Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

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


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.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

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.

Similar content being viewed by others


  1. Balents, L. Spin liquids in frustrated magnets. Nature 464, 199–208 (2010)

    Article  CAS  ADS  Google Scholar 

  2. Wen, X.-G. Quantum orders and symmetric spin liquids. Phys. Rev. B 65, 165113 (2002)

    Article  ADS  Google Scholar 

  3. Kivelson, S. A., Rokhsar, D. S. & Sethna, J. P. Topology of the resonating valence-bond state: solitons and high-Tc superconductivity. Phys. Rev. B 35, 8865(R)–8868(R) (1987)

    Article  ADS  Google Scholar 

  4. Anderson, P. W. Resonating valence bonds: a new kind of insulator? Mater. Res. Bull. 8, 153–160 (1973)

    Article  CAS  Google Scholar 

  5. Anderson, P. W. The resonating valence bond state in La2CuO4 and superconductivity. Science 235, 1196–1198 (1987)

    Article  CAS  ADS  Google Scholar 

  6. Moessner, R. & Sondhi, S. L. Resonating valence bond liquid physics on the triangular lattice. Prog. Theor. Phys . 145 (Suppl.), 37–42 (2002)

    Article  CAS  Google Scholar 

  7. Lee, P. A. An end to the drought of quantum spin liquids. Science 321, 1306–1307 (2008)

    Article  CAS  Google Scholar 

  8. Kurosaki, Y., Shimizu, Y., Miyagawa, K., Kanoda, K. & Saito, G. Mott transition from a spin liquid to a Fermi liquid in the spin-frustrated organic conductor κ-(ET)2Cu2(CN)3 . Phys. Rev. Lett. 95, 177001 (2005)

    Article  CAS  ADS  Google Scholar 

  9. Itou, T., Oyamada, A., Maegawa, S., Tamura, M. & Kato, R. Quantum spin liquid in the spin-1/2 triangular antiferromagnet EtMe3Sb[Pd(dmit)2]2 . Phys. Rev. B 77, 104413 (2008)

    Article  ADS  Google Scholar 

  10. Shimizu, Y., Miyagawa, K., Kanoda, K., Maesato, M. & Saito, G. Spin liquid state in an organic Mott insulator with a triangular lattice. Phys. Rev. Lett. 91, 107001 (2003)

    Article  CAS  ADS  Google Scholar 

  11. Coldea, R., Tennant, D. A. & Tylczynski, Z. Extended scattering continua characteristic of spin fractionalization in the two-dimensional frustrated quantum magnet Cs2CuCl4 observed by neutron scattering. Phys. Rev. B 68, 134424 (2003)

    Article  ADS  Google Scholar 

  12. Han, T.-H. et al. Fractionalized excitations in the spin-liquid state of a kagome-lattice antiferromagnet. Nature 492, 406–410 (2012)

    Article  CAS  ADS  Google Scholar 

  13. Oshikawa, M. Commensurability, excitation gap, and topology in quantum many-particle systems on a periodic lattice. Phys. Rev. Lett. 84, 1535–1538 (2000)

    Article  CAS  ADS  Google Scholar 

  14. Hastings, M. B. Lieb–Schultz–Mattis in higher dimensions. Phys. Rev. B 69, 104431 (2004)

    Article  ADS  Google Scholar 

  15. Lieb, E., Schultz, T. & Mattis, D. Two soluble models of an antiferromagnetic chain. Ann. Phys. 16, 407–466 (1961)

    Article  ADS  MathSciNet  Google Scholar 

  16. Punk, M., Chowdhury, D. & Sachdev, S. Topological excitations and the dynamic structure factor of spin liquids on the kagome lattice. Nat. Phys. 10, 289–293 (2014)

    Article  CAS  Google Scholar 

  17. Watanabe, H., Po, H. C., Vishwanath, A. & Zaletel, M. Filling constraints for spin–orbit coupled insulators in symmorphic and nonsymmorphic crystals. Proc. Natl Acad. Sci. USA 112, 14551–14556 (2015)

    Article  CAS  ADS  Google Scholar 

  18. Li, Y. et al. Gapless quantum spin liquid ground state in the two-dimensional spin-1/2 triangular antiferromagnet YbMgGaO4 . Sci. Rep. 5, 16419 (2015)

    Article  CAS  ADS  Google Scholar 

  19. Li, Y. et al. Rare-earth triangular lattice spin liquid: a single-crystal study of YbMgGaO4 . Phys. Rev. Lett. 115, 167203 (2015)

    Article  ADS  Google Scholar 

  20. Li, Y.-D., Wang, X. & Chen, G. Anisotropic spin model of strong spin–orbit-coupled triangular antiferromagnets. Phys. Rev. B 94, 035107 (2016)

    Article  ADS  Google Scholar 

  21. Li, Y.-D., Shen, Y., Li, Y., Zhao, J. & Chen, G. The effect of spin–orbit coupling on the effective-spin correlation in YbMgGaO4. Preprint at (2016)

  22. Ross, K. A., Savary, L., Gaulin, B. D. & Balents, L. Quantum excitations in quantum spin ice. Phys. Rev. X 1, 021002 (2011)

    Google Scholar 

  23. Zhao, J. et al. Neutron scattering measurements of spatially anisotropic magnetic exchange interactions in semiconducting K0.85Fe1.54Se2 (TN = 280 K). Phys. Rev. Lett. 112, 177002 (2014)

    Article  ADS  Google Scholar 

  24. Wang, Q. et al. Magnetic ground state of FeSe. Nat. Commun. 7, 12182 (2016)

    Article  CAS  ADS  Google Scholar 

  25. Ran, Y., Hermele, M., Lee, P. A. & Wen, X.-G. Projected-wave-function study of the spin-1/2 Heisenberg model on the Kagomé lattice. Phys. Rev. Lett. 98, 117205 (2007)

    Article  ADS  Google Scholar 

  26. Sachdev, S. Kagomé- and triangular-lattice Heisenberg antiferromagnets: ordering from quantum fluctuations and quantum-disordered ground states with unconfined bosonic spinons. Phys. Rev. B 45, 12377–12396 (1992)

    Article  CAS  ADS  Google Scholar 

  27. Lee, S.-S. & Lee, P. A. U(1) gauge theory of the Hubbard model: spin liquid states and possible application to κ-(BEDT-TTF)2Cu2(CN)3 . Phys. Rev. Lett. 95, 036403 (2005)

    Article  ADS  Google Scholar 

  28. Motrunich, O. I. Variational study of triangular lattice spin-1/2 model with ring exchanges and spin liquid state in κ-(ET)2Cu2(CN)3 . Phys. Rev. B 72, 045105 (2005)

    Article  ADS  Google Scholar 

  29. Lee, P. A. & Nagaosa, N. Gauge theory of the normal state of high-Tc superconductors. Phys. Rev. B 46, 5621–5639 (1992)

    Article  CAS  ADS  Google Scholar 

  30. Paddison, J. A. M. et al. Continuous excitations of the triangular-lattice quantum spin liquid YbMgGaO4. Preprint at (2016)

  31. Rodríguez-Carvajal, J. Recent advances in magnetic structure determination by neutron powder diffraction. Physica B 192, 55–69 (1993)

    Article  ADS  Google Scholar 

  32. Le, M. D. et al. Gains from the upgrade of the cold neutron triple-axis spectrometer FLEXX at the BER-II reactor. Nucl. Instrum. Methods A 729, 220–226 (2013)

    Article  CAS  ADS  Google Scholar 

  33. Lee, S. S. Stability of the U(1) spin liquid with a spinon Fermi surface in 2 + 1 dimensions. Phys. Rev. B 78, 085129 (2008)

    Article  ADS  Google Scholar 

  34. Hermele, M. et al. Stability of U(1) spin liquids in two dimensions. Phys. Rev. B 70, 214437 (2004)

    Article  ADS  Google Scholar 

  35. Polyakov, A. M. Gauge Fields and Strings Ch. 4 (Harwood Academic, 1987)

  36. Lee, S. S. Low-energy effective theory of Fermi surface coupled with U(1) gauge field in 2 + 1 dimensions. Phys. Rev. B 80, 165102 (2009)

    Article  ADS  Google Scholar 

  37. Metlitski, M. A., Mross, D. F., Sachdev, S. & Senthil, T. Cooper pairing in non-Fermi liquids. Phys. Rev. B 91, 115111 (2015)

    Article  ADS  Google Scholar 

  38. Lee, S. S., Lee, P. A. & Senthil, T. Amperean pairing instability in the U(1) spin liquid state with Fermi surface and application to κ-(BEDT-TTF)2Cu2(CN)3 . Phys. Rev. Lett. 98, 067006 (2007)

    Article  ADS  Google Scholar 

Download references


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



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. bf, 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

PowerPoint slides

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing