Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Relevance of on-site and intersite Coulomb interactions in the Kitaev-Heisenberg magnet Na3Co2SbO6

Pritam Bhattacharyya1,2,3,*, Abdul Basit4, Thorben Petersen1, Stephan Rachel4, Satoshi Nishimoto1,5, and Liviu Hozoi1,†

  • *Contact author: pritambhattacharyya01@gmail.com
  • †Contact author: l.hozoi@ifw-dresden.de

Phys. Rev. B 113, L161103 – Published 1 April, 2026

DOI: https://doi.org/10.1103/8fz7-9wj9

Abstract

The detection of considerable spin frustration in honeycomb cobalt oxide compounds indicates the presence of sizable Kitaev interactions in these systems, enlarging the pool of Kitaev spin liquid candidates. Several key questions remain to be answered, as basic as the mechanisms behind Kitaev couplings in Co2+ t2g5eg2 magnets. Analyzing the quantum chemistry of interacting magnetic moments in Na3Co2SbO6, a representative LS-coupled t2g5eg2 oxide, we find that the Kitaev and off-diagonal Γ interactions are substantial and antiferromagnetic but somewhat weaker than the Heisenberg contribution. All nearest-neighbor couplings feature massive contributions from direct Coulomb exchange and/or on-site multiconfigurational dressing, mechanisms not considered so far in descriptive models of Kitaev-Heisenberg magnetism. These findings call for systematic wave function quantum chemical studies to understand direct-indirect exchange synergies in Kitaev-Heisenberg magnets and how to possibly tune intersite couplings toward the Kitaev spin liquid ground state.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (52)

  1. A. Kitaev, Anyons in an exactly solved model and beyond, Ann. Phys. (NY) 321, 2 (2006).
  2. T. Helgaker, P. Jørgensen, and J. Olsen, Molecular Electronic Structure Theory (John Wiley & Sons, Chichester, 2000).
  3. P. Fulde, Correlated Electrons in Quantum Matter (World Scientific, Singapore, 2012).
  4. G. Khaliullin, Orbital order and fluctuations in Mott insulators, Prog. Theor. Phys. Suppl. 160, 155 (2005).
  5. G. Jackeli and G. Khaliullin, Mott insulators in the strong spin-orbit coupling limit: From Heisenberg to a quantum compass and Kitaev models, Phys. Rev. Lett. 102, 017205 (2009).
  6. S. M. Winter, A. A. Tsirlin, M. Daghofer, J. van den Brink, Y. Singh, P. Gegenwart, and R. Valenti, Models and materials for generalized Kitaev magnetism, J. Phys.: Condens. Matter 29, 493002 (2017).
  7. H. Liu and G. Khaliullin, Pseudospin exchange interactions in d7 cobalt compounds: Possible realization of the Kitaev model, Phys. Rev. B 97, 014407 (2018).
  8. H. Liu, J. Chaloupka, and G. Khaliullin, Kitaev spin liquid in 3d transition metal compounds, Phys. Rev. Lett. 125, 047201 (2020).
  9. R. Sano, Y. Kato, and Y. Motome, Kitaev-Heisenberg Hamiltonian for high-spin d7 Mott insulators, Phys. Rev. B 97, 014408 (2018).
  10. S. M. Winter, Magnetic couplings in edge-sharing high-spin d7 compounds, J. Phys. Mater. 5, 045003 (2022).
  11. X. Liu and H.-Y. Kee, Non-Kitaev versus Kitaev honeycomb cobaltates, Phys. Rev. B 107, 054420 (2023).
  12. M. Songvilay, J. Robert, S. Petit, J. A. Rodriguez-Rivera, W. D. Ratcliff, F. Damay, V. Balédent, M. Jiménez-Ruiz, P. Lejay, E. Pachoud, A. Hadj-Azzem, V. Simonet, and C. Stock, Kitaev interactions in the Co honeycomb antiferromagnets Na3Co2SbO6 and Na2Co2TeO6, Phys. Rev. B 102, 224429 (2020).
  13. C. Kim, J. Jeong, G. Lin, P. Park, T. Masuda, S. Asai, S. Itoh, H.-S. Kim, H. Zhou, J. Ma, and J.-G. Park, Antiferromagnetic Kitaev interaction in Jeff = 1/2 cobalt honeycomb materials Na3Co2SbO6 and Na2Co2TeO6, J. Phys.: Condens. Matter 34, 045802 (2022).
  14. A. L. Sanders, R. A. Mole, J. Liu, A. J. Brown, D. Yu, C. D. Ling, and S. Rachel, Dominant Kitaev interactions in the honeycomb materials Na3Co2SbO6 and Na2Co2TeO6, Phys. Rev. B 106, 014413 (2022).
  15. X. Li, Y. Gu, Y. Chen, V. O. Garlea, K. Iida, K. Kamazawa, Y. Li, G. Deng, Q. Xiao, X. Zheng, Z. Ye, Y. Peng, I. A. Zaliznyak, J. M. Tranquada, and Y. Li, Giant magnetic in-plane anisotropy and competing instabilities in Na3Co2SbO6, Phys. Rev. X 12, 041024 (2022).
  16. M. van Veenendaal, E. H. T. Poldi, L. S. I. Veiga, P. Bencok, G. Fabbris, R. Tartaglia, J. L. McChesney, J. W. Freeland, R. J. Hemley, H. Zheng, J. F. Mitchell, J.-Q. Yan, and D. Haskel, Electronic structure of Co 3d states in the Kitaev material candidate honeycomb cobaltate Na3Co2SbO6 probed with x-ray dichroism, Phys. Rev. B 107, 214443 (2023).
  17. L. Hozoi, U. Birkenheuer, H. Stoll, and P. Fulde, Spin-state transition and spin-polaron physics in cobalt oxide perovskites: abinitio approach based on quantum chemical methods, New J. Phys. 11, 023023 (2009).
  18. M. Iakovleva, T. Petersen, A. Alfonsov, Y. Skourski, H.-J. Grafe, E. Vavilova, R. Nath, L. Hozoi, and V. Kataev, Static magnetic and ESR spectroscopic properties of the dimer-chain antiferromagnet BiCoPO5, Phys. Rev. Mater. 6, 094413 (2022).
  19. C. Albert, T. J. Ballé, F. A. Breitner, Y. Krupskaya, A. Alfonsov, Z. Zangeneh, S. Avdoshenko, M. S. Eldeeb, L. Hozoi, A. Vilangottunjalil, E. Haubold, A. Charnukha, B. Büchner, A. Jesche, and V. Kataev, Terahertz magneto-optical excitations of the sd-hybrid states of lithium nitridocobaltate Li2(Li1−xCox)N, Inorg. Chem. 60, 4497 (2021).
  20. S. Sugano, Y. Tanabe, and H. Kamimura, Multiplets of Transition-Metal Ions in Crystals (Academic Press, New York, 1970).
  21. L. Viciu, Q. Huang, E. Morosan, H. Zandbergen, N. Greenbaum, T. McQueen, and R. Cava, Structure and basic magnetic properties of the honeycomb lattice compounds Na2Co2TeO6 and Na3Co2SbO6, J. Solid State Chem. 180, 1060 (2007).
  22. See Supplemental Material at http://link.aps.org/supplemental/10.1103/8fz7-9wj9 for detailed information about the numerical calculations, which includes Refs. [2, 8, 21, 23, 26, 28, 29, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51].
  23. D. A. Kreplin, P. J. Knowles, and H.-J. Werner, MCSCF optimization revisited. II. Combined first- and second-order orbital optimization for large molecules, J. Chem. Phys. 152, 074102 (2020).
  24. T. Petersen, L. Prodan, K. Geirhos, H. Nakamura, I. Kézsmárki, and L. Hozoi, Dressed jeff-1/2 objects in mixed-valence lacunar spinel molybdates, Sci. Rep. 13, 2411 (2023).
  25. T. Petersen, P. Bhattacharyya, U. K. Rößler, and L. Hozoi, Resonating holes vs molecular spin-orbit coupled states in group-5 lacunar spinels, Nat. Commun. 14, 5218 (2023).
  26. P. J. Knowles and H.-J. Werner, Internally contracted multiconfiguration-reference configuration interaction calculations for excited states, Theor. Chim. Acta 84, 95 (1992).
  27. J. Chaloupka and G. Khaliullin, Hidden symmetries of the extended Kitaev-Heisenberg model: Implications for the honeycomb-lattice iridates A2IrO3, Phys. Rev. B 92, 024413 (2015).
  28. N. A. Bogdanov, V. M. Katukuri, J. Romhányi, V. Yushankhai, V. Kataev, B. Büchner, J. van den Brink, and L. Hozoi, Orbital reconstruction in nonpolar tetravalent transition-metal oxide layers, Nat. Commun. 6, 7306 (2015).
  29. R. Yadav, N. A. Bogdanov, V. M. Katukuri, S. Nishimoto, J. van den Brink, and L. Hozoi, Kitaev exchange and field-induced quantum spin-liquid states in honeycomb α−RuCl3, Sci. Rep. 6, 37925 (2016).
  30. Y. Gu, X. Li, Y. Chen, K. Iida, A. Nakao, K. Munakata, V. O. Garlea, Y. Li, G. Deng, I. A. Zaliznyak, J. M. Tranquada, and Y. Li, In-plane multi-q magnetic ground state of Na3Co2SbO6, Phys. Rev. B 109, L060410 (2024).
  31. R. E. Watson and A. J. Freeman, Hartree-Fock atomic scattering factors for the iron transition series, Acta. Cryst. 14, 27 (1961).
  32. J.-Q. Yan, S. Okamoto, Y. Wu, Q. Zheng, H. D. Zhou, H. B. Cao, and M. A. McGuire, Magnetic order in single crystals of Na3Co2SbO6 with a honeycomb arrangement of 3d7Co2+ ions, Phys. Rev. Mater. 3, 074405 (2019).
  33. W. G. F. Krüger, W. Chen, X. Jin, Y. Li, and L. Janssen, Triple-q order in Na2Co2TeO6 from proximity to hidden-SU(2)-symmetric point, Phys. Rev. Lett. 131, 146702 (2023).
  34. N. Francini and L. Janssen, Spin vestigial orders in extended Heisenberg-Kitaev models near hidden SU(2) points: Application to Na2Co2TeO6, Phys. Rev. B 109, 075104 (2024).
  35. Y. Gu, X. Jin, and Y. Li, On the multi-q characteristics of magnetic ground states of honeycomb cobalt oxides, Chinese Phys. Lett. 42, 027303 (2025).
  36. Y. Li, T. T. Mai, M. Karaki, E. V. Jasper, K. F. Garrity, C. Lyon, D. Shaw, T. DeLazzer, A. J. Biacchi, R. L. Dally, D. M. Heligman, J. Gdanski, T. Adel, M. F. Muñoz, A. Giovannone, A. Pawbake, C. Faugeras, J. R. Simpson, K. Ross, N. Trivedi, et al., Ring-exchange interaction effects on magnons in the Dirac magnet CoTiO3, Phys. Rev. B 109, 184436 (2024).
  37. Describing kinetic exchange and superexchange (i.e., intersite excitations) through the (exchange-)correlation functional remains, however, elusive.
  38. P. Bhattacharyya, T. Petersen, N. A. Bogdanov, and L. Hozoi, Coulomb exchange as source of Kitaev and off-diagonal symmetric anisotropic couplings, Commun. Phys. 7, 121 (2024).
  39. P. Bhattacharyya, N. A. Bogdanov, S. Nishimoto, S. D. Wilson, and L. Hozoi, NaRuO2: Kitaev-Heisenberg exchange in triangular-lattice setting, npj Quantum Mater. 8, 52 (2023).
  40. P. P. Stavropoulos, D. Pereira, and H.-Y. Kee, Microscopic mechanism for a higher-spin Kitaev model, Phys. Rev. Lett. 123, 037203 (2019).
  41. H.-J. Werner, P. J. Knowles, G. Knizia, F. R. Manby, and M. Schütz, Molpro: A general-purpose quantum chemistry program package, WIREs Comput. Mol. Sci. 2, 242 (2012).
  42. M. Klintenberg, S. Derenzo, and M. Weber, Accurate crystal fields for embedded cluster calculations, Comput. Phys. Commun. 131, 120 (2000).
  43. S. E. Derenzo, M. K. Klintenberg, and M. J. Weber, Determining point charge arrays that produce accurate ionic crystal fields for atomic cluster calculations, J. Chem. Phys. 112, 2074 (2000).
  44. A. Berning, M. Schweizer, H.-J. Werner, P. J. Knowles, and P. Palmieri, Spin-orbit matrix elements for internally contracted multireference configuration interaction wavefunctions, Mol. Phys. 98, 1823 (2000).
  45. N. B. Balabanov and K. A. Peterson, Systematically convergent basis sets for transition metals. I. All-electron correlation consistent basis sets for the 3d elements Sc-Zn, J. Chem. Phys. 123, 064107 (2005).
  46. T. H. Dunning, Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen, J. Chem. Phys. 90, 1007 (1989).
  47. F. Schautz, H.-J. Flad, and M. Dolg, Quantum Monte Carlo study of Be2 and group 12 dimers M2 (M = Zn, Cd, Hg), Theor. Chem. Acc. 99, 231 (1998).
  48. H. Stoll, B. Metz, and M. Dolg, Relativistic energy-consistent pseudopotentials—Recent developments, J. Comput. Chem. 23, 767 (2002).
  49. K. Pierloot, B. Dumez, P.-O. Widmark, and B. O. Roos, Density matrix averaged atomic natural orbital (ANO) basis sets for correlated molecular wave functions, Theor. Chim. Acta 90, 87 (1995).
  50. P. Fuentealba, H. Preuss, H. Stoll, and L. Von Szentpály, A proper account of core-polarization with pseudopotentials: single valence-electron alkali compounds, Chem. Phys. Lett. 89, 418 (1982).
  51. J. Pipek and P. G. Mezey, A fast intrinsic localization procedure applicable for ab initio and semiempirical linear combination of atomic orbital wave functions, J. Chem. Phys. 90, 4916 (1989).
  52. P. Bhattacharyya, Kitaev-Heisenberg exchange on t2g5eg2 cobaltate platform, Leibniz Institute for Solid State and Materials Research (2025), doi:10.22000/tny338gct87gzce4.

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation