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A magnetic continuum in the cobalt-based honeycomb magnet BaCo2(AsO4)2

Abstract

Quantum spin liquids (QSLs) are topologically ordered states of matter that host fractionalized excitations. A particular route towards a QSL is via strongly bond-dependent interactions on the hexagonal lattice. A number of Ru- and Ir-based candidate Kitaev QSL materials have been pursued, but all have appreciable non-Kitaev interactions. Using time-domain terahertz spectroscopy, we observed a broad magnetic continuum over a wide range of temperatures and fields in the honeycomb cobalt-based magnet BaCo2(AsO4)2, which has been proposed to be a more ideal version of a Kitaev QSL. Applying an in-plane magnetic field of ~0.5 T suppresses the magnetic order, and at higher fields, applying the field gives rise to a spin-polarized state. Under a 4 T magnetic field that was oriented principally out of plane, a broad magnetic continuum was observed that may be consistent with a field-induced QSL. Our results indicate BaCo2(AsO4)2 is a promising QSL candidate.

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Fig. 1: The broad magnetic continuum investigated by time-domain terahertz spectroscopy.
Fig. 2: The magnetic excitations with in-plane magnetic field and phase diagram.
Fig. 3: The evolution of the magnetic excitations with primarily out-of-plane field.

Data availability

The data that support the findings of this study are present in the paper and/or in the Supplementary Information, and are deposited in the Zenodo repository: https://doi.org/10.5281/zenodo.7026702. Additional data related to the paper are available from the corresponding author upon reasonable request.

References

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

    Article  CAS  Google Scholar 

  2. Broholm, C. et al. Quantum spin liquids. Science 367, eaay0668 (2020).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  4. Kitaev, A. Anyons in an exactly solved model and beyond. Ann. Phys. 321, 2–111 (2006).

    Article  CAS  Google Scholar 

  5. Takagi, H. et al. Concept and realization of Kitaev quantum spin liquids. Nat. Rev. Phys. 1, 264–280 (2019).

    Article  Google Scholar 

  6. Chun, S. H. et al. Direct evidence for dominant bond-directional interactions in a honeycomb lattice iridate Na2IrO3. Nat. Phys. 11, 462–466 (2015).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  8. Plumb, K. W. et al. α–RuCl3: a spin-orbit assisted Mott insulator on a honeycomb lattice. Phys. Rev. B 90, 041112 (2014).

    Article  CAS  Google Scholar 

  9. Banerjee, A. et al. Neutron scattering in the proximate quantum spin liquid α-RuCl3. Science 356, 1055–1059 (2017).

    Article  CAS  Google Scholar 

  10. Wang, Z. et al. Magnetic excitations and continuum of a possibly field-induced quantum spin liquid in α–RuCl3. Phys. Rev. Lett. 119, 227202 (2017).

    Article  Google Scholar 

  11. Zheng, J. et al. Gapless spin excitations in the field-induced quantum spin liquid phase of α–RuCl3. Phys. Rev. Lett. 119, 227208 (2017).

    Article  Google Scholar 

  12. Banerjee, A. et al. Excitations in the field-induced quantum spin liquid state of α-RuCl3. npj Quantum Mater. 3, 8 (2018).

    Article  Google Scholar 

  13. Kasahara, Y. et al. Majorana quantization and half-integer thermal quantum Hall effect in a Kitaev spin liquid. Nature 559, 227–231 (2018).

    Article  CAS  Google Scholar 

  14. Yokoi, T. et al. Half-integer quantized anomalous thermal Hall effect in the Kitaev material candidate α-RuCl3. Science 373, 568–572 (2021).

    Article  CAS  Google Scholar 

  15. Sears, J. A. et al. Ferromagnetic Kitaev interaction and the origin of large magnetic anisotropy in α-RuCl3. Nat. Phys. 16, 837–840 (2020).

    Article  CAS  Google Scholar 

  16. Sears, J. A. et al. Magnetic order in α–RuCl3: a honeycomb-lattice quantum magnet with strong spin-orbit coupling. Phys. Rev. B 91, 144420 (2015).

    Article  Google Scholar 

  17. Li, H. et al. Identification of magnetic interactions and high-field quantum spin liquid in α-RuCl3. Nat. Commun. 12, 4007 (2021).

    Article  CAS  Google Scholar 

  18. Liu, H. & Khaliullin, G. Pseudospin exchange interactions in d7 cobalt compounds: possible realization of the Kitaev model. Phys. Rev. B 97, 014407 (2018).

    Article  CAS  Google Scholar 

  19. Sano, R., Kato, Y. & Motome, Y. Kitaev-Heisenberg Hamiltonian for high-spin d7 Mott insulators. Phys. Rev. B 97, 014408 (2018).

    Article  CAS  Google Scholar 

  20. Liu, H., Chaloupka, J. & Khaliullin, G. Kitaev spin liquid in 3d transition metal compounds. Phys. Rev. Lett. 125, 047201 (2020).

    Article  CAS  Google Scholar 

  21. Morris, C. M. et al. Duality and domain wall dynamics in a twisted Kitaev chain. Nat. Phys. 17, 832–836 (2021).

    Article  CAS  Google Scholar 

  22. Kim, C., Kim, H. & Park, J. Spin-orbital entangled state and realization of Kitaev physics in 3d cobalt compounds: a progress report. J. Phys. Condens. Matter 34, 023001 (2021).

    Article  Google Scholar 

  23. Vivanco, H. K., Trump, B. A., Brown, C. M. & McQueen, T. M. Competing antiferromagnetic-ferromagnetic states in a d7 Kitaev honeycomb magnet. Phys. Rev. B 102, 224411 (2020).

    Article  CAS  Google Scholar 

  24. Lin, G. et al. Field-induced quantum spin disordered state in spin-1/2 honeycomb magnet Na2Co2TeO6 with small Kitaev interaction. Nat. Commun. 12, 5559 (2021).

    Article  Google Scholar 

  25. Zhong, R., Gao, T., Ong, N. P. & Cava, R. J. Weak-field induced nonmagnetic state in a Co-based honeycomb. Sci. Adv. 6, eaay6953 (2020).

    Article  CAS  Google Scholar 

  26. Shi, L. Y. et al. Magnetic excitations of the field-induced states in BaCo2(AsO4)2 probed by time-domain terahertz spectroscopy. Phys. Rev. B 104, 144408 (2021).

    Article  CAS  Google Scholar 

  27. Das, S. et al. XY magnetism, Kitaev exchange, and long-range frustration in the Jeff = 1/2 honeycomb cobaltates. Phys. Rev. B 104, 134425 (2021).

    Article  CAS  Google Scholar 

  28. Cao, H. B. et al. Low-temperature crystal and magnetic structure of α–RuCl3. Phys. Rev. B 93, 134423 (2016).

    Article  Google Scholar 

  29. Do, S. H. et al. Majorana fermions in the Kitaev quantum spin system α-RuCl3. Nat. Phys. 13, 1079–1084 (2017).

    Article  CAS  Google Scholar 

  30. Little, A. et al. Antiferromagnetic resonance and terahertz continuum in α–RuCl3. Phys. Rev. Lett. 119, 227201 (2017).

    Article  CAS  Google Scholar 

  31. Reschke, S. et al. Terahertz excitations in α–RuCl3: Majorana fermions and rigid-plane shear and compression modes. Phys. Rev. B 100, 100403(R) (2019).

    Article  Google Scholar 

  32. Sahasrabudhe, A. et al. High-field quantum disordered state in α–RuCl3: spin flips, bound states, and multiparticle continuum. Phys. Rev. B 101, 140410 (2020).

    Article  CAS  Google Scholar 

  33. Zhang, X. et al. Hierarchy of exchange interactions in the triangular-lattice spin liquid YbMgGaO4. Phys. Rev. X 8, 031001 (2018).

    CAS  Google Scholar 

  34. Knolle, J., Kovrizhin, D. L., Chalker, J. T. & Moessner, R. Dynamics of a two-dimensional quantum spin liquid: signatures of emergent Majorana fermions and fluxes. Phys. Rev. Lett. 112, 207203 (2014).

    Article  Google Scholar 

  35. Yoshitake, J., Nasu, J. & Motome, Y. Fractional spin fluctuations as a precursor of quantum spin liquids: Majorana dynamical mean-field study for the Kitaev model. Phys. Rev. Lett. 117, 157203 (2016).

    Article  Google Scholar 

  36. Sandilands, L. J., Tian, Y., Plumb, K. W. & Kim, Y. J. Scattering continuum and possible fractionalized excitations in α–RuCl3. Phys. Rev. Lett. 114, 147201 (2015).

    Article  Google Scholar 

  37. Winter, S. M. et al. Breakdown of magnons in a strongly spin-orbital coupled magnet. Nat. Commun. 8, 1152 (2017).

    Article  Google Scholar 

  38. Winter, S. M. et al. Probing α–RuCl3 beyond magnetic order: effects of temperature and magnetic field. Phys. Rev. Lett. 120, 077203 (2018).

    Article  CAS  Google Scholar 

  39. Regnault, L. P., Burlet, P. & Mignod, J. R. Magnetic ordering in a planar X - Y model: BaCo2(AsO4)2. Phys. B 86, 660–662 (1977).

    Article  Google Scholar 

  40. Regnault, L. P., Boullier, C. & Lorenzo, J. E. Polarized-neutron investigation of magnetic ordering and spin dynamics in BaCo2(AsO4)2 frustrated honeycomb-lattice magnet. Heliyon 4, e00507 (2018).

    Article  Google Scholar 

  41. Czajka, P. et al. Oscillations of the thermal conductivity in the spin-liquid state of α-RuCl3. Nat. Phys. 17, 915–919 (2021).

    Article  CAS  Google Scholar 

  42. Yadav, R. et al. Kitaev exchange and field-induced quantum spin-liquid states in honeycomb α-RuCl3. Sci. Rep. 6, 37925 (2016).

    Article  CAS  Google Scholar 

  43. Gordon, J. S., Catuneanu, A., Sørensen, E. S. & Kee, H. Y. Theory of the field-revealed Kitaev spin liquid. Nat. Commun. 10, 2470 (2019).

    Article  Google Scholar 

  44. Maksimov, P. A. & Chernyshev, A. L. Rethinking α–RuCl3. Phys. Rev. Res. 2, 033011 (2020).

    Article  CAS  Google Scholar 

  45. Ran, K. et al. Spin wave excitations evidencing the Kitaev interaction in single crystalline α–RuCl3. Phys. Rev. Lett. 118, 107203 (2017).

    Article  Google Scholar 

  46. Patela, N. D. & Trivedia, T. Magnetic field-induced intermediate quantum spin liquid with a spinon Fermi surface. Proc. Natl Acad. Sci. USA 116, 12199–12203 (2019).

    Article  Google Scholar 

  47. Hickey, C. & Trebst, S. Emergence of a field-driven U(1) spin liquid in the Kitaev honeycomb model. Nat. Commun. 10, 530 (2019).

    Article  Google Scholar 

  48. Jiang, Y. F., Devereaux, T. P. & Jiang, H. C. Field-induced quantum spin liquid in the Kitaev-Heisenberg model and its relation to α–RuCl3. Phys. Rev. B 100, 165123 (2019).

    Article  CAS  Google Scholar 

  49. Modic, K. A. et al. Scale-invariant magnetic anisotropy in α-RuCl3 at high magnetic fields. Nat. Phys. 17, 240–244 (2021).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

This research was supported as part of the Institute for Quantum Matter, an Energy Frontier Research Center funded by the US Department of Energy’s Basic Energy Sciences programme under DE-SC0019331. N.P.A. had additional support from the Quantum Materials programme at the Canadian Institute for Advanced Research. We thank P. Chauhan and A. Legros for critical comments on this manuscript and H.-Y. Kee, G. Khaliullin and H. Liu for helpful conversations.

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X.Z. performed the terahertz experiments and analysed the data. R.Z. and R.J.C. grew the single crystals. Y.X. and N.D. performed the Raman spectroscopy. T.H. and C.B. performed the magnetization experiments. X.Z. and N.P.A. prepared the first draft, and all authors contributed to writing the manuscript.

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Correspondence to N. P. Armitage.

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Supplementary Figs. 1–16.

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Zhang, X., Xu, Y., Halloran, T. et al. A magnetic continuum in the cobalt-based honeycomb magnet BaCo2(AsO4)2. Nat. Mater. (2022). https://doi.org/10.1038/s41563-022-01403-1

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