Letter | Published:

Direct evidence for dominant bond-directional interactions in a honeycomb lattice iridate Na2IrO3

Nature Physics volume 11, pages 462466 (2015) | Download Citation

Abstract

Heisenberg interactions are ubiquitous in magnetic materials and play a central role in modelling and designing quantum magnets. Bond-directional interactions1,2,3 offer a novel alternative to Heisenberg exchange and provide the building blocks of the Kitaev model4, which has a quantum spin liquid as its exact ground state. Honeycomb iridates, A2IrO3 (A = Na, Li), offer potential realizations of the Kitaev magnetic exchange coupling, and their reported magnetic behaviour may be interpreted within the Kitaev framework. However, the extent of their relevance to the Kitaev model remains unclear, as evidence for bond-directional interactions has so far been indirect. Here we present direct evidence for dominant bond-directional interactions in antiferromagnetic Na2IrO3 and show that they lead to strong magnetic frustration. Diffuse magnetic X-ray scattering reveals broken spin-rotational symmetry even above the Néel temperature, with the three spin components exhibiting short-range correlations along distinct crystallographic directions. This spin- and real-space entanglement directly uncovers the bond-directional nature of these interactions, thus providing a direct connection between honeycomb iridates and Kitaev physics.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

References

  1. 1.

    On the anisotropy of cubic ferromagnetic crystals. Phys. Rev. 52, 1178–1198 (1937).

  2. 2.

    Orbital order and fluctuations in Mott insulators. Prog. Theor. Phys. Suppl. 160, 155–202 (2005).

  3. 3.

    & Mott insulators in the strong spin–orbit coupling limit: From Heisenberg to a quantum compass and Kitaev models. Phys. Rev. Lett. 102, 017205 (2009).

  4. 4.

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

  5. 5.

    et al. Novel Jeff = 1/2 Mott state induced by relativistic spin–orbit coupling in Sr2IrO4. Phys. Rev. Lett. 101, 076402 (2008).

  6. 6.

    et al. Phase-sensitive observation of a spin–orbital Mott state in Sr2IrO4. Science 323, 1329–1332 (2009).

  7. 7.

    et al. Hyper-honeycomb iridate β-Li2IrO3 as a platform for Kitaev magnetism. Phys. Rev. Lett. 114, 077202 (2015).

  8. 8.

    et al. Realization of a three-dimensional spin-anisotropic harmonic honeycomb iridate. Nature Commun. 5, 4203 (2014).

  9. 9.

    & Kitaev–Heisenberg models for iridates on the triangular, hyperkagome, kagome, fcc, and pyrochlore lattices. Phys. Rev. B 89, 014414 (2014).

  10. 10.

    & Quantum spin liquid with a Majorana Fermi surface on the three-dimensional hyperoctagon lattice. Phys. Rev. B 89, 235102 (2014).

  11. 11.

    , , & Emergent quantum phases in a frustrated J1J2 Heisenberg model on the hyperhoneycomb lattice. Phys. Rev. B 90, 134425 (2014).

  12. 12.

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

  13. 13.

    et al. Li2RhO3: A spin-glassy relativistic Mott insulator. Phys. Rev. B 87, 161121 (2013).

  14. 14.

    et al. Long-range magnetic ordering in Na2IrO3. Phys. Rev. B 83, 220403 (2011).

  15. 15.

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

  16. 16.

    et al. Direct evidence of a zigzag spin-chain structure in the honeycomb lattice: A neutron and X-ray diffraction investigation of single-crystal Na2IrO3. Phys. Rev. B 85, 180403 (2012).

  17. 17.

    , & Spiral order in the honeycomb iridate Li2IrO3. Phys. Rev. B 90, 100405 (2014).

  18. 18.

    et al. Noncoplanar and counterrotating incommensurate magnetic order stabilized by Kitaev interactions in γ-Li2IrO3. Phys. Rev. Lett. 113, 197201 (2014).

  19. 19.

    et al. Unconventional magnetic order on the hyperhoneycomb Kitaev lattice in β-Li2IrO3: Full solution via magnetic resonant X-ray diffraction. Phys. Rev. B 90, 205116 (2014).

  20. 20.

    , & Kitaev–Heisenberg model on a honeycomb lattice: Possible exotic phases in iridium oxides A2IrO3. Phys. Rev. Lett. 105, 027204 (2010).

  21. 21.

    , & Zigzag magnetic order in the iridium oxide Na2IrO3. Phys. Rev. Lett. 110, 097204 (2013).

  22. 22.

    & Theory of magnetic phase diagrams in hyperhoneycomb and harmonic-honeycomb iridates. Phys. Rev. B 91, 064407 (2015).

  23. 23.

    , & Generic spin model for the honeycomb iridates beyond the Kitaev limit. Phys. Rev. Lett. 112, 077204 (2014).

  24. 24.

    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).

  25. 25.

    , , , & 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).

  26. 26.

    et al. Quantum spin Hall effect in a transition metal oxide Na2IrO3. Phys. Rev. Lett. 102, 256403 (2009).

  27. 27.

    , , , & Na2IrO3 as a molecular orbital crystal. Phys. Rev. Lett. 109, 197201 (2012).

  28. 28.

    , , , & Topological quantum phase transition in 5d transition metal oxide Na2IrO3. Phys. Rev. Lett. 108, 106401 (2012).

  29. 29.

    et al. Magnetic excitation spectrum of Na2IrO3 probed with resonant inelastic X-ray scattering. Phys. Rev. B 87, 220407 (2013).

  30. 30.

    & Finite-temperature phase diagram of the classical Kitaev–Heisenberg model. Phys. Rev. B 88, 024410 (2013).

  31. 31.

    et al. Two-dimensional Heisenberg behavior of Jeff = 1/2 isospins in the paramagnetic state of the spin–orbital Mott insulator Sr2IrO4. Phys. Rev. Lett. 108, 247212 (2012).

  32. 32.

    & Kitaev–Heisenberg-J2-J3 model for the iridates A2IrO3. Phys. Rev. B 84, 180407 (2011).

  33. 33.

    & Antiferromagnetic Mott insulating state in single crystals of the honeycomb lattice material Na2IrO3. Phys. Rev. B 82, 064412 (2010).

  34. 34.

    et al. Large spin-wave energy gap in the bilayer iridate Sr3Ir2O7: Evidence for enhanced dipolar interactions near the Mott metal–insulator transition. Phys. Rev. Lett. 109, 157402 (2012).

Download references

Acknowledgements

Work in the Materials Science Division of Argonne National Laboratory (sample preparation, characterization, and contributions to data analysis) was supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Science and Engineering Division. Use of the Advanced Photon Source, an Office of Science User Facility operated for the US Department of Energy (DOE) Office of Science by Argonne National Laboratory, was supported by the US DOE under Contract No. DE-AC02-06CH11357. K.M. acknowledges support from UGC-CSIR, India. Y.S. acknowledges DST, India for support through Ramanujan Grant #SR/S2/RJN-76/2010 and through DST grant #SB/S2/CMP-001/2013. J.C. was supported by ERDF under project CEITEC (CZ.1.05/1.1.00/02.0068) and EC 7th Framework Programme (286154/SYLICA).

Author information

Affiliations

  1. Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA

    • Sae Hwan Chun
    • , H. Zheng
    • , Constantinos C. Stoumpos
    • , C. D. Malliakas
    •  & J. F. Mitchell
  2. Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA

    • Jong-Woo Kim
    • , Jungho Kim
    • , Y. Choi
    •  & T. Gog
  3. Indian Institute of Science Education and Research (IISER) Mohali, Knowledge City, Sector 81, Mohali 140306, India

    • Kavita Mehlawat
    •  & Yogesh Singh
  4. European Synchrotron Radiation Facility, BP 220, F-38043 Grenoble Cedex, France

    • A. Al-Zein
    • , M. Moretti Sala
    •  & M. Krisch
  5. Central European Institute of Technology, Masaryk University, Kotlářská 2, 61137 Brno, Czech Republic

    • J. Chaloupka
  6. Max Planck Institute for Solid State Research, Heisenbergstraße 1, D-70569 Stuttgart, Germany

    • G. Jackeli
    • , G. Khaliullin
    •  & B. J. Kim
  7. Institute for Functional Matter and Quantum Technologies, University of Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany

    • G. Jackeli

Authors

  1. Search for Sae Hwan Chun in:

  2. Search for Jong-Woo Kim in:

  3. Search for Jungho Kim in:

  4. Search for H. Zheng in:

  5. Search for Constantinos C. Stoumpos in:

  6. Search for C. D. Malliakas in:

  7. Search for J. F. Mitchell in:

  8. Search for Kavita Mehlawat in:

  9. Search for Yogesh Singh in:

  10. Search for Y. Choi in:

  11. Search for T. Gog in:

  12. Search for A. Al-Zein in:

  13. Search for M. Moretti Sala in:

  14. Search for M. Krisch in:

  15. Search for J. Chaloupka in:

  16. Search for G. Jackeli in:

  17. Search for G. Khaliullin in:

  18. Search for B. J. Kim in:

Contributions

B.J.K. conceived the project. S.H.C., J-W.K., J.K. and B.J.K. performed the experiment with support from Y.C., T.G., A.A-Z., M.M.S. and M.K. H.Z. and K.M. grew the single crystals; C.C.S., C.D.M. and K.M. characterized the samples under the supervision of J.F.M. and Y.S. S.H.C., J-W.K. and B.J.K. analysed the data. J.C. performed the numerical calculations. J.C., G.J. and G.K. developed the theoretical model. All authors discussed the results. B.J.K. led the manuscript preparation with contributions from all authors.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to B. J. Kim.

Supplementary information

PDF files

  1. 1.

    Supplementary Information

    Supplementary Information

About this article

Publication history

Received

Accepted

Published

DOI

https://doi.org/10.1038/nphys3322

Further reading