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Continuous excitations of the triangular-lattice quantum spin liquid YbMgGaO4

Abstract

A quantum spin liquid (QSL) is an exotic state of matter in which electrons’ spins are quantum entangled over long distances, but do not show magnetic order in the zero-temperature limit1. The observation of QSL states is a central aim of experimental physics, because they host collective excitations that transcend our knowledge of quantum matter; however, examples in real materials are scarce2. Here, we report neutron-scattering experiments on YbMgGaO4, a QSL candidate in which Yb3+ ions with effective spin-1/2 occupy a triangular lattice3,4,5,6. Our measurements reveal a continuum of magnetic excitations—the essential experimental hallmark of a QSL7—at very low temperature (0.06 K). The origin of this peculiar excitation spectrum is a crucial question, because isotropic nearest-neighbour interactions do not yield a QSL ground state on the triangular lattice8. Using measurements in the field-polarized state, we identify antiferromagnetic next-nearest-neighbour interactions9,10,11,12, spin-space anisotropies4,10,13,14, and chemical disorder15 between the magnetic layers as key ingredients in YbMgGaO4.

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Figure 1: Structure and magnetic properties of YbMgGaO4.
Figure 2: Neutron-scattering data for YbMgGaO4 measured in zero applied field.
Figure 3: Field-polarized neutron-scattering data and evidence for next-nearest-neighbour interactions in YbMgGaO4.

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References

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

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  3. 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  ADS  Google Scholar 

  4. 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 

  5. 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).

    Article  ADS  Google Scholar 

  6. Shen, Y. et al. Spinon Fermi surface in a triangular lattice quantum spin liquid YbMgGaO4. Preprint at http://arXiv.org/abs/1607.02615 (2016).

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

    Article  ADS  Google Scholar 

  8. Capriotti, L., Trumper, A. E. & Sorella, S. Long-range Néel order in the triangular Heisenberg model. Phys. Rev. Lett. 82, 3899–3902 (1999).

    Article  ADS  Google Scholar 

  9. Manuel, L. O. & Ceccatto, H. A. Magnetic and quantum disordered phases in triangular-lattice Heisenberg antiferromagnets. Phys. Rev. B 60, 9489–9493 (1999).

    Article  ADS  Google Scholar 

  10. Li, P. H. Y., Bishop, R. F. & Campbell, C. E. Quasiclassical magnetic order and its loss in a spin-1/2 Heisenberg antiferromagnet on a triangular lattice with competing bonds. Phys. Rev. B 91, 014426 (2015).

    Article  ADS  Google Scholar 

  11. Zhu, Z. & White, S. R. Spin liquid phase of the spin-1/2 J1–J2 Heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015).

    Article  ADS  Google Scholar 

  12. Iqbal, Y., Hu, W.-J., Thomale, R., Poilblanc, D. & Becca, F. Spin liquid nature in the Heisenberg J1–J2 triangular antiferromagnet. Phys. Rev. B 93, 144411 (2016).

    Article  ADS  Google Scholar 

  13. 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 

  14. 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 http://arXiv.org/abs/1608.06445 (2016).

  15. Savary, L. & Balents, L. Disorder-induced entanglement in spin ice pyrochlores. Preprint at http://arXiv.org/abs/1604.04630 (2016).

  16. Tennant, D. A., Perring, T. G., Cowley, R. A. & Nagler, S. E. Unbound spinons in the spin-1/2 antiferromagnetic chain KCuF3 . Phys. Rev. Lett. 70, 4003–4006 (1993).

    Article  ADS  Google Scholar 

  17. Coldea, R., Tennant, D. A., Tsvelik, A. M. & Tylczynski, Z. Experimental realization of a 2D fractional quantum spin liquid. Phys. Rev. Lett. 86, 1335–1338 (2001).

    Article  ADS  Google Scholar 

  18. Banerjee, A. et al. Proximate Kitaev quantum spin liquid behaviour in a honeycomb magnet. Nat. Mater. 15, 733–740 (2016).

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  20. de Vries, M. A. et al. Scale-free antiferromagnetic fluctuations in the spin-1/2 kagome antiferromagnet herbertsmithite. Phys. Rev. Lett. 103, 237201 (2009).

    Article  ADS  Google Scholar 

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

    Google Scholar 

  22. Misguich, G., Lhuillier, C., Bernu, B. & Waldtmann, C. Spin-liquid phase of the multiple-spin exchange Hamiltonian on the triangular lattice. Phys. Rev. B 60, 1064–1074 (1999).

    Article  ADS  Google Scholar 

  23. Yaouanc, A., Dalmas de Réotier, P., Marin, C. & Glazkov, V. Single-crystal versus polycrystalline samples of magnetically frustrated Yb2Ti2O7: specific heat results. Phys. Rev. B 84, 172408 (2011).

    Article  ADS  Google Scholar 

  24. Marshall, W. & Lowde, R. D. Magnetic correlations and neutron scattering. Rep. Prog. Phys. 31, 705–775 (1968).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  26. Yan, S., Huse, D. A. & White, S. R. Spin-liquid ground state of the spin-1/2 kagome Heisenberg antiferromagnet. Science 332, 1173 (2011).

    Article  ADS  Google Scholar 

  27. Ross, K. A., Krizan, J. W., Rodriguez-Rivera, J. A., Cava, R. J. & Broholm, C. L. Static and dynamic XY-like short-range order in a frustrated magnet with exchange disorder. Phys. Rev. B 93, 014433 (2016).

    Article  ADS  Google Scholar 

  28. Onoda, S. Effective quantum pseudospin-1/2 model for Yb pyrochlore oxides. J. Phys. Conf. Ser. 320, 012065 (2011).

    Article  Google Scholar 

  29. Yamamoto, D., Marmorini, G. & Danshita, I. Quantum phase diagram of the triangular-lattice XXZ model in a magnetic field. Phys. Rev. Lett. 112, 127203 (2014).

    Article  ADS  Google Scholar 

  30. Mourigal, M. et al. Fractional spinon excitations in the quantum Heisenberg antiferromagnetic chain. Nat. Phys. 9, 435–441 (2013).

    Article  Google Scholar 

  31. Alicea, J., Motrunich, O. I. & Fisher, M. P. A. Algebraic vortex liquid in spin-1/2 triangular antiferromagnets: scenario for Cs2CuCl4 . Phys. Rev. Lett. 95, 247203 (2005).

    Article  ADS  Google Scholar 

  32. Nakatsuji, S. et al. Spin disorder on a triangular lattice. Science 309, 1697–1700 (2005).

    Article  ADS  Google Scholar 

  33. 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  ADS  Google Scholar 

  34. Pratt, F. L. et al. Magnetic and non-magnetic phases of a quantum spin liquid. Nature 471, 612–616 (2011).

    Article  ADS  Google Scholar 

  35. Sheckelton, J. P., Neilson, J. R., Soltan, D. G. & McQueen, T. M. Possible valence-bond condensation in the frustrated cluster magnet LiZn2Mo3O8 . Nat. Mater. 11, 493–496 (2012).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  37. Dollase, W. A. Correction of intensities for preferred orientation in powder diffractometry: application of the March model. J. Appl. Crystallogr. 19, 267–272 (1986).

    Article  Google Scholar 

  38. Ehlers, G., Podlesnyak, A. A., Niedziela, J. L., Iverson, E. B. & Sokol, P. E. The new cold neutron chopper spectrometer at the Spallation Neutron Source: design and performance. Rev. Sci. Instrum. 82, 085108 (2011).

    Article  ADS  Google Scholar 

  39. Granroth, G. E. et al. SEQUOIA: a newly operating chopper spectrometer at the SNS. J. Phys. Conf. Ser. 251, 12058 (2010).

    Article  Google Scholar 

  40. Squires, G. L. Introduction to the Theory of Thermal Neutron Scattering 129–145 (Cambridge Univ. Press, 1978).

    Google Scholar 

  41. Gaudet, J. et al. Neutron spectroscopic study of crystalline electric field excitations in stoichiometric and lightly stuffed Yb2Ti2O7 . Phys. Rev. B 92, 134420 (2015).

    Article  ADS  Google Scholar 

  42. Arnold, O. et al. Mantid—data analysis and visualization package for neutron scattering and μSR experiments. Nucl. Instrum. Methods Phys. Res. A 764, 156–166 (2014).

    Article  ADS  Google Scholar 

  43. Ewings, R. A. et al. HORACE: software for the analysis of data from single crystal spectroscopy experiments at time-of-flight neutron instruments. Nucl. Instrum. Methods Phys. Res. A 884, 132–142 (2016).

    Article  ADS  Google Scholar 

  44. Michels-Clark, T. M., Savici, A. T., Lynch, V. E., Wang, X. P. & Hoffmann, C. M. Expanding Lorentz and spectrum corrections to large volumes of reciprocal space for single-crystal time-of-flight neutron diffraction. J. Appl. Crystallogr. 49, 497–506 (2016).

    Article  Google Scholar 

  45. Brown, P. J. International Tables for Crystallography Vol. C, 454–460 (Kluwer-Academic, 2004).

    Google Scholar 

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Acknowledgements

We are very grateful to L. Ge for his help with heat-capacity measurements and J. Carruth, S. Elorfi, M. Everett and C. Fletcher for sample environment and instrument support during our neutron-scattering experiments. It is our pleasure to thank S. Chernyshev, R. Coldea, K. Ross, M. Waterbury, Y. Wan and M. Zhitomirsky for insightful discussions. The work and equipment at the Georgia Institute of Technology (J.A.M.P., M.D. and M.M.) was supported by the College of Sciences and the Executive Vice-President for Research. The work at the University of Tennessee (Z.D. and H.Z.) was supported by the National Science Foundation through award DMR-1350002. The research at Oak Ridge National Laboratory’s Spallation Neutron Source was sponsored by the US Department of Energy, Office of Basic Energy Sciences, Scientific User Facilities Division.

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Contributions

J.A.M.P., M.D., Z.D., G.E., Y.L., M.B.S. and M.M. performed neutron-scattering experiments. J.A.M.P., M.D. and M.M. analysed the data. Z.D. and H.Z. made the sample. Z.D. and M.M. characterized the sample. M.D. and M.M. aligned the sample. M.M. made the figures and J.A.M.P. wrote the paper with input from all authors. H.Z. and M.M. designed and supervised the project.

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Correspondence to Martin Mourigal.

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Paddison, J., Daum, M., Dun, Z. et al. Continuous excitations of the triangular-lattice quantum spin liquid YbMgGaO4. Nature Phys 13, 117–122 (2017). https://doi.org/10.1038/nphys3971

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