Role of local geometry in the spin and orbital structure of transition metal compounds

  • D. I. Khomskii
  • K. I. Kugel
  • A. O. Sboychakov
  • S. V. Streltsov
Special issue in honor of L.V. Keldysh’s 85th birthday Issue Editor: S. Tikhodeev


We analyze the role of local geometry in the spin and orbital interaction in transition metal compounds with orbital degeneracy. We stress that the tendency observed in the most studied case (transition metals in O6 octahedra with one common oxygen—common corner of neighboring octahedra—and with ~180° metal–oxygen–metal bonds), that ferro-orbital ordering renders antiferro-spin coupling and, vice versa, antiferro-orbitals give ferro-spin ordering, is not valid in the general case, in particular, for octahedra with a common edge and with ~90° M–O–M bonds. Special attention is paid to the “third case,” that of neighboring octahedra with a common face (three common oxygens), which has largely been disregarded until now, although there are many real systems with this geometry. Interestingly enough, the spin-orbit exchange in this case turns out to be simpler and more symmetric than in the first two cases. We also consider, which form the effective exchange takes for different geometries in the case of strong spin–orbit coupling.


Orbit Coupling Local Geometry Common Edge Orbital Structure Transition Metal Compound 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    J. B. Goodenough, Magnetism and the Chemical Bond (Wiley Interscience, New York, 1963).Google Scholar
  2. 2.
    J. Chakhalian, J. W. Freeland, H.-U. Habermeier, et al., Science 318, 1114 (2007).ADSCrossRefGoogle Scholar
  3. 3.
    M. D. Kaplan and B. G. Vekhter, Cooperative Phenomena in Jahn–Teller Crystals (Plenum, New York, 1995).CrossRefGoogle Scholar
  4. 4.
    K. I. Kugel and D. I. Khomskii, Sov. Phys. Usp. 25, 231 (1982).ADSCrossRefGoogle Scholar
  5. 5.
    D. I. Khomskii, Transition Metal Compounds (Cambridge Univ. Press, Cambridge, 2014).CrossRefGoogle Scholar
  6. 6.
    S. V. Streltsov and D. I. Khomskii, Phys. Rev. B 89, 161112 (2014).ADSCrossRefGoogle Scholar
  7. 7.
    K. I. Kugel, D. I. Khomskii, A. O. Sboychakov, and S. V. Streltsov, Phys. Rev. B 91, 155125 (2015).ADSCrossRefGoogle Scholar
  8. 8.
    J. van den Brink and D. Khomskii, Phys. Rev. B 63, 140416 (2001).CrossRefGoogle Scholar
  9. 9.
    I. Affleck, Nucl. Phys. B 265, 409 (1986).ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    Y. Yamashita, N. Shibata, and K. Ueda, Phys. Rev. B 58, 9114 (1998).ADSCrossRefGoogle Scholar
  11. 11.
    B. Frischmuth, F. Mila, and M. Troyer, Phys. Rev. Lett. 82, 835 (1999).ADSCrossRefGoogle Scholar
  12. 12.
    K. I. Kugel and D. I. Khomskii, Sov. Phys. Solid State 17, 285 (1975).Google Scholar
  13. 13.
    A. Abragam and B. Bleaney, Electron Paramagnetic Resonance of Transition Ions (Clarendon, Oxford, 1970).Google Scholar
  14. 14.
    G. Jackeli and G. Khaliullin, Phys. Rev. Lett. 102, 017205 (2009).ADSCrossRefGoogle Scholar
  15. 15.
    M. V. Mostovoy and D. I. Khomskii, Phys. Rev. Lett. 89, 227203 (2002).ADSCrossRefGoogle Scholar
  16. 16.
    J. Zaanen, G. A. Sawatzky, and J. W. Allen, Phys. Rev. Lett. 55, 418 (1985).ADSCrossRefGoogle Scholar
  17. 17.
    G. Chen and L. Balents, Phys. Rev. B 78, 094403 (2008).ADSCrossRefGoogle Scholar
  18. 18.
    S. V. Streltsov and D. I. Khomskii, Phys. Rev. B 77, 064405 (2008).ADSCrossRefGoogle Scholar
  19. 19.
    Y. Singh and P. Gegenwart, Phys. Rev. B 82, 064412 (2010).ADSCrossRefGoogle Scholar
  20. 20.
    K. W. Plumb, J. P. Clancy, L. J. Sandilands, et al., Phys. Rev. B 90, 041112(R) (2014).ADSCrossRefGoogle Scholar
  21. 21.
    A. Kitaev, Ann. Phys. (N.Y.) 321, 2 (2006).ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    Z. Nussinov and J. van den Brink, Rev. Mod. Phys. 87, 1 (2015).ADSCrossRefGoogle Scholar
  23. 23.
    K. Yamaura, H. W. Zandbergen, K. Abe, and R. J. Cava, J. Solid State Chem. 146, 96 (1999).ADSCrossRefGoogle Scholar
  24. 24.
    S. Hirotsu, J. Phys. C 10, 967 (1977).ADSCrossRefGoogle Scholar
  25. 25.
    K. E. Stitzer, M. D. Smith, J. Darriet, and H.-C. zur Loye, Chem. Commun. 17, 1680 (2001).CrossRefGoogle Scholar
  26. 26.
    J. Terzic, J. C. Wang, F. Ye, W. H. Song, S. J. Yuan, S. Aswartham, L. E. Delong, S. V. Streltsov, D. I. Khomskii, and G. Cao, Phys. Rev. B 91, 235147 (2015).ADSCrossRefGoogle Scholar
  27. 27.
    T. Siegrist and B. L. Chamberland, J. Less-Common Met. 170, 93 (1991).CrossRefGoogle Scholar
  28. 28.
    S.-T. Hong and A. W. Sleight, J. Solid State Chem. 122, 251 (1997).ADSCrossRefGoogle Scholar
  29. 29.
    J. G. Zhao, L. X. Yang, Y. Yu, F. Y. Li, R. C. Yu, Z. Fang, L. C. Chen, and C. Q. Jin, J. Solid State Chem. 180, 2816 (2007).ADSCrossRefGoogle Scholar
  30. 30.
    P. Köhl and D. Reinen, Z. Anorg. Allg. Chem. 433, 81 (1977).CrossRefGoogle Scholar
  31. 31.
    A. H. Carim, P. Dera, L. W. Finger, B. Mysen, C. T. Prewitt, and D. G. Schlom, J. Solid State Chem. 149, 137 (2000).ADSCrossRefGoogle Scholar
  32. 32.
    C. A. Bates, P. E. Chandler, and K. W. H. Stevens, J. Phys. C 4, 2017 (1971).ADSCrossRefGoogle Scholar
  33. 33.
    J. C. Slater and G. F. Koster, Phys. Rev. 94, 1498 (1954).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2016

Authors and Affiliations

  • D. I. Khomskii
    • 1
  • K. I. Kugel
    • 2
  • A. O. Sboychakov
    • 2
  • S. V. Streltsov
    • 3
    • 4
  1. 1.II. Physikalisches InstitutUniversität zu KölnKölnGermany
  2. 2.Institute for Theoretical and Applied ElectrodynamicsRussian Academy of SciencesMoscowRussia
  3. 3.Mikheev Institute of Metal Physics, Ural BranchRussian Academy of SciencesYekaterinburgRussia
  4. 4.Ural Federal UniversityYekaterinburgRussia

Personalised recommendations