Ferromagnetic Kitaev interaction and the origin of large magnetic anisotropy in α-RuCl3

Abstract

α-RuCl3 is drawing much attention as a promising candidate for the Kitaev quantum spin liquid1,2,3,4,5,6,7,8. However, despite intensive research efforts, controversy remains about the form of the basic interactions governing the physics of this material. Even the sign of the Kitaev interaction (the bond-dependent anisotropic interaction responsible for Kitaev physics) is still under debate, with conflicting results from theoretical and experimental studies5,6,9,10,11,12,13,14,15. The significance of the symmetric off-diagonal exchange interaction (referred to as the Γ term) is another contentious question16,17,18. Here, we present resonant elastic X-ray scattering data that provide unambiguous experimental constraints to the two leading terms in the magnetic interaction Hamiltonian. We show that the Kitaev interaction (K) is ferromagnetic, and that the Γ term is antiferromagnetic and comparable in size to the Kitaev interaction. Our findings also provide a natural explanation for the large anisotropy of the magnetic susceptibility in α-RuCl3 as arising from the large Γ term. We therefore provide a crucial foundation for understanding the interactions underpinning the exotic magnetic behaviours observed in α-RuCl3.

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: Characterization of magnetic scattering.
Fig. 2: Azimuthal dependence of magnetic scattering intensity.
Fig. 3: Fitting the magnetization data through simulated annealing calculations on the classical spin model.

Data availability

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

Code availability

The computer code used to generate results that are reported in the paper is available from the authors on reasonable request.

References

  1. 1.

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

    ADS  Google Scholar 

  2. 2.

    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).

    ADS  Google Scholar 

  3. 3.

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

    ADS  Google Scholar 

  4. 4.

    Johnson, R. D. et al. Monoclinic crystal structure of α-RuCl3 and the zigzag antiferromagnetic ground state. Phys. Rev. B 92, 235119 (2015).

    ADS  Google Scholar 

  5. 5.

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

    ADS  Google Scholar 

  6. 6.

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

    ADS  Google Scholar 

  7. 7.

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

    Google Scholar 

  8. 8.

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

    ADS  Google Scholar 

  9. 9.

    Kim, H.-S., Shankar, V. V., Catuneanu, A. & Kee, H.-Y. Kitaev magnetism in honeycomb RuCl3 with intermediate spin-orbit coupling. Phys. Rev. B 91, 241110(R) (2015).

    ADS  Google Scholar 

  10. 10.

    Kim, H.-S. & Kee, H.-Y. Crystal structure and magnetism in α-RuCl3: an ab initio study. Phys. Rev. B 93, 155143 (2016).

    ADS  Google Scholar 

  11. 11.

    Winter, S. M., Li, Y., Jeschke, H. O. & Valentí, R. Challenges in design of Kitaev materials: magnetic interactions from competing energy scales. Phys. Rev. B 93, 214431 (2016).

    ADS  Google Scholar 

  12. 12.

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

    ADS  Google Scholar 

  13. 13.

    Hou, Y. S., Xiang, H. J. & Gong, X. G. Unveiling magnetic interactions of ruthenium trichloride via constraining direction of orbital moments: potential routes to realize a quantum spin liquid. Phys. Rev. B 96, 054410 (2017).

    ADS  Google Scholar 

  14. 14.

    Wang, W., Dong, Z.-Y., Yu, S.-L. & Li, J.-X. Theoretical investigation of magnetic dynamics in α-RuCl3. Phys. Rev. B 96, 115103 (2017).

    ADS  Google Scholar 

  15. 15.

    Eichstaedt, C. et al. Deriving models for the Kitaev spin-liquid candidate material α-RuCl3 from first principles. Phys. Rev. B 100, 075110 (2019).

    ADS  Google Scholar 

  16. 16.

    Rau, J. G., Lee, E. K.-H. & Kee, H.-Y. Generic spin model for the honeycomb iridates beyond the Kitaev limit. Phys. Rev. Lett. 112, 077204 (2014).

    ADS  Google Scholar 

  17. 17.

    Katukuri, V. M. et al. Kitaev interactions between j = 1/2 moments in honeycomb Na2IrO3 are large and ferromagnetic: insights from ab initio quantum chemistry calculations. New J. Phys. 16, 013056 (2014).

    ADS  Google Scholar 

  18. 18.

    Chaloupka, J. & Khaliullin, G. Hidden symmetries of the extended Kitaev-Heisenberg model: implications for the honeycomb-lattice iridates A2IrO3. Phys. Rev. B 92, 024413 (2015).

    ADS  Google Scholar 

  19. 19.

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

    ADS  MathSciNet  MATH  Google Scholar 

  20. 20.

    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 

  21. 21.

    Yamaji, Y., Nomura, Y., Kurita, M., Arita, R. & Imada, M. First-principles study of the honeycomb-lattice iridates Na2IrO3 in the presence of strong spin-orbit interaction and electron correlations. Phys. Rev. Lett. 113, 107201 (2014).

    ADS  Google Scholar 

  22. 22.

    Janssen, L., Andrade, E. C. & Vojta, M. Magnetization processes of zigzag states on the honeycomb lattice: identifying spin models for α-RuCl3 and Na2IrO3. Phys. Rev. B 96, 064430 (2017).

    ADS  Google Scholar 

  23. 23.

    Modic, K. A. et al. Resonant torsion magnetometry in anisotropic quantum materials. Nat. Commun. 9, 3975 (2018).

    ADS  Google Scholar 

  24. 24.

    Modic, K. A., Ramshaw, B. J., Shekhter, A. & Varma, C. M. Chiral spin order in some purported Kitaev spin-liquid compounds. Phys. Rev. B 98, 205110 (2018).

    ADS  Google Scholar 

  25. 25.

    Riedl, K., Li, Y., Winter, S. M. & Valentí, R. Sawtooth torque in anisotropic j eff = 1/2 magnets: application to α-RuCl3. Phys. Rev. Lett. 122, 197202 (2019).

    ADS  Google Scholar 

  26. 26.

    Koitzsch, A. et al. Low temperature enhancement of ferromagnetic Kitaev correlations in α-RuCl3. Preprint at https://arxiv.org/abs/1709.02712v1 (2017).

  27. 27.

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

    ADS  Google Scholar 

  28. 28.

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

    ADS  Google Scholar 

  29. 29.

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

    ADS  Google Scholar 

  30. 30.

    Chaloupka, J. & Khaliullin, G. Magnetic anisotropy in the Kitaev model systems Na2IrO3 and RuCl3. Phys. Rev. B 94, 064435 (2016).

    ADS  Google Scholar 

  31. 31.

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

    ADS  Google Scholar 

  32. 32.

    Hill, J. P. & McMorrow, D. F. Resonant exchange scattering: polarization dependence and correlation functions. Acta Crystallogr. A 52, 236–244 (1996).

    Google Scholar 

  33. 33.

    Moretti Sala, M., Boseggia, S., McMorrow, D. F. & Monaco, G. Resonant x-ray scattering and the j eff = 1⁄2 electronic ground state in iridate perovskites. Phys. Rev. Lett. 112, 026403 (2014).

    ADS  Google Scholar 

  34. 34.

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

    Google Scholar 

  35. 35.

    Kubota, Y. et al. Successive magnetic phase transitions in α-RuCl3: XY-like frustrated magnet on the honeycomb lattice. Phys. Rev. B 91, 094422 (2015).

    ADS  Google Scholar 

  36. 36.

    Majumder, M. et al. Anisotropic Ru3+ 4d 5 magnetism in the α-RuCl3 honeycomb system: susceptibility, specific heat, and zero-field NMR. Phys. Rev. B 91, 180401(R) (2015).

    ADS  Google Scholar 

  37. 37.

    Agrestini, S. et al. Electronically highly cubic conditions for Ru in α-RuCl3. Phys. Rev. B 96, 161107(R) (2017).

    ADS  Google Scholar 

  38. 38.

    Lampen-Kelley, P. et al. Anisotropic susceptibilities in the honeycomb Kitaev system α-RuCl3. Phys. Rev. B 98, 100403(R) (2018).

    ADS  Google Scholar 

  39. 39.

    Gohlke, M., Wachtel, G., Yamaji, Y., Pollmann, F. & Kim, Y.-B. Quantum spin liquid signatures in Kitaev-like frustrated magnets. Phys. Rev. B 97, 075126 (2018).

    ADS  Google Scholar 

  40. 40.

    Momma, K. & Izumi, F. VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data. J. Appl. Crystallogr. 44, 1272–1276 (2011).

    Google Scholar 

  41. 41.

    Strempfer, J. et al. Resonant scattering and diffraction beamline P09 at PETRA III. J. Synchrotron Rad. 20, 541–549 (2013).

    Google Scholar 

  42. 42.

    Sears, J. A., Zhao, Y., Xu, Z., Lynn, J. W. & Kim, Y.-J. Phase diagram of α-RuCl3 in an in-plane magnetic field. Phys. Rev. B 95, 180411(R) (2017).

    ADS  Google Scholar 

  43. 43.

    Brückel, T. et al. Antiferromagnetic order and phase transitions in GdS as studied with X-ray resonance-exchange scattering. Eur. Phys. J. B 19, 475–490 (2001).

    ADS  Google Scholar 

Download references

Acknowledgements

We would like to thank J. Bertinshaw and H. Suzuki for their help with the experiment. We acknowledge DESY (Hamburg, Germany), a member of the Helmholtz Association HGF, for the provision of experimental facilities. Parts of this research were carried out at PETRA III. Work at the University of Toronto was supported by the Natural Science and Engineering Research Council (NSERC) of Canada, Canadian Foundation for Innovation, Ontario Innovation Trust, and the Center for Quantum Materials at the University of Toronto. Y.B.K. is also supported by the Killam Research Fellowship from the Canada Council for the Arts. This work was performed in part at Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1607611.

Author information

Affiliations

Authors

Contributions

J.A.S. and Y.-J.K. conceived the experiments. J.A.S., P.J.B. and S.F. performed the experiments and J.A.S. analysed the data. J.A.S. synthesized and characterized the sample. S.K. provided the magnetic susceptibility data. L.E.C. and Y.B.K. performed theoretical calculations. J.A.S. and Y.-J.K. wrote the paper with contributions from all co-authors.

Corresponding author

Correspondence to Young-June Kim.

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 Figs. 1 and 2, and discussion.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Sears, J.A., Chern, L.E., Kim, S. et al. Ferromagnetic Kitaev interaction and the origin of large magnetic anisotropy in α-RuCl3. Nat. Phys. 16, 837–840 (2020). https://doi.org/10.1038/s41567-020-0874-0

Download citation

Further reading