Generalized Hund’s Rule for Two-Atom Systems

  • Hiroki IsobeEmail author
Part of the Springer Theses book series (Springer Theses)


Hund’s rule is one of the fundamentals of the correlation physics at the atomic level, determining the ground state multiplet of the electrons. In real systems, the electrons hop between the atoms and gain the itinerancy, which is usually described by the band theory. The whole content of theories on correlation is to provide a reliable way to describe the intermediate situation between the two limits. Here we propose an approach toward this goal, i.e., we study the two-atom systems of three \(t_{2g}\) orbitals and see how the Hund’s rule is modified by the transfer integral t between them. It is found that the competition between t and the Hund’s coupling J at each atom determines the crossover from the molecular orbital limit to the strong correlation limit. Especially, our focus is on the generalization of the third rule about the spin-orbit interactions (SOIs), in the presence of the correlation. We have found that there are cases where the effective SOIs are appreciably enhanced by the Hund’s coupling at the filling of four or five electrons. This result provides a useful guideline to realize effectively strong SOI with common and lighter elements, which helps to realize nontrivial electronic states without heavy and rare elements.


Hund’s rule Spin-orbit interaction Electron correlation 


  1. 1.
    F. Hund, Z. Phys. 40, 742 (1927)ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    F. Hund, Z. Phys. 42, 93 (1927)ADSCrossRefGoogle Scholar
  3. 3.
    W. Heitler, F. London, Z. Phys. 44, 455 (1927)ADSCrossRefGoogle Scholar
  4. 4.
    N. Nagaosa, J. Sinova, S. Onoda, A.H. MacDonald, N.P. Ong, Rev. Mod. Phys. 82, 1539 (2010)ADSCrossRefGoogle Scholar
  5. 5.
    S. Murakami, N. Nagaosa, in Comprehensive Semiconductor Science and Technology, ed. by P. Bhattacharya, R. Fornari, H. Kamimura (Elsevier, Amsterdam, 2011), p. 222CrossRefGoogle Scholar
  6. 6.
    M.Z. Hasan, C.L. Kane, Rev. Mod. Phys. 82, 3045 (2010)ADSCrossRefGoogle Scholar
  7. 7.
    X.-L. Qi, S.-C. Zhang, Rev. Mod. Phys. 83, 1057 (2011)ADSCrossRefGoogle Scholar
  8. 8.
    B.J. Kim, H. Jin, S.J. Moon, J.-Y. Kim, B.-G. Park, C.S. Leem, J. Yu, T.W. Noh, C. Kim, S.-J. Oh, J.-H. Park, V. Durairaj, G. Cao, E. Rotenberg, Phys. Rev. Lett. 101, 076402 (2008)ADSCrossRefGoogle Scholar
  9. 9.
    A. Shitade, H. Katsura, J. Kuneš, X.-L. Qi, S.-C. Zhang, N. Nagaosa, Phys. Rev. Lett. 102, 256403 (2009)ADSCrossRefGoogle Scholar
  10. 10.
    G. Jackeli, G. Khaliullin, Phys. Rev. Lett. 102, 017205 (2009)ADSCrossRefGoogle Scholar
  11. 11.
    E. Rashba, Sov. Phys. Solid State 2, 1109 (1960)Google Scholar
  12. 12.
    K. Yoshida, Theory of Magnetism (Springer, New York, 1996)CrossRefGoogle Scholar
  13. 13.
    S. Raghu, X.-L. Qi, C. Honerkamp, S.-C. Zhang, Phys. Rev. Lett. 100, 156401 (2008)ADSCrossRefGoogle Scholar
  14. 14.
    Y. Zhang, Y. Ran, A. Vishwanath, Phys. Rev. B 79, 245331 (2009)ADSCrossRefGoogle Scholar
  15. 15.
    J. Wen, A. Rüegg, C.-C.J. Wang, G.A. Fiete, Phys. Rev. B 82, 075125 (2010)ADSCrossRefGoogle Scholar
  16. 16.
    M. Kurita, Y. Yamaji, M. Imada, J. Phys. Soc. Jpn. 80, 044708 (2011)ADSCrossRefGoogle Scholar
  17. 17.
    M. Imada, A. Fujimori, Y. Tokura, Rev. Mod. Phys. 70, 1039 (1998)ADSCrossRefGoogle Scholar
  18. 18.
    J.C. Slater, G.F. Koster, Phys. Rev. 94, 1498 (1954)ADSCrossRefGoogle Scholar
  19. 19.
    S. Sugano, Y. Tanabe, H. Kamimura, Multiplets of Transition-Metal Ions in Crystals (Academic Press, New York, 1970)Google Scholar
  20. 20.
    J. Kanamori, Prog. Theor. Phys. 30, 275 (1963)ADSCrossRefGoogle Scholar
  21. 21.
    C.L. Kane, E.J. Mele, Phys. Rev. Lett. 95, 146802 (2005)ADSCrossRefGoogle Scholar
  22. 22.
    C.L. Kane, E.J. Mele, Phys. Rev. Lett. 95, 226801 (2005)ADSCrossRefGoogle Scholar
  23. 23.
    L. Fu, C.L. Kane, E.J. Mele, Phys. Rev. Lett. 98, 106803 (2007)ADSCrossRefGoogle Scholar
  24. 24.
    H. Isobe, N. Nagaosa, Phys. Rev. B 90, 115122 (2014)ADSCrossRefGoogle Scholar
  25. 25.
    A. Georges, L.D. Medici, J. Mravlje, Annu. Rev. Condens. Matter Phys. 4, 137 (2013)ADSCrossRefGoogle Scholar
  26. 26.
    J.B. Goodenough, J. Phys. Chem. Solids 6, 287 (1958)ADSCrossRefGoogle Scholar
  27. 27.
    J. Kanamori, J. Phys. Chem. Solids 10, 87 (1959)ADSCrossRefGoogle Scholar
  28. 28.
    L. de’ Medici, J. Mravlje, A. Georges, Phys. Rev. Lett. 107, 256401 (2011)Google Scholar
  29. 29.
    L. Amico, R. Fazio, A. Osterloh, V. Vedral, Rev. Mod. Phys. 80, 517 (2008)ADSCrossRefGoogle Scholar
  30. 30.
    C.H. Bennett, D.P. DiVincenzo, J.A. Smolin, W.K. Wootters, Phys. Rev. A 54, 3824 (1996)ADSMathSciNetCrossRefGoogle Scholar
  31. 31.
    Y. Tokura, Physica C 235–240, 138 (1994)CrossRefGoogle Scholar
  32. 32.
    T. Arima, Y. Tokura, J.B. Torrance, Phys. Rev. B 48, 17006 (1993)ADSCrossRefGoogle Scholar
  33. 33.
    S. Miyasaka, Y. Okimoto, Y. Tokura, J. Phys. Soc. Jpn. 71, 2086 (2002)ADSCrossRefGoogle Scholar
  34. 34.
    T. Nakamura, G. Petzow, L. Gauckler, Mater. Res. Bull. 14, 649 (1979)CrossRefGoogle Scholar
  35. 35.
    A.M. Arévalo-López, E. Castillo-Martínez, M.A. Alario-Franco, J. Phys. Condens. Matter 20, 505207 (2008)CrossRefGoogle Scholar
  36. 36.
    B. Chamberland, Solid State Commun. 5, 663 (1967)ADSCrossRefGoogle Scholar
  37. 37.
    D. Peck, M. Miller, K. Hilpert, Solid State Ion. 123, 59 (1999)CrossRefGoogle Scholar
  38. 38.
    J. Longo, P. Raccah, J. Solid State Chem. 6, 526 (1973)ADSCrossRefGoogle Scholar

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© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.Massachusetts Institute of TechnologyCambridgeUSA

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