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Metallic Magnetism at Finite Temperatures

  • Yoshiro Kakehashi
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 175)

Abstract

With elevating temperature, various excited states of electrons appear. We present in Chap. 3 theories of the metallic ferromagnetism at finite temperatures. We start from the Stoner theory (i.e., the Hartree–Fock theory) and show that the theory without thermal spin fluctuations overestimates the Curie temperatures by a factor of ten in 3d transition metals. To describe the spin fluctuations, we introduce the functional integral method, and present the single-site spin fluctuation theory (SSF) obtained by a high-temperature approximation. We show how the local magnetic moments (LM) are developed in solids with increasing intra-atomic Coulomb interaction at finite temperatures. Next we present the dynamical CPA which completely describes both the dynamical charge and spin fluctuations within the single-site approximation. The dynamical CPA is the quantum version of the SSF and is equivalent to the dynamical mean-field theory. We prove the equivalence in Sect. 3.6. Finally we present the first-principles version of the dynamical CPA and discuss the quantitative aspects of the finite-temperature magnetism in 3d transition metals.

Keywords

Green Function Local Density Approximation Local Magnetic Moment Spin Fluctuation Dyson Equation 
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.

References

  1. 39.
    O. Gunnarsson, J. Phys. F, Met. Phys. 6, 587 (1976)ADSCrossRefGoogle Scholar
  2. 40.
    J.B. Staunton, B.L. Gyorffy, Phys. Rev. Lett. 69, 371 (1992)ADSCrossRefGoogle Scholar
  3. 41.
    J.R. Schrieffer, W.E. Evenson, S.Q. Wang, J. Phys. (Paris) 32, C1 (1971)CrossRefGoogle Scholar
  4. 42.
    G. Morandi, E. Galleani D’Agliano, F. Napoli, C.F. Ratto, Adv. Phys. 23, 867 (1974)ADSCrossRefGoogle Scholar
  5. 43.
    A.L. Fetter, J.D. Walecka, Quantum Theory of Many-Particle Systems (McGraw Hill, New York, 1971)Google Scholar
  6. 44.
    A.A. Abrikosov, L.P. Gor’kov, I.E. Dzyaloshinskii, Quantum Field Theoretical Methods in Statistical Physics (Pergamon, Oxford, 1965)zbMATHGoogle Scholar
  7. 45.
    J. Hubbard, Phys. Rev. B 19, 2626 (1979)ADSCrossRefGoogle Scholar
  8. 46.
    J. Hubbard, Phys. Rev. B 20, 4584 (1979)ADSCrossRefGoogle Scholar
  9. 47.
    J. Hubbard, Phys. Rev. B 23, 5974 (1981)ADSCrossRefGoogle Scholar
  10. 48.
    H. Hasegawa, J. Phys. Soc. Jpn. 46, 1504 (1979)ADSCrossRefGoogle Scholar
  11. 49.
    H. Hasegawa, J. Phys. Soc. Jpn. 49, 178 (1980)ADSCrossRefGoogle Scholar
  12. 50.
    B. Velický, S. Kirkpatrick, H. Ehrenreich, Phys. Rev. 175, 747 (1968)ADSCrossRefGoogle Scholar
  13. 51.
    H. Ehrenreich, L.M. Schwartz, in Solid State Physics, vol. 31, ed. by H. Ehrenreich, F. Seitz, D. Turnbull (Academic, New York, 1976)Google Scholar
  14. 52.
    Y. Kakehashi, P. Fulde, Phys. Rev. B 32, 1595 (1985)ADSCrossRefGoogle Scholar
  15. 53.
    T. Tamashiro, S. Nohara, K. Miyagi, Y. Kakehashi, J. Phys. Soc. Jpn. 80, 064702 (2011)ADSCrossRefGoogle Scholar
  16. 54.
    Y. Kakehashi, Phys. Rev. B 65, 184420 (2002)ADSCrossRefGoogle Scholar
  17. 55.
    Y. Kakehashi, Phys. Rev. B 45, 7196 (1992)ADSCrossRefGoogle Scholar
  18. 56.
    Y. Kakehashi, J. Magn. Magn. Mater. 104–107, 677 (1992)CrossRefGoogle Scholar
  19. 57.
    Y. Kakehashi, Adv. Phys. 53, 497 (2004)ADSCrossRefGoogle Scholar
  20. 58.
    D.J. Amit, C.M. Bender, Phys. Rev. B 4, 3115 (1971)ADSCrossRefGoogle Scholar
  21. 59.
    D.J. Amit, H.J. Keiter, J. Low Temp. Phys. 11, 603 (1973)ADSCrossRefGoogle Scholar
  22. 60.
    X. Dai, J. Phys. Condens. Matter 3, 4389 (1991)CrossRefGoogle Scholar
  23. 61.
    S. Hirooka, M. Shimizu, J. Phys. Soc. Jpn. 43, 70 (1977)ADSCrossRefGoogle Scholar
  24. 62.
    A. Georges, G. Kotliar, W. Krauth, M.J. Rosenberg, Rev. Mod. Phys. 68, 13 (1996)ADSCrossRefGoogle Scholar
  25. 63.
    V.I. Anisimov, Yu.A. Izyumov, Electronic Structure of Strongly Correlated Materials (Springer, Berlin, 2010)CrossRefGoogle Scholar
  26. 64.
    Y. Kakehashi, P. Fulde, Phys. Rev. B 69, 045101 (2004)ADSCrossRefGoogle Scholar
  27. 65.
    J.W. Negele, H. Orland, Quantum Many Particle Systems (Addison-Wesley, New York, 1998)Google Scholar
  28. 66.
    E. Müller-Hartmann, Z. Phys. B 74, 507 (1989)ADSCrossRefGoogle Scholar
  29. 67.
    R. Bulla, Phys. Rev. Lett. 83, 136 (1999)ADSCrossRefGoogle Scholar
  30. 68.
    P. Fulde, Electron Correlations in Molecules and Solids (Springer, Berlin, 1995), Chap. 6CrossRefGoogle Scholar
  31. 69.
    Y. Kakehashi, T. Nakamura, P. Fulde, J. Phys. Soc. Jpn. 78, 124710 (2009)ADSCrossRefGoogle Scholar
  32. 70.
    V.I. Anisimov, J. Zaanen, O.K. Andersen, Phys. Rev. B 44, 943 (1991)ADSCrossRefGoogle Scholar
  33. 71.
    Y. Kakehashi, J. Phys. Soc. Jpn. 77, 094706 (2008)ADSCrossRefGoogle Scholar
  34. 72.
    Y. Kakehashi, M. Atiqur, R. Patoary, J. Phys. Soc. Jpn. 80, 034706 (2011)ADSCrossRefGoogle Scholar
  35. 73.
    A.I. Lichtenstein, M.I. Katsnelson, G. Kotliar, Phys. Rev. Lett. 87, 067205 (2001)ADSCrossRefGoogle Scholar
  36. 74.
    T. Miyake, F. Aryasetiawan, Phys. Rev. B 77, 085122 (2008)ADSCrossRefGoogle Scholar
  37. 75.
    I. Schnell, G. Czycholl, R.C. Albers, Phys. Rev. B 68, 245102 (2003)ADSCrossRefGoogle Scholar
  38. 76.
    H.H. Potter, Proc. R. Soc. Lond. A 146, S362 (1934)ADSCrossRefGoogle Scholar
  39. 77.
    M. Fallot, J. de Phys. Rad. V 153 (1944)Google Scholar
  40. 78.
    A. Arrott, J.E. Noakes, Phys. Rev. Lett. 19, 786 (1967)ADSCrossRefGoogle Scholar
  41. 79.
    R.V. Colvin, S. Arajs, J. Phys. Chem. Solids 26, 435 (1965)ADSCrossRefGoogle Scholar
  42. 80.
    J.E. Noakes, N.E. Tornberg, A. Arrott, J. Appl. Phys. 37, 1264 (1966)ADSCrossRefGoogle Scholar
  43. 81.
    W. Sucksmith, R.R. Pearce, Proc. R. Soc. Lond. A 167, 189 (1938)ADSCrossRefGoogle Scholar
  44. 82.
    P. Weiss, R. Forrer, Ann. Phys. Paris 5, 153 (1926)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Yoshiro Kakehashi
    • 1
  1. 1.Faculty of Science, Department of PhysicsUniversity of the RyukyusNishiharaJapan

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