A high-temperature quantum spin liquid with polaron spins

Abstract

The existence of a quantum spin liquid (QSL) in which quantum fluctuations of spins are sufficiently strong to preclude spin ordering down to zero temperature was originally proposed theoretically more than 40 years ago, but its experimental realization turned out to be very elusive. Here we report on an almost ideal spin liquid state that appears to be realized by atomic-cluster spins on the triangular lattice of a charge-density wave state of 1T-TaS2. In this system, the charge excitations have a well-defined gap of 0.3 eV, while nuclear quadrupole resonance and muon-spin-relaxation experiments reveal that the spins show gapless QSL dynamics and no long-range magnetic order at least down to 70 mK. Canonical T2 power-law temperature dependence of the spin relaxation dynamics characteristic of a QSL is observed from 200 K to Tf = 55 K. Below this temperature, we observe a new gapless state with reduced density of spin excitations and high degree of local disorder signifying new quantum spin order emerging from the QSL.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Figure 1: μ+SR rules out any long-range magnetic order down to 70 mK.
Figure 2: 181Ta NQR spectrum reveals the symmetry and the structure of deformations in the Star-of-David Ta cluster.
Figure 3: 181Ta relaxation rates probe the quantum spin liquid.
Figure 4: The low-temperature state of 1T-TaS2.

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

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

    ADS  Article  Google Scholar 

  3. 3

    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 

  4. 4

    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 

  5. 5

    Itou, T., Oyamada, A., Maegawa, S. & Kato, R. Instability of a quantum spin liquid in an organic triangular-lattice antiferromagnet. Nat. Phys. 6, 673–676 (2010).

    Article  Google Scholar 

  6. 6

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

    ADS  Article  Google Scholar 

  7. 7

    Rossnagel, K. On the origin of charge-density waves in select layered transition-metal dichalcogenides. J. Phys. Condens. Matter 23, 213001 (2011).

    ADS  Article  Google Scholar 

  8. 8

    Huse, D. A. & Elser, V. Simple variational wave functions for two-dimensional Heisenberg spin-1/2 antiferromagnets. Phys. Rev. Lett. 60, 2531–2534 (1988).

    ADS  Article  Google Scholar 

  9. 9

    White, S. R. & Chernyshev, A. L. Neél order in square and triangular lattice Heisenberg models. Phys. Rev. Lett. 99, 127004 (2007).

    ADS  Article  Google Scholar 

  10. 10

    Stojchevska, L. et al. Ultrafast switching to a stable hidden quantum state in an electronic crystal. Science 344, 177–180 (2014).

    ADS  Article  Google Scholar 

  11. 11

    Yoshida, M., Suzuki, R., Zhang, Y., Nakano, M. & Iwasa, Y. Memristive phase switching in two-dimensional 1T-TaS2 crystals. Sci. Adv. 1, e1500606 (2015).

    ADS  Article  Google Scholar 

  12. 12

    Vaskivskyi, I. et al. Fast electronic resistance switching involving hidden charge density wave states. Nat. Commun. 7, 11442 (2016).

    ADS  Article  Google Scholar 

  13. 13

    Hellmann, S. et al. Time-domain classification of charge-density-wave insulators. Nat. Commun. 3, 1069 (2012).

    ADS  Article  Google Scholar 

  14. 14

    Fazekas, P. & Tosatti, E. Electrical, structural and magnetic properties of pure and doped 1T-TaS2 . Philos. Mag. B 39, 229–244 (1979).

    ADS  Article  Google Scholar 

  15. 15

    Perfetti, L., Gloor, T. A., Mila, F., Berger, H. & Grioni, M. Unexpected periodicity in the quasi-two-dimensional Mott insulator 1T-TaS2 revealed by angle-resolved photoemission. Phys. Rev. B 71, 153101 (2005).

    ADS  Article  Google Scholar 

  16. 16

    Gasparov, L. V. et al. Phonon anomaly at the charge ordering transition in 1T-TaS2 . Phys. Rev. B 66, 094301 (2002).

    ADS  Article  Google Scholar 

  17. 17

    Ma, L. et al. A metallic mosaic phase and the origin of Mott-insulating state in 1T-TaS2 . Nat. Commun. 7, 10956 (2016).

    ADS  Article  Google Scholar 

  18. 18

    Cho, D. et al. Nanoscale manipulation of the Mott insulating state coupled to charge order in 1T-TaS2 . Nat. Commun. 7, 10453 (2016).

    ADS  Article  Google Scholar 

  19. 19

    Svetin, D., Vaskivskyi, I., Brazovskii, S. & Mihailovič, D. Three-dimensional resistivity switching between correlated electronic states in 1T-TaS2 . Sci. Rep. 7, 46048 (2017).

    ADS  Article  Google Scholar 

  20. 20

    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 

  21. 21

    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).

    ADS  Article  Google Scholar 

  22. 22

    Yaouanc, A. & de Rotier, P. D. Muon Spin Rotation, Relaxation, and Resonance (Oxford Univ. Press, 2010).

    Google Scholar 

  23. 23

    Naito, M., Nishihara, H. & Tanaka, S. Nuclear quadrupole resonance in the charge density wave state of 1T-TaS2 . J. Phys. Soc. Jpn 53, 1610–1613 (1984).

    ADS  Article  Google Scholar 

  24. 24

    Naito, M., Nishihara, H. & Tanaka, S. Nuclear magnetic resonance and nuclear quadrupole resonance study of 181Ta in the commensurate charge density wave state of 1T-TaS2 . J. Phys. Soc. Jpn 55, 2410–2421 (1986).

    ADS  Article  Google Scholar 

  25. 25

    Torgeson, D. R. & Borsa, F. Temperature dependence of the electric field gradient in a quasi-two-dimensional metal: NbSe2 . Phys. Rev. Lett. 37, 956–959 (1976).

    ADS  Article  Google Scholar 

  26. 26

    Darancet, P., Millis, A. J. & Marianetti, C. A. Three-dimensional metallic and two-dimensional insulating behavior in octahedral tantalum dichalcogenides. Phys. Rev. B 90, 045134 (2014).

    ADS  Article  Google Scholar 

  27. 27

    Kaneko, R., Morita, S. & Imada, M. Gapless spin-liquid phase in an extended spin 1/2 triangular Heisenberg model. J. Phys. Soc. Jpn 83, 093707 (2014).

    ADS  Article  Google Scholar 

  28. 28

    Walstedt, R. E. Spin-lattice relaxation of nuclear spin echoes in metals. Phys. Rev. Lett. 19, 146–149 (1967).

    ADS  Article  Google Scholar 

  29. 29

    Khuntia, P., Kumar, R., Mahajan, A. V., Baenitz, M. & Furukawa, Y. Spin liquid state in the disordered triangular lattice Sc2Ga2CuO7 revealed by NMR. Phys. Rev. B 93, 140408 (2016).

    ADS  Article  Google Scholar 

  30. 30

    Shiroka, T. et al. Distribution of NMR relaxations in a random Heisenberg chain. Phys. Rev. Lett. 106, 137202 (2011).

    ADS  Article  Google Scholar 

  31. 31

    Fisher, D. S. Random antiferromagnetic quantum spin chains. Phys. Rev. B 50, 3799–3821 (1994).

    ADS  Article  Google Scholar 

  32. 32

    Klanjšek, M. et al. Controlling Luttinger liquid physics in spin ladders under a magnetic field. Phys. Rev. Lett. 101, 137207 (2008).

    ADS  Article  Google Scholar 

  33. 33

    Klanjšek, M. et al. Phonon-modulated magnetic interactions and spin Tomonaga-Luttinger liquid in the p-orbital antiferromagnet CsO2 . Phys. Rev. Lett. 115, 057205 (2015).

    ADS  Article  Google Scholar 

  34. 34

    Uchida, S., Tanabe, K. & Tanaka, S. Nonlinear conduction in two-dimensional CDW system: 1T-TaS2 . Solid State Commun. 27, 637 (1978).

    ADS  Article  Google Scholar 

  35. 35

    Bain, G. A. & Berry, J. F. Diamagnetic corrections and Pascal’s constants. J. Chem. Educ. 85, 532–536 (2008).

    Article  Google Scholar 

  36. 36

    DiSalvo, F. J. & Waszczak, J. V. Paramagnetic moments and localization in 1T-TaS2 . Phys. Rev. B 22, 4241–4246 (1980).

    ADS  Article  Google Scholar 

  37. 37

    Ganal, P., Butz, T., Lerf, A., Naito, M. & Nishiharad, H. The 181Ta nuclear quadrupole interaction in the charge density wave phases of 1T-TaS2 . Z. Nat. forsch. 45a, 439–444 (1990).

    ADS  Google Scholar 

  38. 38

    Chepin, J. & Ross, J. H. Magnetic spin-lattice relaxation in nuclear quadrupole resonance: the eta not=0 case. J. Phys. Condens. Matter 3, 8103–8112 (1991).

    ADS  Article  Google Scholar 

  39. 39

    Abragam, A. Principles of Nuclear Magnetism (Oxford Univ. Press, 2011).

    Google Scholar 

  40. 40

    Wilson, J., Salvo, F. D. & Mahajan, S. Charge-density waves and superlattices in the metallic layered transition metal dichalcogenides. Adv. Phys. 24, 117–201 (1975).

    ADS  Article  Google Scholar 

Download references

Acknowledgements

The authors acknowledge fruitful discussions with P. Carretta. The authors also acknowledge the contribution of P. Šutar in sample preparation and structural characterization. D.A. acknowledges the financial support by the Slovenian Research Agency, grant No. N1-0052; D.M. acknowledges funding by the ERC AdG Trajectory.

Author information

Affiliations

Authors

Contributions

D.A., D.M. and P.P. conceived and designed the project and directed and coordinated the research. M.K., A.Z. and P.K.B. performed the μ+SR experiments and analysed the data. M.K. and A.Z. carried out NQR measurements and analysed the data. Z.J. measured spin susceptibility and together with D.A. analysed the data. All authors discussed the results. D.A. wrote the paper with input from all authors.

Corresponding author

Correspondence to Denis Arčon.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 581 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Klanjšek, M., Zorko, A., Žitko, R. et al. A high-temperature quantum spin liquid with polaron spins. Nature Phys 13, 1130–1134 (2017). https://doi.org/10.1038/nphys4212

Download citation

Further reading

Search

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