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Multi-Band Gutzwiller Wave Functions for Itinerant Ferromagnetism

Foundations of Physics volume 30, pages 2011–2031 (2000)Cite this article

Abstract

Multi-band Gutzwiller-correlated wave functions reconcile the contrasting concepts of itinerant band electrons versus electrons localized in partially filled atomic shells. The approximate evaluation of these variational ground states becomes exact in the limit of large coordination number. The result allows the identification of quasi-particle band structures for correlated electron systems. As a first application, we summarize a study of itinerant ferromagnetism in a two-band model, thereby elucidating the co-operation of the Coulomb repulsion and the Hund's-rule exchange. Then, we present results of calculations for ferromagnetic nickel, using a realistic 18 spin-orbital basis of 4s, 4p and 3d valence electrons. Good agreement with the experimental ground-state properties of nickel is obtained. In particular, the quasi-particle energy bands agree much better with the photo-emission and Fermi surface data than the band structure obtained from spin-density functional theory. Finally, we present results for the variational spinwave dispersion for our two-band model.

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REFERENCES

  1. J. C. Slater, Phys. Rev. 49, 537 (1936); ibid., 931 (1936).

    Google Scholar 

  2. E. C. Stoner, Proc. Roy. Soc. A 165, 372 (1938); for early reviews, see J. C. Slater, Rev. Mod. Phys. 25, 199 (1953) and E. P. Wohlfarth, Rev. Mod. Phys. 25, 211 (1953).

    Google Scholar 

  3. J. H. van Vleck, Rev. Mod. Phys. 25, 220 (1953).

    Google Scholar 

  4. V. L. Moruzzi, J. F. Janak, and A. R. Williams, Calculated Electronic Properties of Metals (Pergamon, New York, 1978).

    Google Scholar 

  5. W. Nolting, W. Borgieł, V. Dose, and Th. Fauster, Phys. Rev. B 40, 5015 (1989). W. Borgieł and W. Nolting, Z. Phys. B 78, 241 (1990).

    Google Scholar 

  6. H. Hasegawa, J. Phys. Soc. Jpn 66, 3522 (1997); Phys. Rev. B 56, 1196 (1997). R. Frésard and G. Kotliar, Phys. Rev. B 56, 12909 (1997).

    Google Scholar 

  7. Th. Obermeier, Th. Pruschke, and J. Keller, Phys. Rev. B 56, 8479 (1997). Th. Maier, M. B. Zölfl, Th. Pruschke, and J. Keller, Euro. Phys. J. B 7, 377 (1999). M. B. Zölfl, Th. Pruschke, J. Keller, A. I. Poteryaev, I. A. Nekrasov, and V.I. Anisimov, Phys. Rev. B 61, 12810 (2000).

    Google Scholar 

  8. D. Vollhardt, N. Blümer, K. Held, M. Kollar, J. Schlipf, M. Ulmke, and J. Wahle, Adv. Solid-State Phys. 38, 383 (1999). I. A. Nekrasov, K. Held, N. Blümer, A. I. Poteryaev, V. I. Anisimov, D. Vollhardt, preprint cond-mat/0005207 (2000).

    Google Scholar 

  9. J. Bünemann, W. Weber, and F. Gebhard, Phys. Rev. B 57, 6896 (1998).

    Google Scholar 

  10. M. C. Gutzwiller, Phys. Rev. Lett. 10, 159 (1963).

    Google Scholar 

  11. M. C. Gutzwiller, Phys. Rev. A 134, 923 (1964); Phys. Rev. A 137, 1726 (1965).

    Google Scholar 

  12. J. Hubbard, Proc. Roy. Soc. London Ser. A 276, 238 (1963); Proc. Roy. Soc. London Ser. A 277, 237 (1964).

    Google Scholar 

  13. J. Kanamori, Prog. Theor. Phys. 30, 275 (1963).

    Google Scholar 

  14. G. Stollhoff and P. Fulde, J. Chem. Phys. 73, 4548 (1980). G. Stollhoff and P. Thalmeier, Z. Phys. B 43, 13 (1981). A. M. OleŚ and G. Stollhoff, Phys. Rev. B 29, 314 (1984). For further details on the “local ansatz” technique, see P. Fulde, Electron Correlations in Molecules and Solids, Springer Series in Solid-State Sciences 100 (Springer, Berlin, 1991).

    Google Scholar 

  15. D. Baeriswyl and K. Maki, Phys. Rev. B 31, 6633 (1985). D. Baeriswyl, J. Carmelo, and K. Maki, Synth. Met. 21, 271 (1987).

    Google Scholar 

  16. D. Vollhardt, Rev. Mod. Phys. 56, 99 (1984).

    Google Scholar 

  17. K. A. Chao and M. C. Gutzwiller, J. Appl. Phys. 42 1420 (1971). K. A. Chao, Phys. Rev. B 4 4034 (1971); Phys. Rev. B 4 1088 (1973); J. Phys. C 7 127 (1974).

    Google Scholar 

  18. P. Fazekas, Lecture Notes on Electron Correlation and Magnetism, Series in Mod. Cond. Matt. Phys. 5 (World Scientific, Singapore, 1999), gives an introduction to the theory of ferromagnetism, and a concise description and some applications of the Gutzwiller approximation.

    Google Scholar 

  19. W. Metzner and D. Vollhardt, Phys. Rev. Lett. 59, 121 (1987); Phys. Rev. B 37, 7382 (1988).

    Google Scholar 

  20. F. Gebhard and D. Vollhardt, Phys. Rev. Lett. 59, 1472 (1987); Phys. Rev. B 38, 6911 (1988).

    Google Scholar 

  21. W. Metzner and D. Vollhardt, Phys. Rev. Lett. 62, 324 (1989).

    Google Scholar 

  22. For a review, see F. Gebhard, The Mott Metal-Insulator Transition (Springer, Berlin, 1997).

    Google Scholar 

  23. F. Gebhard, Phys. Rev. B 41, 9452 (1990).

    Google Scholar 

  24. J. Bünemann and W. Weber, Phys. Rev. B 55, 4011 (1997).

    Google Scholar 

  25. J. Bünemann, Eur. Phys. J. B 4, 29 (1998).

    Google Scholar 

  26. J. Bünemann, F. Gebhard, and W. Weber, J. Phys. Cond. Matt. 8, 7343 (1997).

    Google Scholar 

  27. J. Bünemann, preprint cond-mat/0005154 (2000).

  28. S. Sugano, Y. Tanabe, and H. Kamimura, Multiplets of Transition-Metal Ions in Crystals, Pure and Applied Physics 33 (Academic, New York, 1970).

    Google Scholar 

  29. W. Eberhardt and E. W. Plummer, Phys. Rev. B 21, 3245 (1980).

    Google Scholar 

  30. M. Dixon, F. E. Hoare, T. M. Holden, and D. E. Moody, Proc. R. Soc. A 285, 561 (1965).

    Google Scholar 

  31. J. Callaway in Physics of Transition Metals, P. Rhodes, ed. (Conf. Ser. Notes 55, Inst. of Physics, Bristol, 1981), p. 1.

    Google Scholar 

  32. M. Donath, Surface Science Reports 20, 251 (1994).

    Google Scholar 

  33. K.-P. Kämper, W. Schmitt, and G. Güntherodt, Phys. Rev. B 42, 10696 (1990).

    Google Scholar 

  34. H. A. Mook, Phys. Rev. 148, 495 (1966).

    Google Scholar 

  35. R. Raue, H. Hopster, and R. Clanberg, Phys. Rev. Lett. 50, 1623 (1983).

    Google Scholar 

  36. C. S. Wang and J. Callaway, Phys. Rev. B 15, 298 (1977).

    Google Scholar 

  37. E. P. Wohlfahrt in Handbook of Magnetic Materials 1, E. P. Wohlfarth, ed. (North Holland, Amsterdam, 1980).

    Google Scholar 

  38. D. C. Tsui, Phys. Rev. 164, 561 (1967).

    Google Scholar 

  39. O. Jepsen, J. Madsen, and O. K. Andersen, Phys. Rev. B 26, 2790 (1982).

    Google Scholar 

  40. J. F. Cooke, J. W. Lynn, and H. L. Davis, Phys. Rev. B 21, 4118 (1980).

    Google Scholar 

  41. A. Liebsch, Phys. Rev. B 23, 5203 (1981).

    Google Scholar 

  42. J. Bünemann, F. Gebhard, and W. Weber, in preparation.

  43. P. Heimann, F. J. Himpsel, and D. E. Eastman, Solid State Comm. 39, 219 (1981).

    Google Scholar 

  44. F. J. Himpsel, J. A. Knapp, and D. E. Eastman, Phys. Rev. B 19, 2919 (1979).

    Google Scholar 

  45. A. Messiah, Quantum Mechanics, 3rd printing (North Holland, Amsterdam, 1965).

    Google Scholar 

  46. R. P. Feynman, Statistical Mechanics, Frontiers in Physics 36 (Benjamin, Reading, 1972).

    Google Scholar 

  47. R. D. Lowde and C. G. Windsor, Adv. Phys. 19, 813 (1970).

    Google Scholar 

  48. See, e.g., S. V. Halilov, H. Eschrig, A. Y. Perlov, and P. M. Oppeneer, Phys. Rev. B 58, 293 (1998).

    Google Scholar 

  49. K. Chen, A. M. Ferrenberg, and D. P. Landau, Phys. Rev. B 48, 3249 (1993).

    Google Scholar 

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Authors and Affiliations

  1. Fachbereich Physik, Philipps-Universität Marburg, D-35032, Marburg, Germany

    Jörg Bünemann & Florian Gebhard

  2. Institut für Physik, Universität Dortmund, D-44221, Dortmund, Germany

    Werner Weber

Authors
  1. Jörg Bünemann
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  2. Florian Gebhard
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  3. Werner Weber
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Bünemann, J., Gebhard, F. & Weber, W. Multi-Band Gutzwiller Wave Functions for Itinerant Ferromagnetism. Foundations of Physics 30, 2011–2031 (2000). https://doi.org/10.1023/A:1003733306203

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Keywords

  • Atomic Shell
  • Correlate Electron System
  • Rule Exchange
  • Variational Ground
  • Large Coordination