Skip to main content

Thank you for visiting nature.com. 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.

Field-tunable quantum disordered ground state in the triangular-lattice antiferromagnet NaYbO2

Abstract

Antiferromagnetically coupled S = 1/2 spins on an isotropic triangular lattice are the paradigm of frustrated quantum magnetism, but structurally ideal realizations are rare. Here, we investigate NaYbO2, which hosts an ideal triangular lattice of effective Jeff = 1/2 moments with no inherent site disorder. No signatures of conventional magnetic order appear down to 50 mK, strongly suggesting a quantum spin liquid ground state. We observe a two-peak specific heat and a nearly quadratic temperature dependence, in agreement with expectations for a two-dimensional Dirac spin liquid. Application of a magnetic field strongly perturbs the quantum disordered ground state and induces a clear transition into a collinear ordered state, consistent with a long-predicted up–up–down structure for a triangular-lattice XXZ Hamiltonian driven by quantum fluctuations. The observation of spin liquid signatures in zero field and quantum-induced ordering in intermediate fields in the same compound demonstrates an intrinsically quantum disordered ground state. We conclude that NaYbO2 is a model, versatile platform for exploring spin liquid physics with full tunability of field and temperature.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Fig. 1: Crystal structure and magnetic (H, T) phase diagram of NaYbO2.
Fig. 2: Low-field magnetization and magnetic susceptibility data.
Fig. 3: High-field magnetic susceptibility and heat capacity data.
Fig. 4: Neutron diffraction and inelastic neutron-scattering data.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request. Neutron data were collected on the BT-1 diffractometer and the Disk Chopper Spectrometer at the NIST Center for Neutron Research.

References

  1. 1.

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

    Article  Google Scholar 

  2. 2.

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

    ADS  Article  Google Scholar 

  3. 3.

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

    Article  Google Scholar 

  4. 4.

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

    ADS  Article  Google Scholar 

  5. 5.

    Savary, L. & Balents, L. Quantum spin liquids: a review. Rep. Prog. Phys. 80, 016502 (2017).

    ADS  Article  Google Scholar 

  6. 6.

    Witczak-Krempa, W., Chen, G., Kim, Y. B. & Balents, L. Correlated quantum phenomena in the strong spin–orbit regime. Annu. Rev. Condens. Matter Phys. 5, 57–82 (2014).

    ADS  Article  Google Scholar 

  7. 7.

    Zhou, Y., Kanoda, K. & Ng, T.-K. Quantum spin liquid states. Rev. Mod. Phys. 89, 025003 (2017).

    ADS  MathSciNet  Article  Google Scholar 

  8. 8.

    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).

    ADS  Article  Google Scholar 

  9. 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).

    ADS  Article  Google Scholar 

  10. 10.

    Ma, J. et al. Static and dynamical properties of the spin-1/2 equilateral triangular-lattice antiferromagnet Ba3CoSb2O9. Phys. Rev. Lett. 116, 087201 (2016).

    ADS  Article  Google Scholar 

  11. 11.

    Shirata, Y., Tanaka, H., Matsuo, A. & Kindo, K. Experimental realization of a spin-1/2 triangular-lattice Heisenberg antiferromagnet. Phys. Rev. Lett. 108, 057205 (2012).

    ADS  Article  Google Scholar 

  12. 12.

    Jackeli, G. & Ivanov, D. A. Dimer phases in quantum antiferromagnets with orbital degeneracy. Phys. Rev. B 76, 132407 (2007).

    ADS  Article  Google Scholar 

  13. 13.

    Clarke, S. J., Fowkes, A. J., Harrison, A., Ibberson, R. M. & Rosseinsky, M. J. Synthesis, structure, and magnetic properties of NaTiO2. Chem. Mater. 10, 372–384 (1998).

    Article  Google Scholar 

  14. 14.

    McQueen, T. M. et al. Successive orbital ordering transitions in NaVO2. Phys. Rev. Lett. 101, 166402 (2008).

    ADS  Article  Google Scholar 

  15. 15.

    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).

    ADS  Article  Google Scholar 

  16. 16.

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

    ADS  Article  Google Scholar 

  17. 17.

    Li, Y. et al. Muon spin relaxation evidence for the U(1) quantum spin-liquid ground state in the triangular antiferromagnet YbMgGaO4. Phys. Rev. Lett. 117, 097201 (2016).

    ADS  Article  Google Scholar 

  18. 18.

    Shen, Y. et al. Evidence for a spinon Fermi surface in a triangular-lattice quantum-spin-liquid candidate. Nature 540, 559–562 (2016).

    ADS  Article  Google Scholar 

  19. 19.

    Xu, Y. et al. Absence of magnetic thermal conductivity in the quantum spin-liquid candidate YbMgGaO4. Phys. Rev. Lett. 117, 267202 (2016).

    ADS  Article  Google Scholar 

  20. 20.

    Paddison, J. A. M. et al. Continuous excitations of the triangular-lattice quantum spin liquid YbMgGaO4. Nat. Phys. 13, 117–122 (2017).

    Article  Google Scholar 

  21. 21.

    Li, Y. et al. Crystalline electric-field randomness in the triangular lattice spin-liquid YbMgGaO4. Phys. Rev. Lett. 118, 107202 (2017).

    ADS  Article  Google Scholar 

  22. 22.

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

    ADS  Article  Google Scholar 

  23. 23.

    Li, Y.-D., Shen, Y., Li, Y., Zhao, J. & Chen, G. Effect of spin–orbit coupling on the effective-spin correlation in YbMgGaO4. Phys. Rev. B 97, 125105 (2018).

    ADS  Article  Google Scholar 

  24. 24.

    Zhu, Z., Maksimov, P. A., White, S. R. & Cheryshev, A. L. Disorder-induced mimicry of a spin liquid in YbMgGaO4. Phys. Rev. Lett. 119, 157201 (2017).

    ADS  Article  Google Scholar 

  25. 25.

    Kimchi, I., Nahum, A. & Senthil, T. Valence bonds in random quantum magnets: theory and application to YbMgGaO4. Phys. Rev. X 8, 031028 (2018).

    Google Scholar 

  26. 26.

    Ma, Z. et al. Spin-glass ground state in a triangular-lattice compound YbZnGaO4. Phys. Rev. Lett. 120, 087201 (2018).

    ADS  Article  Google Scholar 

  27. 27.

    Hashimoto, Y., Wakeshima, M. & Hinatsu, Y. Magnetic properties of ternary sodium oxides NaLnO2 (Ln = rare earths). J. Solid State Chem. 176, 266–272 (2003).

    ADS  Article  Google Scholar 

  28. 28.

    Liu, W. et al. Rare-earth chalcogenides: a large family of triangular lattice spin liquid candidates. Chin. Phys. Lett. 35, 117501 (2018).

    ADS  Article  Google Scholar 

  29. 29.

    Baenitz, M. et al. NaYbS2: a planar spin-1/2 triangular-lattice magnet and putative spin liquid. Phys. Rev. B 98, 220409(R) (2018).

    ADS  Article  Google Scholar 

  30. 30.

    Zeng, C. & Elser, V. Numerical studies of antiferromagnetism on a Kagomé net. Phys. Rev. B 42, 8436 (1990).

    ADS  Article  Google Scholar 

  31. 31.

    Chen, L. et al. Two-temperature scales in the triangular-lattice Heisenberg antiferromagnet. Phys. Rev. B 99, 140404(R) (2019).

    ADS  Article  Google Scholar 

  32. 32.

    Nambu, Y., Nakatsuji, S. & Maeno, Y. Coherent behavior and nonmagnetic impurity effects of spin disordered state in NiGa2S4. J. Phys. Soc. Jpn 75, 043711 (2006).

    ADS  Article  Google Scholar 

  33. 33.

    Gardner, J. S., Gingras, M. J. P. & Greedan, J. E. Magnetic pyrochlore oxides. Rev. Mod. Phys. 82, 53–107 (2010).

    ADS  Article  Google Scholar 

  34. 34.

    Wang, Y. R. Specific heat of a quantum Heisenberg model on a triangular lattice with two exchange parameters and its application to 3He adsorbed on graphite. Phys. Rev. B 45, 12608(R) (1992).

    ADS  Article  Google Scholar 

  35. 35.

    Isoda, M., Nakano, H. & Sakai, T. Specific heat and magnetic susceptibility of Ising-like anisotropic Heisenberg model on kagome lattice. J. Phys. Soc. Jpn 80, 084704 (2011).

    ADS  Article  Google Scholar 

  36. 36.

    Elstner, N. & Young, A. P. Spin-1/2 Heisenberg antiferromagnet on the kagomé lattice: high-temperature expansion and exact-diagonalization studies. Phys. Rev. B 50, 6871–6876 (1994).

    ADS  Article  Google Scholar 

  37. 37.

    Singh, R. R. P. & Oitmaa, J. High-temperature series expansion study of the Heisenberg antiferromagnet on the hyperkagome lattice: comparison with Na4Ir3O8. Phys. Rev. B 85, 104406 (2012).

    ADS  Article  Google Scholar 

  38. 38.

    Garlea, V. O. et al. Exotic magnetic field-induced spin-superstructures in a mixed honeycomb-triangular lattice system. Phys. Rev. X 9, 011038 (2019).

    Google Scholar 

  39. 39.

    Iaconis, J., Liu, C., Haláz, G. B. & Balents, L. Spin liquid versus spin orbit coupling on the triangular lattice. SciPost Phys. 4, 003 (2018).

    ADS  Article  Google Scholar 

  40. 40.

    Zhu, Z., Maksimov, P. A., White, S. R. & Chernyshev, A. L. Topography of spin liquids on a triangular lattice. Phys. Rev. Lett. 120, 207203 (2018).

    ADS  Article  Google Scholar 

  41. 41.

    Starykh, O. A. Unusual ordered phases of highly frustrated magnets: a review. Rep. Prog. Phys. 78, 052502 (2015).

    ADS  Article  Google Scholar 

  42. 42.

    Chubokov, A. V. & Golosov, D. I. Quantum theory of an antiferromagnet on a triangular lattice in a magnetic field. J. Phys.: Condens. Matter 3, 69–82 (1991).

    ADS  Google Scholar 

  43. 43.

    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).

    ADS  Article  Google Scholar 

  44. 44.

    Rastelli, E. & Tassi, A. The rhombohedral Heisenberg antiferromagnet: infinite degeneracy of the ground state and magnetic properties of solid oxygen. J. Phys. C: Solid State Phys. 19, L423–L428 (1986).

    ADS  Article  Google Scholar 

  45. 45.

    Ono, T. et al. Magnetization plateaux of the S = 1/2 two-dimensional frustrated antiferromagnet Cs2CuBr4. J. Phys.: Condens. Matter 16, S773–S778 (2004).

    Google Scholar 

  46. 46.

    Helton, J. S. et al. Spin dynamics of the spin-1/2 kagome lattice antiferromagnet ZnCu3(OH)6Cl2. Phys. Rev. Lett. 98, 107204 (2007).

    ADS  Article  Google Scholar 

  47. 47.

    Maryasin, V. S. & Zhitomirsky, M. E. Triangular antiferromagnet with nonmagnetic impurities. Phys. Rev. Lett. 111, 247201 (2013).

    ADS  Article  Google Scholar 

  48. 48.

    Rawl, R. et al. Ba8CoNb6O24: a spin-1/2 triangular-lattice Heisenberg antiferromagnet in the two-dimensional limit. Phys. Rev. B 95, 060412(R) (2017).

    ADS  Article  Google Scholar 

  49. 49.

    Cui, Y. et al. Mermin–Wagner physics, (H, T) phase diagram, and candidate quantum spin-liquid phase in the spin-1/2 triangular-lattice antiferromagnet Ba8CoNb6O24. Phys. Rev. Mater. 2, 044403 (2018).

    Article  Google Scholar 

  50. 50.

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

    ADS  Article  Google Scholar 

  51. 51.

    Larson, A. C. & Von Dreele, R. B. General Structure Analysis System (GSAS) Report LAUR 86-748 (Los Alamos National Laboratory, 2004).

  52. 52.

    Toby, B. H. EXPGUI, a graphical user interface for GSAS. J. Appl. Crystallogr. 34, 210–213 (2001).

    Article  Google Scholar 

  53. 53.

    Stoll, S. & Schweiger, A. EasySpin, a comprehensive software package for spectral simulation and analysis in EPR. J. Magn. Reson. 178, 42–55 (2006).

    ADS  Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the US Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under award DE-SC0017752 (S.D.W. and M.B.). M.B. acknowledges partial support by the National Science Foundation Graduate Research Fellowship Program under grant no. 1650114. Work by L.B. and C.L. was supported by the DOE, Office of Science, Basic Energy Sciences under award no. DE-FG02-08ER46524. Identification of commercial equipment does not imply recommendation or endorsement by NIST.

Author information

Affiliations

Authors

Contributions

M.B., S.D.W., C.L. and L.B. wrote the manuscript. M.B. and S.D.W. analysed experiment data and planned experiments. M.J.G. and E.K. performed susceptibility measurements. M.B. and T.H. performed heat capacity and magnetization measurements. C.L. and L.B. performed theoretical analysis of the material. C.B. performed the neutron diffraction measurements, and M.B. and N.P.B. performed inelastic neutron-scattering experiments. M.S., M.K., Y.L. and M.B. performed electron spin resonance measurements. M.B. and L.P. synthesized the materials.

Corresponding author

Correspondence to Stephen D. Wilson.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary text, Figs. 1–5 and references.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Bordelon, M.M., Kenney, E., Liu, C. et al. Field-tunable quantum disordered ground state in the triangular-lattice antiferromagnet NaYbO2. Nat. Phys. 15, 1058–1064 (2019). https://doi.org/10.1038/s41567-019-0594-5

Download citation

Further reading

Search

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