Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Observation of two types of fractional excitation in the Kitaev honeycomb magnet


Quantum spin liquid is a disordered but highly entangled magnetic state with fractional spin excitations1. The ground state of an exactly solved Kitaev honeycomb model is perhaps its clearest example2. Under a magnetic field, a spin flip in this model fractionalizes into two types of anyon, a quasiparticle with more complex exchange statistics than standard fermions or bosons: a pair of gauge fluxes and a Majorana fermion2,3. Here, we demonstrate this kind of fractionalization in the Kitaev paramagnetic state of the honeycomb magnet α-RuCl3. The spin excitation gap determined by nuclear magnetic resonance consists of the predicted Majorana fermion contribution following the cube of the applied magnetic field2,4,5, and a finite zero-field contribution matching the predicted size of the gauge flux gap2,6. The observed fractionalization into gapped anyons survives in a broad range of temperatures and magnetic fields, which establishes α-RuCl3 as a unique platform for future investigations of anyons.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Structure of α-RuCl3 and the key signature of anyons.
Fig. 2: Signature of the Kitaev spin excitations.
Fig. 3: Determination of the spin excitation gap.


  1. 1.

    Savary, L. & Balents, L. Quantum spin liquids: a review. Rep. Prog. Phys. 80, 016502 (2017).

    ADS  Article  Google Scholar 

  2. 2.

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

    ADS  MathSciNet  Article  MATH  Google Scholar 

  3. 3.

    Baskaran, G., Mandal, S. & Shankar, R. Exact results for spin dynamics and fractionalization in the Kitaev model. Phys. Rev. Lett. 98, 247201 (2007).

    ADS  Article  Google Scholar 

  4. 4.

    Jiang, H.-C., Gu, Z.-C., Qi, X.-L. & Trebst, S. Possible proximity of the Mott insulating iridate Na2IrO3 to a topological phase: phase diagram of the Heisenberg-Kitaev model in a magnetic field. Phys. Rev. B 83, 245104 (2011).

    ADS  Article  Google Scholar 

  5. 5.

    Nasu, J., Yoshitake, J. & Motome, Y. Thermal transport in the Kitaev model. Phys. Rev. Lett. 119, 127204 (2017).

    ADS  Article  Google Scholar 

  6. 6.

    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).

    ADS  Article  Google Scholar 

  7. 7.

    de-Picciotto, R. et al. Direct observation of a fractional charge. Nature 389, 162–164 (1997).

    ADS  Article  Google Scholar 

  8. 8.

    Jompol, Y. et al. Probing spin-charge separation in a Tomonaga-Luttinger liquid. Science 325, 597–601 (2009).

    ADS  Article  Google Scholar 

  9. 9.

    Castelnovo, C., Moessner, R. & Sondhi, S. L. Magnetic monopoles in spin ice. Nature 451, 42–45 (2008).

    ADS  Article  Google Scholar 

  10. 10.

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

    ADS  Article  Google Scholar 

  11. 11.

    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 

  12. 12.

    Nasu, J., Knolle, J., Kovrizhin, D. L., Motome, Y. & Moessner, R. Fermionic response from fractionalization in an insulating two-dimensional magnet. Nat. Phys. 12, 912–915 (2016).

    Article  Google Scholar 

  13. 13.

    Nasu, J., Udagawa, M. & Motome, Y. Thermal fractionalization of quantum spins in a Kitaev model: temperature-linear specific heat and coherent transport of Majorana fermions. Phys. Rev. B 92, 115122 (2015).

    ADS  Article  Google Scholar 

  14. 14.

    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  Article  Google Scholar 

  15. 15.

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

    ADS  Article  Google Scholar 

  16. 16.

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

    ADS  Article  Google Scholar 

  17. 17.

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

    Article  Google Scholar 

  18. 18.

    Choi, S. K. et al. Spin waves and revised crystal structure of honeycomb iridate Na2IrO3. Phys. Rev. Lett. 108, 127204 (2012).

    ADS  Article  Google Scholar 

  19. 19.

    Singh, Y. et al. Relevance of the Heisenberg-Kitaev model for the honeycomb lattice iridates A 2IrO3. Phys. Rev. Lett. 108, 127203 (2012).

    ADS  Article  Google Scholar 

  20. 20.

    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  Article  Google Scholar 

  21. 21.

    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  Article  Google Scholar 

  22. 22.

    Kubota, Y., Tanaka, H., Ono, T., Narumi, Y. & Kindo, K. Successive magnetic phase transitions in α-RuCl3: XY-like frustrated magnet on the honeycomb lattice. Phys. Rev. B 91, 094422 (2015).

    ADS  Article  Google Scholar 

  23. 23.

    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  Article  Google Scholar 

  24. 24.

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

    ADS  Article  Google Scholar 

  25. 25.

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

    ADS  Article  Google Scholar 

  26. 26.

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

    ADS  Article  Google Scholar 

  27. 27.

    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).

    ADS  Article  Google Scholar 

  28. 28.

    Yoshitake, J., Nasu, J. & Motome, Y. Temperature evolution of spin dynamics in two- and three-dimensional Kitaev models: influence of fluctuating Z 2 flux. Phys. Rev. B 96, 064433 (2017).

    ADS  Article  Google Scholar 

  29. 29.

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

    ADS  Article  Google Scholar 

  30. 30.

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

    ADS  Article  Google Scholar 

  31. 31.

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

    ADS  Article  Google Scholar 

  32. 32.

    Baek, S.-H. et al. Evidence for a field-induced quantum spin liquid in α-RuCl3. Phys. Rev. Lett. 119, 037201 (2017).

    ADS  Article  Google Scholar 

  33. 33.

    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  Article  Google Scholar 

  34. 34.

    Hentrich, R. et al. Unusual phonon heat transport in α-RuCl3: strong spin-phonon scattering and field-induced spin gap. Phys. Rev. Lett. 120, 117204 (2018).

    ADS  Article  Google Scholar 

  35. 35.

    Ponomaryov, A. N. et al. Unconventional spin dynamics in the honeycomb-lattice material α-RuCl3: high-field electron spin resonance studies. Phys. Rev. B 96, 241107(R) (2017).

    ADS  Article  Google Scholar 

  36. 36.

    Wolter, A. U. B. et al. Field-induced quantum criticality in the Kitaev system α-RuCl3. Phys. Rev. B 96, 041405(R) (2017).

    ADS  Article  Google Scholar 

  37. 37.

    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  Article  Google Scholar 

  38. 38.

    Mourik, V. et al. Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices. Science 336, 1003–1007 (2012).

    ADS  Article  Google Scholar 

  39. 39.

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

    Google Scholar 

  40. 40.

    Jeong, M. et al. Attractive Tomonaga-Luttinger liquid in a quantum spin ladder. Phys. Rev. Lett. 111, 106404 (2013).

    ADS  Article  Google Scholar 

  41. 41.

    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 

  42. 42.

    Horvatić, M. & Berthier, C. in High Magnetic Fields: Applications in Condensed Matter Physics and Spectroscopy (eds Berthier, C. et al.) 191–210 (Vol. 595, Lecture Notes in Physics, Springer, Berlin, 2002).

  43. 43.

    Moriya, T. Nuclear magnetic relaxation in antiferromagnetics. Prog. Theor. Phys. 16, 23–44 (1956).

    ADS  Article  Google Scholar 

  44. 44.

    Beeman, D. & Pincus, P. Nuclear spin-lattice relaxation in magnetic insulators. Phys. Rev. 166, 359–375 (1968).

    ADS  Article  Google Scholar 

Download references


M.K. acknowledges discussions with M. Horvatić and C. Berthier. The work was partly supported by the Slovenian ARRS program No. P1-0125 and project No. PR-07587. A.B. and Ch.R. acknowledge financial support by the Marie Curie FP7 COFUND PSI Fellowship programme, the Swiss National Science Foundation (Sinergia Network Mott Physics Beyond the Heisenberg Model), and the ERC Grant Hyper Quantum Criticality (HyperQC).

Author information




M.K. conceived, designed and led the project. N.J. and M.K. performed the NMR experiments and analysed the data. K.W.K. and D.B. grew the samples. A.B. performed the magnetic susceptibility measurements. All the authors discussed the results. M.K. wrote the paper with feedback from all the authors.

Corresponding author

Correspondence to Martin Klanjšek.

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 Figures 1–9, Supplementary References

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Janša, N., Zorko, A., Gomilšek, M. et al. Observation of two types of fractional excitation in the Kitaev honeycomb magnet. Nature Phys 14, 786–790 (2018).

Download citation

Further reading


Quick links

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