S.S., B.P., Q.W., H.C.W., P.S. and J.Z. carried out the neutron experiments with experimental assistance from M.B., D.L.Q.-C., L.W.H., L.H., M.D.F. and S.M. J.Z. and Y.S. analysed the data. Y.-D.L. and G.C. provided the theoretical explanation and calculations. J.Z., G.C., Y.S. and Y.-D.L. wrote the paper. All authors provided comments on the paper.

Corresponding authors

Correspondence to Gang Chen or Jun Zhao.

Additional information

Reviewer Information Nature thanks C. Rüegg and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Extended data figures and tables

Extended Data Figure 1 Photographs, XRD patterns and field dependence of the magnetization of YbMgGaO4.

a, Photographs of a representative YbMgGaO4 single crystal. b, XRD pattern of a YbMgGaO4 single crystal from the cleaved surface. c, Rocking curve of the (0, 0, 18) peak. The horizontal bar indicates the instrumental resolution. d, Laue pattern of the YbMgGaO4 single crystal viewed from the c axis. e, Observed (red) and calculated (green) XRD diffraction intensities of ground single crystals. The X-ray has a wavelength of 1.54 Å. The blue curve indicates the difference between the observed and calculated intensities. f, Magnetic field dependence of magnetization at T = 2 K. Fitted g factors and Van Vleck susceptibilities χVV are shown (μB is the Bohr magneton). The dashed lines are linear fits above 12 T.

Extended Data Figure 2 Elastic neutron scattering measurements

. Elastic neutron scattering map in the (HK0) plane at 30 mK. No magnetic Bragg peaks are observed. The ring-like pattern is due to scattering from the polycrystalline Cu and Al sample holder. Because of the very large c-axis lattice constant and a small tilt of the scattering plane, some of the tails of the nuclear Bragg peaks for L = ±1 can be also seen. Dashed lines indicate the Brillouin zone boundaries.

Extended Data Figure 3 Correction of neutron beam self-attenuation.

a, Elastic incoherent scattering image at 20 K. b–f, Raw constant-energy images at 70 mK and at the indicated energies. The scattering intensities in d, e and f have been multiplied by 2, 4 and 8, respectively, for clarity. Dashed lines indicate the Brillouin zone boundaries.

Extended Data Figure 4 Additional neutron scattering data at 20 K.

a, b, Constant-energy images at 0.3 meV (a) and 0.6 meV (b) at 20 K. c, Intensity contour plot of the spin excitation spectrum along the high-symmetry momentum directions at 20 K. The scattering is broadened and weakened compared with that at 70 mK.

Extended Data Figure 5 Calculation of the zero-flux Hamiltonian.

a, Spinon dispersion ωk of the zero-flux Hamiltonian. The grey plane marks the Fermi level at ω = 0; its intersection with the band gives the Fermi surface. The light orange hexagon represents the projection of the first Brillouin zone. The maximum of ωk is 3t and the minimum is −6t, providing a bandwidth of 9t. b, Calculated dynamic spin structure factor along high-symmetry directions. A reciprocal lattice unit (r.l.u.) is used here, which is obtained using and . c, Measured spin excitation spectrum along high-symmetry directions at 70 mK. d, Calculated energy dispersion at the indicated momenta (marked by arrows in b). e, Measured constant-Q scans at the indicated momenta. The dashed line is the incoherent elastic line for Ef = 4 meV.

Extended Data Figure 6 Calculation of the π-flux Hamiltonian.

a, Flux pattern and real nearest-neighbour hoppings on the triangular lattice. In the figure, ‘+t’ denotes tij = tji = t and ‘−t’ denotes tij = tji = −t; ‘π’ denotes triangles that are threaded by a π flux. b, Spinon band structure of the π-flux Hamiltonian. The two bands are particle–hole related, both with bandwidths of 3t. c, Calculated momentum dependence of the dynamic spin structure factor at low energy ω = 2.1t. Strong peaks can be distinguished at the Γ point, the point ((1/2, −1/2) in r.l.u.) and equivalent positions. White dashed lines denote the zone boundaries. d, Calculated dynamic spin structure factor along high-symmetry points with η = 0.3t.

Extended Data Table 1 Refined structural parameters for YbMgGaO4 at room temperature
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Shen, Y., Li, YD., Wo, H. et al. Evidence for a spinon Fermi surface in a triangular-lattice quantum-spin-liquid candidate. Nature 540, 559–562 (2016). https://doi.org/10.1038/nature20614

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