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Fully Relativistic Band Structure Calculations for Magnetic Solids - Formalism and Application

  • H. Ebert
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 535)

Abstract

Relativistic effects, in particular the spin-orbit coupling, give rise for magnetic systems to a great number of interesting and technologically important phenomena. The formal and technical aspects of corresponding fully relativistic theoretical investigations are reviewed. The properties of the underlying Dirac equation, set up within the framework of density functional theory (DFT) are discussed together with the Breit-interaction and Brooks’ orbital polarization mechanism. As an example for a corresponding band structure method, the Korringa-Kohn-Rostoker (KKR) Green’s function method is adopted. In particular, some technical aspects specific to this technique are discussed. The numerous applications that will be presented are primarily meant to demonstrate the many different facets of relativistic - this means in general - of spin-orbit induced effiects in magnetic solids. In addition, these also demonstrate the tremendous flexibility of band structure schemes based on the Green’s function formalism.

Keywords

Dirac Equation Knight Shift Coherent Potential Approxi Orbital Magnetic Moment Spin Character 
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.

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References

  1. 1.
    N. E. Christensen and B. O. Seraphin, Phys. Rev. B 4, 3321 (1971).ADSCrossRefGoogle Scholar
  2. 2.
    P. Pyykkö, Adv. Quantum. Chem. 11, 353 (1978).CrossRefADSGoogle Scholar
  3. 3.
    Y. Cauchois and I. Manescu, C. R. Acad. Sci. 210, 172 (1940).Google Scholar
  4. 4.
    N. F. Mott, Proc. Phys. Soc. A 62, 416 (1949).ADSCrossRefGoogle Scholar
  5. 5.
    A. R. Mackintosh and O. K. Andersen, in Electrons at the Fermi Surface, edited by M. Springford (Cambridge University Press, Cambridge, 1980), Chap. The Electronic Structure of Transition Metals.Google Scholar
  6. 6.
    L. Tterlikkis, S. D. Mahanti, and T. P. Das, Phys. Rev. 176, 10 (1968).ADSCrossRefGoogle Scholar
  7. 7.
    M. E. Rose, Relativistic Electron Theory (Wiley, New York, 1961).zbMATHGoogle Scholar
  8. 8.
    F. Rosicky and F. Mark, J. Phys. B: Atom. Molec. Phys. 8, 2581 (1975).ADSCrossRefGoogle Scholar
  9. 9.
    F. Rosicky, P. Weinberger, and F. Mark, J. Phys. B: Atom. Molec. Phys. 9, 2971 (1976).ADSCrossRefGoogle Scholar
  10. 10.
    D. D. Koelling and B. N. Harmon, J. Phys. C: Solid State Phys. 10, 3107 (1977).ADSCrossRefGoogle Scholar
  11. 11.
    H. Gollisch and L. Fritsche, phys. stat. sol. (b) 86, 145 (1978).CrossRefADSGoogle Scholar
  12. 12.
    T. Takeda, Z. Physik B 32, 43 (1978).CrossRefADSGoogle Scholar
  13. 13.
    J. H. Wood and A. M. Boring, Phys. Rev. B 18, 2701 (1978).ADSCrossRefGoogle Scholar
  14. 14.
    H. L. Skriver, The LMTO-method (Springer, Berlin, 1983).Google Scholar
  15. 15.
    N. J. M. Geipel and B. A. Hess, Chem. Phys. Lett. 273, 62 (1997).CrossRefADSGoogle Scholar
  16. 16.
    E. van Lenthe E J Baerends and J. G. Snijders, J. Chem. Phys. 101, 1272 (1994).ADSCrossRefGoogle Scholar
  17. 17.
    F. Gesztesy, H. Grosse, and B. Thaller, Ann. Inst. Poincaré 40, 159 (1984).zbMATHMathSciNetGoogle Scholar
  18. 18.
    C. Brouder, M. Alouani, and K. H. Bennemann, Phys. Rev. B 54, 7334 (1996).ADSCrossRefGoogle Scholar
  19. 19.
    D. D. Koelling and A. H. MacDonald, in Relativistic Effects in Atoms Molecules and Solids, edited by G. L. Malli (Plenum Press, New York, 1983).Google Scholar
  20. 20.
    S. Blügel, H. Akai, R. Zeller, and P. H. Dederichs, Phys. Rev. B 35, 3271 (1987).ADSCrossRefGoogle Scholar
  21. 21.
    T. Gasche, Ph.D. thesis, University of Uppsala, 1993.Google Scholar
  22. 22.
    J. E. Lee, C. L. Fu, and A. J. Freeman, J. Magn. Magn. Materials 62, 93 (1986).ADSCrossRefGoogle Scholar
  23. 23.
    T. Asada and K. Terakura, J. Phys. F: Met. Phys. 12, 1387 (1982).ADSCrossRefGoogle Scholar
  24. 24.
    H. Ebert, P. Strange, and B. L. Gyorffy, J. Phys. F: Met. Phys. 18, L135 (1988).ADSCrossRefGoogle Scholar
  25. 25.
    H. Ebert and H. Akai, Hyperfine Interactions 78, 361 (1993).CrossRefADSGoogle Scholar
  26. 26.
    C. S. Wang and J. Callaway, Phys. Rev. B 9, 4897 (1974).ADSCrossRefGoogle Scholar
  27. 27.
    D. K. Misemer, J. Magn. Magn. Materials 72, 267 (1988).ADSCrossRefGoogle Scholar
  28. 28.
    G. Y. Guo and H. Ebert, Phys. Rev. B 51, 12633 (1995).ADSCrossRefGoogle Scholar
  29. 29.
    J. Callaway and C. S. Wang, Phys. Rev. B 7, 1096 (1973).ADSCrossRefGoogle Scholar
  30. 30.
    O. K. Andersen, Phys. Rev. B 12, 3060 (1975).ADSCrossRefGoogle Scholar
  31. 31.
    D. Singh, Plane Waves, Pseudopotentials and the LAPW Method (Kluwer Academic, Amsterdam, 1994).Google Scholar
  32. 32.
    A. Delin, P. Ravindran, O. Eriksson, and J. M. Wills, Intern. J. Quantum. Chem. 69, 349 (1997).CrossRefGoogle Scholar
  33. 33.
    T. L. Loucks, Phys. Rev. A 139, 1333 (1965).ADSCrossRefGoogle Scholar
  34. 34.
    P. Soven, Phys. Rev. 137, A 1706 (1965).ADSGoogle Scholar
  35. 35.
    Y. Onodera and M. Okazaki, J. Phys. Soc. Japan 21, 1273 (1966).ADSCrossRefGoogle Scholar
  36. 36.
    S. Takada, Progr. Theor. Phys. Suppl. 36, 224 (1966).CrossRefGoogle Scholar
  37. 37.
    T. Takeda, J. Phys. F: Met. Phys. 9, 815 (1979).ADSCrossRefGoogle Scholar
  38. 38.
    U. Fano, Phys. Rev. 184, 250 (1969).ADSCrossRefGoogle Scholar
  39. 39.
    U. Fano, Phys. Rev. 178, 131 (1969).ADSCrossRefGoogle Scholar
  40. 40.
    U. Heinzmann, K. Jost, J. Kessler, and B. Ohnemus, Z. Physik 251, 354 (1972).Google Scholar
  41. 41.
    J. Kerr, Phil. Mag. 3, 321 (1877).Google Scholar
  42. 42.
    H. Ebert, Rep. Prog. Phys. 59, 1665 (1996).ADSCrossRefGoogle Scholar
  43. 43.
    G. Schütz et al., Phys. Rev. Letters 58, 737 (1987).ADSCrossRefGoogle Scholar
  44. 44.
    J. Banhart and H. Ebert, Europhys. Lett. 32, 517 (1995).CrossRefADSGoogle Scholar
  45. 45.
    B. Újfalussy, L. Szunyogh, P. Bruno, and P. Weinberger, Phys. Rev. Letters 77, 1805 (1996).ADSCrossRefGoogle Scholar
  46. 46.
    G. Seewald et al., Phys. Rev. Letters 78, 1795 (1997).ADSCrossRefGoogle Scholar
  47. 47.
    M. Singh, C. S. Wang, and J. Callaway, Phys. Rev. B 11, 287 (1975).ADSCrossRefGoogle Scholar
  48. 48.
    M. S. S. Brooks and P. J. Kelly, Phys. Rev. Letters 51, 1708 (1983).ADSCrossRefGoogle Scholar
  49. 49.
    J. Sticht and J. Kübler, Solid State Commun. 53, 529 (1985).CrossRefADSGoogle Scholar
  50. 50.
    W. M. Temmerman and P. A. Sterne, J. Phys.: Condensed Matter 2, 5529 (1990).ADSCrossRefGoogle Scholar
  51. 51.
    O. Eriksson et al., Phys. Rev. B 42, 2707 (1990).ADSCrossRefGoogle Scholar
  52. 52.
    S. P. Lim, D. L. Price, and B. R. Cooper, IEEE transactions on magnetics 27, 3648 (1991).CrossRefADSGoogle Scholar
  53. 53.
    B. I. Min and Y.-R. Jang, J. Phys.: Condensed Matter 3, 5131 (1991).ADSCrossRefGoogle Scholar
  54. 54.
    O. Hjortstam et al., Phys. Rev. B 53, 9204 (1996).ADSCrossRefGoogle Scholar
  55. 55.
    D. S. Wang, R. Q. Wu, L. P. Z. LP, and A. J. Freeman, J. Magn. Magn. Materials 144, 643 (1995).ADSCrossRefGoogle Scholar
  56. 56.
    V. P. Antropov, A. I. Liechtenstein, and B. N. Harmon, J. Magn. Magn. Materials 140144, 1161 (1995).ADSCrossRefGoogle Scholar
  57. 57.
    H. Ebert, Phys. Rev. B 38, 9390 (1988).ADSCrossRefMathSciNetGoogle Scholar
  58. 58.
    J. M. MacLaren and R. H. Victora, J. Appl. Physics 76, 6069 (1994).ADSCrossRefGoogle Scholar
  59. 59.
    H. Akai, private communication, 1995.Google Scholar
  60. 60.
    A. Ankudinov, Ph.D. thesis, University of Washington, 1985.Google Scholar
  61. 61.
    A. K. Rajagopal and J. Callaway, Phys. Rev. B 7, 1912 (1973).ADSCrossRefGoogle Scholar
  62. 62.
    U. von Barth and L. Hedin, J. Phys. C: Solid State Phys. 5, 1629 (1972).ADSCrossRefGoogle Scholar
  63. 63.
    A. H. MacDonald and S. H. Vosko, J. Phys. C: Solid State Phys. 12, 2977 (1979).ADSCrossRefGoogle Scholar
  64. 64.
    M. V. Ramana and A. K. Rajagopal, Adv. Chem. Phys. 54, 231 (1983).CrossRefGoogle Scholar
  65. 65.
    M. Richter and H. Eschrig, Solid State Commun. 72, 263 (1989).CrossRefADSGoogle Scholar
  66. 66.
    S. Doniach and C. Sommers, in Valence Fluctuations in Solids, edited by L. M. Falicov, W. Hanke, and M. B. Maple (North-Holland, Amsterdam, 1981), p. 349.Google Scholar
  67. 67.
    R. Feder, F. Rosicky, and B. Ackermann, Z. Physik B 52, 31 (1983).CrossRefADSGoogle Scholar
  68. 68.
    P. Strange, J. B. Staunton, and B. L. Gyorffy, J. Phys. C: Solid State Phys. 17, 3355 (1984).ADSCrossRefGoogle Scholar
  69. 69.
    I. V. Solovyev et al., Soviet Physics-Solid State 31, 1285 (1989).Google Scholar
  70. 70.
    B. C. H. Krutzen and F. Springelkamp, J. Phys.: Condensed Matter 1, 8369 (1989).ADSCrossRefGoogle Scholar
  71. 71.
    B. Ackermann, R. Feder, and E. Tamura, J. Phys. F: Met. Phys. 14, L173 (1984).ADSCrossRefGoogle Scholar
  72. 72.
    G. Schadler, R. C. Albers, A. M. Boring, and P. Weinberger, Phys. Rev. B 35, 4324 (1987).ADSCrossRefGoogle Scholar
  73. 73.
    H. Ebert, B. Drittler, and H. Akai, J. Magn. Magn. Materials 104107, 733 (1992).ADSCrossRefGoogle Scholar
  74. 74.
    L. Szunyogh, B. Újfalussy, P. Weinberger, and J. Kollar, Phys. Rev. B 49, 2721 (1994).ADSCrossRefGoogle Scholar
  75. 75.
    R. Zeller et al., Phys. Rev. B 52, 8807 (1995).ADSCrossRefGoogle Scholar
  76. 76.
    H. Ebert, V. Popescu, and D. Ahlers, J. Phys. (Paris) 7, C2 131 (1997).Google Scholar
  77. 77.
    H. Ebert, V. Popescu, and D. Ahlers, Phys. Rev. B, submitted (1998).Google Scholar
  78. 78.
    S. V. Beiden et al., Phys. Rev. B 57, 14247 (1998).ADSCrossRefGoogle Scholar
  79. 79.
    E. Tamura, Phys. Rev. B 45, 3271 (1992).ADSCrossRefGoogle Scholar
  80. 80.
    X. Wang et al., Phys. Rev. B 46, 9352 (1992).ADSCrossRefGoogle Scholar
  81. 81.
    S. C. Lovatt, B. L. Gyorffy, and G.-Y. Guo, J. Phys.: Condensed Matter 5, 8005 (1993).ADSCrossRefGoogle Scholar
  82. 82.
    T. Huhne, Master’s thesis, University of Munich, 1997.Google Scholar
  83. 83.
    T. Huhne et al., Phys. Rev. B 58, 10236 (1998).ADSCrossRefGoogle Scholar
  84. 84.
    H. Ebert, P. Strange, and B. L. Gyorffy, J. Appl. Physics 63, 3055 (1988).ADSCrossRefGoogle Scholar
  85. 85.
    H. Ebert, P. Strange, and B. L. Gyorffy, Z. Physik B 73, 77 (1988).CrossRefADSGoogle Scholar
  86. 86.
    P. Strange, P. J. Durham, and B. L. Gyorffy, Phys. Rev. Letters 67, 3590 (1991).ADSCrossRefGoogle Scholar
  87. 87.
    E. Tamura, G. D. Waddill, J. G. Tobin, and P. A. Sterne, Phys. Rev. Letters 73, 1533 (1994).ADSCrossRefGoogle Scholar
  88. 88.
    H. Ebert, L. Baumgarten, C. M. Schneider, and J. Kirschner, Phys. Rev. B 44, 4466 (1991).ADSCrossRefGoogle Scholar
  89. 89.
    H. Ebert and J. Schwitalla, Phys. Rev. B 55, 3100 (1997).ADSCrossRefGoogle Scholar
  90. 90.
    T. Scheunemann, S. V. Halilov, J. Henk, and R. Feder, Solid State Commun. 91, 487 (1994).CrossRefADSGoogle Scholar
  91. 91.
    E. Arola, P. Strange, and B. L. Gyorffy, Phys. Rev. B 55, 472 (1997).ADSCrossRefGoogle Scholar
  92. 92.
    H. J. Gotsis and P. Strange, J. Phys.: Condensed Matter 6, 1409 (1994).ADSCrossRefGoogle Scholar
  93. 93.
    A. B. Shick, V. Drchal, J. Kudrnovský, and P. Weinberger, Phys. Rev. B 54, 1610 (1996).ADSCrossRefGoogle Scholar
  94. 94.
    P. Weinberger, I. Turek, and L. Szunyogh, Intern. J. Quantum. Chem. 63, 165 (1997).CrossRefGoogle Scholar
  95. 95.
    I. Turek et al., Electronic structure of disordered alloys, surfaces and interfaces (Kluwer Academic Publ., Boston, 1997).Google Scholar
  96. 96.
    R. M. Dreizler and E. K. U. Gross, Density Functional Theory (Springer-Verlag, Heidelberg, 1990).zbMATHGoogle Scholar
  97. 97.
    H. Eschrig, The Fundamentals of Density Functional Theory (B G Teubner Verlagsgesellschaft, Stuttgart, Leipzig, 1996).zbMATHGoogle Scholar
  98. 98.
    A. H. MacDonald, J. Phys. C: Solid State Phys. 16, 3869 (1983).ADSCrossRefGoogle Scholar
  99. 99.
    A. K. Rajagopal, J. Phys. C: Solid State Phys. 11, L943 (1978).ADSCrossRefGoogle Scholar
  100. 100.
    M. V. Ramana and A. K. Rajagopal, J. Phys. C: Solid State Phys. 12, L845 (1979).ADSCrossRefGoogle Scholar
  101. 101.
    H. Eschrig, G. Seifert, and P. Ziesche, Solid State Commun. 56, 777 (1985).CrossRefADSGoogle Scholar
  102. 102.
    B. X. Xu, A. K. Rajagopal, and M. V. Ramana, J. Phys. C: Solid State Phys. 17, 1339 (1984).ADSCrossRefGoogle Scholar
  103. 103.
    M. V. Ramana and A. K. Rajagopal, J. Phys. C: Solid State Phys. 14, 4291 (1981).ADSCrossRefGoogle Scholar
  104. 104.
    G. Vignale and M. Rasolt, Phys. Rev. Letters 59, 2360 (1987).ADSCrossRefGoogle Scholar
  105. 105.
    G. Vignale and M. Rasolt, Phys. Rev. B 37, 10685 (1988).ADSCrossRefGoogle Scholar
  106. 106.
    G. Vignale and M. Rasolt, Phys. Rev. Letters 62, 115 (1989).ADSCrossRefGoogle Scholar
  107. 107.
    G. Vignale, in Current Density Functional Theory and Orbital Magnetism, Vol. 337 of Nato ASI Series, Series B, edited by E. K. U. Gross and R. M. Dreizler (Plenum Press, NewYork, 1995), p. 485.Google Scholar
  108. 108.
    P. Skudlarski and G. Vignale, Phys. Rev. B 48, 8547 (1993).ADSCrossRefGoogle Scholar
  109. 109.
    H. Ebert, M. Battocletti, and E. K. U. Gross, Europhys. Lett. 40, 545 (1997).ADSCrossRefGoogle Scholar
  110. 110.
    H. Bethe and E. Salpeter, Quantum Mechanics of One-and Two-Electron Atoms (Springer, New York, 1957).zbMATHGoogle Scholar
  111. 111.
    H. J. F. Jansen, J. Appl. Physics 64, 5604 (1988).ADSCrossRefGoogle Scholar
  112. 112.
    H. Ebert, unpublished (1995).Google Scholar
  113. 113.
    M. S. S. Brooks, Physica B 130, 6 (1985).CrossRefGoogle Scholar
  114. 114.
    O. Eriksson, B. Johansson, and M. S. S. Brooks, J. Phys.: Condensed Matter 1, 4005 (1989).ADSCrossRefGoogle Scholar
  115. 115.
    O. Eriksson, M. S. S. Brooks, and B. Johansson, Phys. Rev. B 41, 7311 (1990).ADSCrossRefGoogle Scholar
  116. 116.
    L. Severin, M. S. S. Brooks, and B. Johansson, Phys. Rev. Letters 71, 3214 (1993).ADSCrossRefGoogle Scholar
  117. 117.
    A. B. Shick and V. A. Gubanov, Phys. Rev. B 49, 12860 (1994).ADSCrossRefGoogle Scholar
  118. 118.
    H. Ebert and M. Battocletti, Solid State Commun. 98, 785 (1996).CrossRefADSGoogle Scholar
  119. 119.
    G. Racah, Phys. Rev. 42, 438 (1942).ADSCrossRefGoogle Scholar
  120. 120.
    R. Pittini, J. Schoenes, O. Vogt, and P. Wachter, Phys. Rev. Letters 77, 944 (1996).ADSCrossRefGoogle Scholar
  121. 121.
    W. M. Temmerman, Z. Szotek, and G. A. Gehring, Phys. Rev. Letters 79, 3970 (1997).ADSCrossRefGoogle Scholar
  122. 122.
    J. Forstreuter, L. Steinbeck, M. Richter, and H. Eschrig, Phys. Rev. B 55, 9415 (1997).ADSCrossRefGoogle Scholar
  123. 123.
    E. Engel et al., Phys. Rev. A 58, 964 (1998).ADSCrossRefGoogle Scholar
  124. 124.
    A. H. MacDonald, J. M. Daams, S. H. Vosko, and D. D. Koelling, Phys. Rev. B 23, 6377 (1981).ADSCrossRefGoogle Scholar
  125. 125.
    L. Severin, M. Richter, and L. Steinbeck, Phys. Rev. B 55, 9211 (1997).ADSCrossRefGoogle Scholar
  126. 126.
    R. N. Schmid et al., Adv. Quantum. Chem. in press (1999).Google Scholar
  127. 127.
    P. Cortona, S. Doniach, and C. Sommers, Phys. Rev. A 31, 2842 (1985).ADSCrossRefGoogle Scholar
  128. 128.
    B. Ackermann, Ph.D. thesis, University of Duisburg, 1985.Google Scholar
  129. 129.
    A. C. Jenkins and P. Strange, J. Phys.: Condensed Matter 6, 3499 (1994).ADSCrossRefGoogle Scholar
  130. 130.
    B. Drittler, H. Ebert, R. Zeller, and P. H. Dederichs, Phys. Rev. B 67, 4573 (1990).Google Scholar
  131. 131.
    P. H. Dederichs, B. Drittler, and R. Zeller, Mat. Res. Soc. Symp. Proc. 253, 185 (1992).Google Scholar
  132. 132.
    O. K. Andersen and R. G. Wooley, Molecular Physics 26, 905 (1973).CrossRefADSGoogle Scholar
  133. 133.
    J. S. Faulkner, J. Phys. C: Solid State Phys. 10, 4661 (1977).ADSCrossRefMathSciNetGoogle Scholar
  134. 134.
    J. S. Faulkner, Phys. Rev. B 19, 6186 (1979).ADSCrossRefGoogle Scholar
  135. 135.
    H. Ebert and B. L. Gyorffy, J. Phys. F: Met. Phys. 18, 451 (1988).ADSCrossRefGoogle Scholar
  136. 136.
    J. S. Faulkner and G. M. Stocks, Phys. Rev. B 21, 3222 (1980).ADSCrossRefGoogle Scholar
  137. 137.
    H. Ebert, H. Freyer, A. Vernes, and G.-Y. Guo, Phys. Rev. B 53, 7721 (1996).ADSCrossRefGoogle Scholar
  138. 138.
    H. Ebert, H. Freyer, and M. Deng, Phys. Rev. B 56, 9454 (1997).ADSCrossRefGoogle Scholar
  139. 139.
    H. Ebert, habilitaion thesis, University of München, 1990.Google Scholar
  140. 140.
    B. L. Gyorffy and M. J. Stott, in Band Structure Spectroscopy of Metals and Alloys, edited by D. J. Fabian and L. M. Watson (Academic Press, New York, 1973), p. 385.Google Scholar
  141. 141.
    T. Fujikawa, R. Yanagisawa, N. Yiwata, and K. Ohtani, J. Phys. Soc. Japan 66, 257 (1997).ADSCrossRefGoogle Scholar
  142. 142.
    H. Wu and S. Y. Tong, Phys. Rev. B submitted (1998).Google Scholar
  143. 143.
    A. P. Cracknell, J. Phys. C: Solid State Phys. 2, 1425 (1969).ADSCrossRefGoogle Scholar
  144. 144.
    A. P. Cracknell, Phys. Rev. B 1, 1261 (1970).ADSCrossRefGoogle Scholar
  145. 145.
    G. Hörmandinger and P. Weinberger, J. Phys.: Condensed Matter 4, 2185 (1992).ADSCrossRefGoogle Scholar
  146. 146.
    C. Zecha, Master’s thesis, University of Munich, 1997.Google Scholar
  147. 147.
    C. Kornherr, Master’s thesis, University of Munich, 1997.Google Scholar
  148. 148.
    J. B. Pendry, Low energy electron diffraction (Academic Press, London, 1974).Google Scholar
  149. 149.
    M. Fluchtmann, J. Braun, and G. Borstel, Phys. Rev. B 52, 9564 (1995).ADSCrossRefGoogle Scholar
  150. 150.
    L. Szunyogh, B. Újfalussy, and P. Weinberger, Phys. Rev. B 51, 9552 (1995).ADSCrossRefGoogle Scholar
  151. 151.
    R. Zeller, P. Lang, B. Drittler, and P. H. Dederichs, Mat. Res. Soc. Symp. Proc. 253, 357 (1992).Google Scholar
  152. 152.
    T. Huhne, Ph.D. thesis, University of München, in preparation, 1989.Google Scholar
  153. 153.
    B. Nonas, Ph.D. thesis, RWTH Aachen, in preparation, 1989.Google Scholar
  154. 154.
    P. Soven, Phys. Rev. 156, 809 (1967).ADSCrossRefGoogle Scholar
  155. 155.
    P. Strange, H. Ebert, J. B. Staunton, and B. L. Gyorffy, J. Phys.: Condensed Matter 1, 2959 (1989).ADSCrossRefGoogle Scholar
  156. 156.
    J. S. Faulkner, Prog. Mater. Sci. 27, 1 (1982).CrossRefGoogle Scholar
  157. 157.
    H. Ebert, A. Vernes, and J. Banhart, Solid State Commun. 104, 243 (1997).CrossRefADSGoogle Scholar
  158. 158.
    H. Eckardt and L. Fritsche, J. Phys. F: Met. Phys. 17, 925 (1987).ADSCrossRefGoogle Scholar
  159. 159.
    I. Mertig, R. Zeller, and P. H. Dederichs, Phys. Rev. B 47, 16178 (1993).ADSCrossRefGoogle Scholar
  160. 160.
    H. Ebert, J. Banhart, and A. Vernes, Phys. Rev. B 54, 8479 (1996).ADSCrossRefGoogle Scholar
  161. 161.
    J. Banhart, H. Ebert, and A. Vernes, Phys. Rev. B 56, 10165 (1997).ADSCrossRefGoogle Scholar
  162. 162.
    A. B. Shick, D. L. Novikov, and A. J. Freeman, Phys. Rev. B 56, R14259 (1997).ADSCrossRefGoogle Scholar
  163. 163.
    A. B. Shick, D. L. Novikov, and A. J. Freeman, J. Appl. Physics 83, 7258 (1998).ADSCrossRefGoogle Scholar
  164. 164.
    X. Wang, D. Wang, R. Wu, and A. J. Freeman, J. Magn. Magn. Materials 159, 337 (1996).ADSCrossRefGoogle Scholar
  165. 165.
    G. H. O. Daalderop, P. J. Kelly, and M. F. H. Schuurmans, Phys. Rev. B 41, 11919 (1990).ADSCrossRefGoogle Scholar
  166. 166.
    P. Strange, J. B. Staunton, and H. Ebert, Europhys. Lett. 9, 169 (1989).ADSCrossRefGoogle Scholar
  167. 167.
    Újfalussy, L. Szunyogh, and P. Weinberger, in Properties of Complex Inorganic Solids, edited by A. Gonis, A. Meike, and P. E. A. Turchi (Plenum Press, New York, 1997), p. 181.Google Scholar
  168. 168.
    V. A. Gubanov, A. I. Lichtenstejn, and A. V. Postnikov, Magnetism and the electronic structure of crystals (Springer, Berlin, 1992).Google Scholar
  169. 169.
    S. S. A. Razee, J. B. Staunton, and F. J. Pinski, Phys. Rev. B 56, 8082 (1997).ADSCrossRefGoogle Scholar
  170. 170.
    G. Y. Guo, H. Ebert, and W. M. Temmerman, J. Phys.: Condensed Matter 3, 8205 (1991).ADSCrossRefGoogle Scholar
  171. 171.
    G. Y. Guo, H. Ebert, and W. M. Temmerman, J. Magn. Magn. Materials 104107, 1772 (1992).ADSCrossRefGoogle Scholar
  172. 172.
    M. B. Stearns, in Magnetic Properties of 3d, 4d and 5d Elements, Alloys and Compounds, Vol. III/19a of Landolt-Börnstein, New Series, edited by K.-H. Hellwege and O. Madelung (Springer, Berlin, 1987).Google Scholar
  173. 173.
    O. Eriksson et al., Phys. Rev. B 41, 11807 (1990).ADSCrossRefGoogle Scholar
  174. 174.
    J. Trygg, B. Johansson, O. Eriksson, and J. M. Wills, Phys. Rev. Letters 75, 2871 (1995).ADSCrossRefGoogle Scholar
  175. 175.
    P. Söderlind et al., Phys. Rev. B 45, 12911 (1992).ADSCrossRefGoogle Scholar
  176. 176.
    M. S. S. Brooks and B. Johansson, in Spin-orbit influenced spectroscopies of magnetic solids, Vol. 466 of Lecture Notes in Physics, edited by H. Ebert and G. Schütz (Springer, Berlin, 1996), p. 211.CrossRefGoogle Scholar
  177. 177.
    G. H. O. Daalderop, P. J. Kelly, and M. F. H. Schuurmans, Phys. Rev. B 44, 12054 (1991).ADSCrossRefGoogle Scholar
  178. 178.
    H. Ebert, A. Vernes, and J. Banhart, Phys. Rev. B submitted (1998).Google Scholar
  179. 179.
    Gasche, M. S. S. Brooks, and B. Johansson, Phys. Rev. B 53, 296 (1996).ADSCrossRefGoogle Scholar
  180. 180.
    H. Ebert, Solid State Commun. 100, 677 (1996).CrossRefADSGoogle Scholar
  181. 181.
    P. Herzig, Theoret. Chim. Acta. (Berlin) 67, 323 (1985).CrossRefGoogle Scholar
  182. 182.
    M. Battocletti, Ph.D. thesis, University of München, 1997.Google Scholar
  183. 183.
    P. C. Riedi and E. Hagn, Phys. Rev. B 30, 5680 (1984).ADSCrossRefGoogle Scholar
  184. 184.
    M. Aiga and J. Itoh, J. Phys. Soc. Japan 37, 967 (1974).ADSCrossRefGoogle Scholar
  185. 185.
    Eder, E. Hagn, and E. Zech, Phys. Rev. C 32, 582 (1985).ADSCrossRefGoogle Scholar
  186. 186.
    M. Kawakami, H. Enokiya, and T. Okamoto, J. Phys. F: Met. Phys. 15, 1613 (1985).ADSCrossRefGoogle Scholar
  187. 187.
    P. Blaha, K. Schwarz, and P. H. Dederichs, Phys. Rev. B 37, 2792 (1988).ADSCrossRefGoogle Scholar
  188. 188.
    H. Ebert, R. Zeller, B. Drittler, and P. H. Dederichs, J. Appl. Physics 67, 4576 (1990).ADSCrossRefGoogle Scholar
  189. 189.
    G. A. Gehring and H. C. W. L. Williams, J. Phys. F: Met. Phys. 4, 291 (1974).ADSCrossRefGoogle Scholar
  190. 190.
    C. Demangeat, J. Phys. F: Met. Phys. 5, 169 (1975).ADSCrossRefGoogle Scholar
  191. 191.
    G. Y. Guo and H. Ebert, Phys. Rev. B 50, 10377 (1994).ADSCrossRefGoogle Scholar
  192. 192.
    D. Weller et al., Phys. Rev. Letters 72, 2097 (1994).ADSCrossRefGoogle Scholar
  193. 193.
    G. Breit, Phys. Rev. 35, 1447 (1930).ADSCrossRefGoogle Scholar
  194. 194.
    N. C. Pyper, Molecular Physics 64, 933 (1988).CrossRefADSGoogle Scholar
  195. 195.
    A. Abragam and M. H. L. Pryce, Proc. Roy. Soc. (London) A 205, 135 (1951).zbMATHADSCrossRefGoogle Scholar
  196. 196.
    M. Battocletti, H. Ebert, and H. Akai, Phys. Rev. B 53, 9776 (1996).ADSCrossRefGoogle Scholar
  197. 197.
    H. Akai and T. Kotani, Hyperfine Interactions, in press (1998).Google Scholar
  198. 198.
    K. Terakura, N. Hamada, T. Oguchi, and T. Asada, J. Phys. F: Met. Phys. 12, 1661 (1982).ADSCrossRefGoogle Scholar
  199. 199.
    J. B. Staunton, Ph.D. thesis, University of Bristol, 1982.Google Scholar
  200. 200.
    M. Matsumoto, J. B. Staunton, and P. Strange, J. Phys.: Condensed Matter 2, 8365 (1990).ADSCrossRefGoogle Scholar
  201. 201.
    M. Matsumoto, J. B. Staunton, and P. Strange, J. Phys.: Condensed Matter 3, 1453 (1991).ADSCrossRefGoogle Scholar
  202. 202.
    J. F. Janak, Phys. Rev. B 16, 255 (1977).ADSCrossRefGoogle Scholar
  203. 203.
    J. Benkowitsch and Winter, J. Phys. F: Met. Phys. 13, 991 (1983).ADSCrossRefGoogle Scholar
  204. 204.
    J. Benkowitsch and Winter, Physica Scripta 31, 222 (1985).ADSCrossRefGoogle Scholar
  205. 205.
    H. Ebert, Ph.D. thesis, University of München, 1986.Google Scholar
  206. 206.
    H. Ebert, H. Winter, and J. Voitländer, J. Phys. F: Met. Phys. 16, 1133 (1986).ADSCrossRefGoogle Scholar
  207. 207.
    M. Yasui and M. Shimizu, J. Phys. F: Met. Phys. 9, 1653 (1979).ADSCrossRefGoogle Scholar
  208. 208.
    M. Yasui and M. Shimizu, J. Phys. F: Met. Phys. 15, 2365 (1985).ADSCrossRefGoogle Scholar
  209. 209.
    G. C. Carter, L. H. Bennett, and D. J. Kahan, Prog. Mater. Sci. 20, 153 (1977).Google Scholar
  210. 210.
    I. V. Solovyev, P. H. Dederichs, and I. Mertig, Phys. Rev. B 5, 13419 (1995).ADSCrossRefGoogle Scholar
  211. 211.
    D. A. Greenwood, Proc. Phys. Soc. 71, 585 (1958).zbMATHCrossRefMathSciNetADSGoogle Scholar
  212. 212.
    W. H. Butler, Phys. Rev. B 31, 3260 (1985).ADSCrossRefGoogle Scholar
  213. 213.
    W. H. Kleiner, Phys. Rev. 142, 318 (1966).ADSCrossRefGoogle Scholar
  214. 214.
    P. R. Birss, Selected Topics in Solid State Physics, vol.III (North-Holland, Amsterdam, 1966).Google Scholar
  215. 215.
    T. R. McGuire and R. I. Potter, IEEE Transactions on Magnetics 11, 1018 (1975).CrossRefADSGoogle Scholar
  216. 216.
    P. J. Durham, B. L. Gyorffy, and A. J. Pindor, J. Phys. F: Met. Phys. 10, 661 (1980).ADSCrossRefGoogle Scholar
  217. 217.
    J. Banhart, H. Ebert, P. Weinberger, and J. Voitländer, Phys. Rev. B 50, 2104 (1994).ADSCrossRefGoogle Scholar
  218. 218.
    S. U. Jen, Phys. Rev. B 45, 9819 (1992).ADSCrossRefGoogle Scholar
  219. 219.
    S. Senoussi, I. A. Campbell, and A. Fert, Solid State Commun. 21, 269 (1977).CrossRefADSGoogle Scholar
  220. 220.
    A. Hamzić, S. Senoussi, I. A. Campbell, and A. Fert, J. Phys. F: Met. Phys. 8, 1947 (1978).ADSCrossRefGoogle Scholar
  221. 221.
    S. U. Jen, T. P. Chen, and B. L. Chao, Phys. Rev. B 48, 12789 (1993).ADSCrossRefGoogle Scholar
  222. 222.
    T. R. McGuire, J. A. Aboaf, and E. Klokholm, J. Appl. Physics 55, 1951 (1984).ADSCrossRefGoogle Scholar
  223. 223.
    J. Banhart, A. Vernes, and H. Ebert, Solid State Commun. 98, 129 (1996).CrossRefADSGoogle Scholar
  224. 224.
    F. P. Beitel and E. M. Pugh, Phys. Rev. 112, 1516 (1958).ADSCrossRefGoogle Scholar
  225. 225.
    P. P. Freitas and L. Berger, Phys. Rev. B 37, 6079 (1988).ADSCrossRefGoogle Scholar
  226. 226.
    J. Smit, Physica 16, 612 (1951).ADSCrossRefGoogle Scholar
  227. 227.
    O. Jaoul, I. A. Campbell, and A. Fert, J. Magn. Magn. Materials 5, 23 (1977).ADSCrossRefGoogle Scholar
  228. 228.
    W. H. Butler, X. G. Zhang, D. M. C. Nicholson, and J. M. MacLaren, J. Magn. Magn. Materials 151, 354 (1995).ADSCrossRefGoogle Scholar
  229. 229.
    P. Weinberger et al., J. Phys.: Condensed Matter 8, 7677 (1996).ADSCrossRefGoogle Scholar
  230. 230.
    J. Banhart, private communication, 1998.Google Scholar
  231. 231.
    T. Huhne and H. Ebert, Solid State Commun. to be submitted (1998).Google Scholar
  232. 232.
    W. Geerts et al., Phys. Rev. B 50, 12581 (1994).ADSCrossRefGoogle Scholar
  233. 233.
    H. Ebert et al., Mat. Res. Soc. Symp. Proc. 475, 407 (1998).Google Scholar
  234. 234.
    Y. Suzuki, T. Katayama, P. B. S. Yuasa, and E. Tamura, Phys. Rev. Letters 80, 5200 (1998).ADSCrossRefGoogle Scholar
  235. 235.
    M. Faraday, Phil. Trans. Roy. Soc. 136, 1 (1846).CrossRefGoogle Scholar
  236. 236.
    H. R. Hulm, Proc. Roy. Soc. (London) A 135, 237 (1932).ADSCrossRefGoogle Scholar
  237. 237.
    J. L. Erskine and E. A. Stern, Phys. Rev. B 12, 5016 (1975).ADSCrossRefGoogle Scholar
  238. 238.
    G. Schütz et al., Phys. Rev. Letters 62, 2620 (1989).ADSCrossRefGoogle Scholar
  239. 239.
    R. Wienke, G. Schütz, and H. Ebert, J. Appl. Physics 69, 6147 (1991).ADSCrossRefGoogle Scholar
  240. 240.
    B. T. Thole, P. Carra, F. Sette, and G. van der Laan, Phys. Rev. Letters 68, 1943 (1992).ADSCrossRefGoogle Scholar
  241. 241.
    G. Schütz, M. Knülle, and H. Ebert, Physica Scripta T49, 302 (1993).ADSCrossRefGoogle Scholar
  242. 242.
    P. Carra, B. T. Thole, M. Altarelli, and X. Wang, Phys. Rev. Letters 70, 694 (1993).ADSCrossRefGoogle Scholar
  243. 243.
    H. Maruyama et al., J. Magn. Magn. Materials 104, 2055 (1992).ADSCrossRefGoogle Scholar
  244. 244.
    H. Ebert et al., Int. J. Mod. Phys. B 7, 750 (1993).ADSCrossRefGoogle Scholar
  245. 245.
    H. Ebert and H. Akai, Int. J. Mod. Phys. B 7, 922 (1993).ADSCrossRefGoogle Scholar
  246. 246.
    F. Baudelet et al., J. Phys. (Paris) 7, C2 441 (1997).Google Scholar
  247. 247.
    S. Stähler et al., J. Appl. Physics 73, 6063 (1993).ADSCrossRefGoogle Scholar
  248. 248.
    J. Mustre de Leon et al., Phys. Rev. B 44, 4146 (1991).ADSCrossRefGoogle Scholar
  249. 249.
    D. O. Ahlers, Ph.D. thesis, Universität Würzburg, 1998.Google Scholar
  250. 250.
    V. Popescu, H. Ebert, and A. C. Jenkins, J. Synchr. Rad. 5, in press (1998).Google Scholar
  251. 251.
    P. J. Feibelman and D. E. Eastman, Phys. Rev. B 10, 4932 (1974).ADSCrossRefGoogle Scholar
  252. 252.
    B. Ackermann and R. Feder, J. Phys. C: Solid State Phys. 18, 1093 (1985).ADSCrossRefGoogle Scholar
  253. 253.
    B. Ginatempo, P. J. Durham, B. L. Gyorffy, and W. M. Temmerman, Phys. Rev. Letters 54, 1581 (1985).ADSCrossRefGoogle Scholar
  254. 254.
    P. J. Durham, in The Electronic Structure of Complex Systems, edited by P. Phariseau and W. M. Temmerman (Plenum Press, New York, 1984), p. 709.Google Scholar
  255. 255.
    P. J. Durham, J. Phys. F: Met. Phys. 11, 2475 (1981).ADSCrossRefGoogle Scholar
  256. 256.
    H. Ebert and G. Y. Guo, J. Magn. Magn. Materials 148, 174 (1995).CrossRefADSGoogle Scholar
  257. 257.
    H. Winter, P. J. Durham, and G. M. Stocks, J. Phys. F: Met. Phys. 14, 1047 (1984).ADSCrossRefGoogle Scholar
  258. 258.
    P. Marksteiner et al., Phys. Rev. B 34, 6730 (1986).ADSCrossRefGoogle Scholar
  259. 259.
    D. Weller and W. Reim, Appl. Physics A 49, 599 (1989).ADSCrossRefGoogle Scholar
  260. 260.
    M. Schröder et al., Phys. Rev. B 52, 188 (1995).ADSCrossRefGoogle Scholar
  261. 261.
    S. Ostanin and H. Ebert, Phys. Rev. B 58, 11577 (1998).ADSCrossRefGoogle Scholar
  262. 262.
    D. Weller et al., Mater. Res. Soc 313, 501 (1993).ADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • H. Ebert
    • 1
  1. 1.Institut für Phys. ChemieUniv. MünchenMünchen

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