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Bond-dependent anisotropy and magnon decay in cobalt-based Kitaev triangular antiferromagnet

Abstract

The Kitaev model, a honeycomb network of spins with bond-dependent anisotropic interactions, is a rare example of a system with a quantum spin liquid ground state. Although most Kitaev model candidate materials eventually order magnetically due to additional non-Kitaev interactions, their bond-dependent anisotropy manifests in unusual spin dynamics. Recent research suggests that bond-dependent anisotropy can stabilize exotic magnetic phases on the geometrically frustrated triangular lattice. Unfortunately, few materials have been identified with simultaneous geometric frustration and bond-dependent anisotropy. Here, we report a frustrated triangular lattice with bond-dependent anisotropy in the cobalt-based van der Waals antiferromagnet CoI2. Momentum and energy-resolved inelastic neutron scattering measurements show substantial magnon decay and level repulsion. A thorough examination of excitations in both the paramagnetic and magnetically ordered states demonstrates that the bond-dependent anisotropy is the origin of the spiral order and the magnon decay found in CoI2. Our results provide the basis for future studies of the interplay between Kitaev magnetism and geometric frustration.

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Fig. 1: Schematic view of Kitaev model, spin-orbital entangled Jeff = 1/2 state, spiral magnetic structure and magnetic phase diagram of CoI2.
Fig. 2: Diffuse and inelastic scattering in the paramagnetic regime of CoI2.
Fig. 3: Spin-wave excitations and magnon decay in magnetically ordered CoI2.
Fig. 4: Two-magnon DOS, magnon decay and selective avoided decay mode.

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Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request. Source data are provided with this paper.

Code availability

The source code used in this study is available from the corresponding author upon reasonable request.

References

  1. Anderson, P. W. The resonating valence bond state in La2CuO4 and superconductivity. Science (1979) 235, 1196–1198 (1987).

    Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  MathSciNet  MATH  Google Scholar 

  4. Takagi, H., Takayama, T., Jackeli, G., Khaliullin, G. & Nagler, S. E. Concept and realization of Kitaev quantum spin liquids. Nat. Rev. Phys. 1, 264–280 (2019).

    Google Scholar 

  5. Jackeli, G. & Khaliullin, G. Mott insulators in the strong spin-orbit coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models. Phys. Rev. Lett. 102, 017205 (2009).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  8. Sugano, S., Tanabe, Y. & Kamimura, H. Multiplets of Transition-Metal Ions in Crystals (Academic, 1970).

  9. Abragam, A. & Bleaney, B. Electron Paramagnetic Resonance of Transition Ions (Oxford Univ., 1986).

    Google Scholar 

  10. Kim, C. et al. Antiferromagnetic Kitaev interaction in Jeff = 1/2 cobalt honeycomb materials Na3Co2SbO6 and Na2Co2TeO6. J. Phys. Condens. Matter 34, 045802 (2022).

    ADS  Google Scholar 

  11. Songvilay, M. et al. Kitaev interactions in the Co honeycomb antiferromagnets Na3Co2SbO6 and Na2Co2TeO6. Phys. Rev. B 102, 224429 (2020).

    ADS  Google Scholar 

  12. Yao, W., Iida, K., Kamazawa, K. & Li, Y. Excitations in the ordered and paramagnetic states of honeycomb magnet Na2Co2TeO6. Phys. Rev. Lett. 129, 147202 (2022).

    ADS  Google Scholar 

  13. Li, X. et al. Giant magnetic in-plane anisotropy and competing instabilities in Na3Co2SbO6. Phys. Rev. X 12, 041024 (2022).

    Google Scholar 

  14. Halloran, T. et al. Geometrical frustration versus Kitaev interactions in BaCo2(AsO4)2. Proc. Natl Acad. Sci. USA 120, e2215509119 (2023).

    Google Scholar 

  15. 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).

    ADS  Google Scholar 

  16. Maksimov, P. A., Zhu, Z., White, S. R. & Chernyshev, A. L. Anisotropic-exchange magnets on a triangular lattice: spin waves, accidental degeneracies, and dual spin liquids. Phys. Rev. X 9, 021017 (2019).

    Google Scholar 

  17. Catuneanu, A., Rau, J. G., Kim, H.-S. & Kee, H.-Y. Magnetic orders proximal to the Kitaev limit in frustrated triangular systems: application to Ba3IrTi2O9. Phys. Rev. B 92, 165108 (2015).

    ADS  Google Scholar 

  18. Aczel, A. A. et al. Highly anisotropic exchange interactions of jeff=1/2 iridium moments on the fcc lattice in La2BIrO6 (B=Mg. Zn). Phys. Rev. B 93, 214426 (2016).

    ADS  Google Scholar 

  19. Chernyshev, A. L. & Zhitomirsky, M. E. Spin waves in a triangular lattice antiferromagnet: decays, spectrum renormalization, and singularities. Phys. Rev. B 79, 144416 (2009).

    ADS  Google Scholar 

  20. Zhitomirsky, M. E. & Chernyshev, A. L. Colloquium: spontaneous magnon decays. Rev. Mod. Phys. 85, 219–242 (2013).

    ADS  Google Scholar 

  21. Verresen, R., Moessner, R. & Pollmann, F. Avoided quasiparticle decay from strong quantum interactions. Nat. Phys. 15, 750–753 (2019).

    Google Scholar 

  22. Ghioldi, E. A. et al. Evidence of two-spinon bound states in the magnetic spectrum of Ba3CoSb2O9. Phys. Rev. B 106, 064418 (2022).

    ADS  Google Scholar 

  23. Macdougal, D. et al. Avoided quasiparticle decay and enhanced excitation continuum in the spin-1/2 near-Heisenberg triangular antiferromagnet Ba3Co2SbO9. Phys. Rev. B 102, 064421 (2020).

    ADS  Google Scholar 

  24. Park, P. et al. Momentum-dependent magnon lifetime in the metallic noncollinear triangular antiferromagnet CrB2. Phys. Rev. Lett. 125, 027202 (2020).

    ADS  Google Scholar 

  25. Plumb, K. W. et al. Quasiparticle-continuum level repulsion in a quantum magnet. Nat. Phys. 12, 224–229 (2016).

    Google Scholar 

  26. Stone, M. B., Zaliznyak, I. A., Hong, T., Broholm, C. L. & Reich, D. H. Quasiparticle breakdown in a quantum spin liquid. Nature 440, 187–190 (2006).

    ADS  Google Scholar 

  27. Fåk, B. & Bossy, J. Temperature dependence of S(Q, E) in liquid 4He beyond the roton. J. Low. Temp. Phys. 112, 1–19 (1998).

    ADS  Google Scholar 

  28. Bai, X. et al. Instabilities of heavy magnons in an anisotropic magnet. Nat. Commun. 14, 4199 (2023).

    ADS  Google Scholar 

  29. McGuire, M. Crystal and magnetic structures in layered, transition metal dihalides and trihalides. Crystals 7, 121 (2017).

    Google Scholar 

  30. Bai, X. et al. Hybridized quadrupolar excitations in the spin-anisotropic frustrated magnet FeI2. Nat. Phys. 17, 467–472 (2021).

    ADS  Google Scholar 

  31. Kurumaji, T. et al. Magnetoelectric responses induced by domain rearrangement and spin structural change in triangular-lattice helimagnets NiI2 and CoI2. Phys. Rev. B 87, 014429 (2013).

    ADS  Google Scholar 

  32. Son, S. et al. Multiferroic-enabled magnetic-excitons in 2D quantum-entangled van der Waals antiferromagnet NiI2. Adv. Mater. 34, 2109144 (2022).

    Google Scholar 

  33. Kuindersma, S. R., Sanchez, J. P. & Haas, C. Magnetic and structural investigations on NiI2 and CoI2. Physica B+C 111, 231–248 (1981).

    ADS  Google Scholar 

  34. Litvin, D. B. The Luttinger-Tisza method. Physica 77, 205–219 (1974).

    ADS  MathSciNet  Google Scholar 

  35. Kim, C. et al. Spin waves in the two-dimensional honeycomb lattice XXZ-type van der Waals antiferromagnet CoPS3. Phys. Rev. B 102, 184429 (2020).

    ADS  Google Scholar 

  36. Paddison, J. A. M. Scattering signatures of bond-dependent magnetic interactions. Phys. Rev. Lett. 125, 247202 (2020).

    ADS  Google Scholar 

  37. Bai, X. et al. Magnetic excitations of the classical spin liquid MgCr2O4. Phys. Rev. Lett. 122, 97201 (2019).

    ADS  Google Scholar 

  38. Zhang, S., Changlani, H. J., Plumb, K. W., Tchernyshyov, O. & Moessner, R. Dynamical structure factor of the three-dimensional quantum spin liquid candidate NaCaNi2F7. Phys. Rev. Lett. 122, 167203 (2019).

    ADS  Google Scholar 

  39. Dahlbom, D. et al. Geometric integration of classical spin dynamics via a mean-field Schrödinger equation. Phys. Rev. B 106, 054423 (2022).

    ADS  Google Scholar 

  40. Zhang, H. & Batista, C. D. Classical spin dynamics based on SU(N) coherent states. Phys. Rev. B 104, 104409 (2021).

    ADS  Google Scholar 

  41. Hong, T. et al. Field induced spontaneous quasiparticle decay and renormalization of quasiparticle dispersion in a quantum antiferromagnet. Nat. Commun. 8, 15148 (2017).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    Google Scholar 

  44. Smit, R. L. et al. Magnon damping in the zigzag phase of the Kitaev-Heisenberg-Γ model on a honeycomb lattice. Phys. Rev. B 101, 054424 (2020).

    ADS  Google Scholar 

  45. Halloran, T. et al. Magnetic excitations and interactions in the Kitaev hyperhoneycomb iridate β-Li2IrO3. Phys. Rev. B 106, 064423 (2022).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  47. Nakajima, K. et al. AMATERAS: a cold-neutron disk chopper spectrometer. J. Phys. Soc. Jpn. 80, SB028 (2011).

    Google Scholar 

  48. SunnySuite / Sunny.jl. GitHub https://github.com/SunnySuite/Sunny.jl/

  49. 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 834, 132–142 (2016).

    ADS  Google Scholar 

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Acknowledgements

We thank P. Maksimov, K. Barros, M. Willson and C. D. Batista for fruitful discussions. This work was supported by the Leading Researcher Program of the National Research Foundation of Korea (Grant No. 2020R1A3B2079375). The INS experiment was performed at the MLF of J-PARC under a user program (Proposal No. 2020B0407). The work of A.L.C. was supported by the US Department of Energy, Office of Science, Basic Energy Sciences under Award No. DE-SC0021221. The work of M.M. was supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division under award DE-SC-0018660. The work of S.K. and S.-J.K was supported by the Pioneer Research Center Program through the National Research Foundation of Korea funded by the Ministry of Science, ICT & Future Planning (NRF-2022M3C1A309198811).

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J.-G.P. initiated and supervised the project. S.K., C.K. and S.-J.K. grew the single crystal using the Bridgman furnace. C.K. aligned the sample for measurements. S.O.-K., N.M., C.K., P.P., T.K., J.-G.P. and K.N. performed the INS measurement. C.K. analysed the data and performed an LSWT calculation. C.K. and M.M. performed the LLD simulations. P.P., M.M. and A.L.C. contributed to the theoretical interpretation and discussion. C.K., M.M. and J.-G.P. wrote the manuscript with input from all authors.

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Correspondence to Je-Geun Park.

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Nature Physics thanks Lebing Chen and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Discussion, Figs. 1–13 and Table 1.

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Statistical source data of Fig. 4d,e.

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Kim, C., Kim, S., Park, P. et al. Bond-dependent anisotropy and magnon decay in cobalt-based Kitaev triangular antiferromagnet. Nat. Phys. 19, 1624–1629 (2023). https://doi.org/10.1038/s41567-023-02180-7

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