Advertisement

The Hall Effect of Ferromagnets

  • L. Berger
  • G. Bergmann

Abstract

The history of the development of ideas concerning the Hall effect of magnetic metals is discussed. The Hall voltage depends on the magnetization rather than on the external field. Also, it arises from electron scattering rather than from the free motion of electrons. Two mechanisms are active for this “anomalous” Hall effect: skew scattering and side jump. While the first one is similar to Mott scattering, the second one represents a finite lateral displacement Δy ≃ 10−10 m. of the electron on scattering. A corresponding displacement of the wavefronts of the scattered wave is discussed. Similar side jumps and forward jumps exist for electrons and photons in other parts of physics. The variation of the anomalous Hall effect with alloy composition in transition-metal series can be predicted on the basis of the simple “split-band” model. As an example, the case of amorphous Au-Fe, Au-Ni and Au-Co films is treated, and the predictions compared with experimental data.

Keywords

Hall Effect Hall Conductivity Anomalous Effect Anomalous Hall Effect Hall Voltage 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    E. H. Hall, Phil. Mag. 10: 301 (1880).Google Scholar
  2. 2.
    E. H. Hall, Phil. Mag. 12:157 (1881).Google Scholar
  3. 3.
    A. Kundt, Wied. Ann. 49: 257 (1893).CrossRefGoogle Scholar
  4. 4.
    A. W. Smith and R. W. Sears, Phys. Rev. 34: 1466 (1929).ADSCrossRefGoogle Scholar
  5. 5.
    J. Smit, Physica 17:612 (1951)ADSCrossRefGoogle Scholar
  6. J. Smit, Physica 21:877 (1955).ADSCrossRefGoogle Scholar
  7. 6.
    A. I. Schindler and E. M. Pugh, Phys. Rev. 89:295 (1953)ADSCrossRefGoogle Scholar
  8. S. Foner and E. M. Pugh, Phys. Rev. 91:20 (1953)ADSCrossRefGoogle Scholar
  9. S. Foner, Phys. Rev. 99:1079 (1955)ADSCrossRefGoogle Scholar
  10. F. E. Allison and E. M. Pugh, Phys. Rev. 102:1281 (1956)ADSCrossRefGoogle Scholar
  11. S. Foner, Phys. Rev. 101:1648 (1956)ADSCrossRefGoogle Scholar
  12. S. Foner, F. E. Allison and E. M. Pugh, Phys. Rev. 109:1129 (1958)ADSCrossRefGoogle Scholar
  13. F. P. Beitel and E. M. Pugh, Phys. Rev. 112:1516 (1958)ADSCrossRefGoogle Scholar
  14. S. Soffer, J. A. Dreesen and E. M. Pugh, Phys. Rev. 140:A668 (1965)ADSCrossRefGoogle Scholar
  15. J. A. Dreesen and E. M. Pugh, Phys. Rev. 120:1218 (1960).ADSCrossRefGoogle Scholar
  16. E. R. Sanford, A. C. Ehrlich, and E. M. Pugh, Phys. Rev. 123:1947 (1961)ADSCrossRefGoogle Scholar
  17. A. C. Ehrlich, J. A. Dreeson and E. M. Pugh, Phys. Rev. 133:A407 (1964)ADSCrossRefGoogle Scholar
  18. G. C. Carter and E. M. Pugh, Phys. Rev. 152: 498 (1966).ADSCrossRefGoogle Scholar
  19. 7.
    I. A. Campbell, Phys. Rev. Letters 24: 269 (1970).ADSCrossRefGoogle Scholar
  20. 8.
    W. A. Reed and E. Fawcett, J. Appl. Phys. 35:754 (1964)ADSCrossRefGoogle Scholar
  21. R. V. Coleman, A.I.P. Conf. Proc. 29:520 (1975); plus references quoted there.ADSCrossRefGoogle Scholar
  22. 9.
    A. W. Smith, Phys. Rev. 30: 1 (1910).ADSGoogle Scholar
  23. 10.
    A. Perrier, Helv. Phys. Acta 3:317, 3:400 (1930).Google Scholar
  24. 11.
    J. P. Jan, Helv. Phys. Acta 22:581 (1949)Google Scholar
  25. J. P. Jan, Helv. Phys. Acta 25:677 (1952).Google Scholar
  26. J. P. Jan and H. M. Gijsman, Physica 18: 339 (1952).ADSCrossRefGoogle Scholar
  27. 12.
    C. Kooi, Phys. Rev. 95: 843 (1954).ADSCrossRefGoogle Scholar
  28. A. I. Schindler and E. I. Salkovitz, Phys. Rev. 99: 1251 (1955).ADSCrossRefGoogle Scholar
  29. J. M. Lavine, Phys. Rev. 123: 1273 (1961).ADSCrossRefGoogle Scholar
  30. 13.
    N. V. Volkenshtein and G. V. Fedorov, Phys. Metals and Metallogr. 18:26 (1964).Google Scholar
  31. 14.
    W. Jellinghaus and M. P. DeAndres, Ann. Physik 7: 189 (1961).ADSCrossRefGoogle Scholar
  32. W. Köster and W. Gmöhling, Z. Metallkunde 52: 713 (1961).Google Scholar
  33. W. Köster and O. Römer, Z. Metallkunde 55: 805 (1964).Google Scholar
  34. 15.
    J. M. Luttinger, Phys. Rev. 112: 739 (1958).MathSciNetADSCrossRefGoogle Scholar
  35. 16.
    R. E. Peierls, “Quantum Theory of Solids,” Oxford U. Press, Oxford (1956), p. 141.Google Scholar
  36. 17.
    Y. Kagan and L. A. Maksimov, Sov. Phys. Solid State 7: 422 (1965).Google Scholar
  37. L. E. Gurevich and I. N. Yassievich ibid. 5:1914 (1964).Google Scholar
  38. Yu. P. Irkhin and V. G. Postovalov, ibid. 8: 346 (1966).Google Scholar
  39. Yu. P. Irkhin, A. N. Voloshinskii and Sh. Sh. Abelskii, Phys. Stat. Sol. 22: 309 (1967).ADSCrossRefGoogle Scholar
  40. A. N. Voloshinskii and N. V. Rijanova, Fiz. Met. Metallov 34:21 (1972)Google Scholar
  41. A. N. Voloshinskii and N. V. Rijanova, Fiz. Met. Metallov 35:269 (1973).Google Scholar
  42. C. Lewiner, O. Betbeder-Matibet, and P. Nozieres, J. Phys. Chem. Solids 34:765 (1973).ADSCrossRefGoogle Scholar
  43. S. K. Lyo, Phys. Rev. B 8: 1185 (1973).ADSCrossRefGoogle Scholar
  44. S. K. Lyo and T. Holstein, Phys. Rev. B 9: 2412 (1974).ADSCrossRefGoogle Scholar
  45. S. K. Lyo, Phys. Rev. B 11: 1260 (1975).ADSCrossRefGoogle Scholar
  46. S. K. Lyo, Phys. Rev. B 15: 2791 (1977).ADSCrossRefGoogle Scholar
  47. 18.
    L. Berger, Phys. Rev. B 2: 4559 (1970).ADSCrossRefGoogle Scholar
  48. 19.
    J. Smith, Physica 24: 39 (1958).ADSCrossRefGoogle Scholar
  49. 20.
    S. K. Lyo and T. Holstein, Phys. Rev. Letters 29: 423 (1972).ADSCrossRefGoogle Scholar
  50. 21.
    P. Nozieres and C. Lewiner, J. Phys. (Paris) 34: 901 (1973).CrossRefGoogle Scholar
  51. 22.
    R. C. Fivaz, Phys. Rev. 183: 586 (1969).ADSCrossRefGoogle Scholar
  52. 23.
    A. K. Majumdar and L. Berger, Phys. Rev. B 7: 4203 (1973).ADSCrossRefGoogle Scholar
  53. 24.
    A. Fert and O. Jaoul, Phys. Rev. Letters 28: 303 (1972).ADSCrossRefGoogle Scholar
  54. 25.
    A. Fert, Physica 86-88B:491 (1977).Google Scholar
  55. A. Fert and P. M. Levy, Phys. Rev. B 16: 5052 (1977).ADSCrossRefGoogle Scholar
  56. 26.
    P. Leroux-Hugon and A. Ghazali, J. Phys. C5:1072 (1972).ADSGoogle Scholar
  57. 27.
    R. Huguenin and D. Rivier, Helv. Phys. Acta 38: 900 (1966).Google Scholar
  58. J.
    W. F. Dorleijn and A. R. Miedema, Physica 86-88B:537 (1977).Google Scholar
  59. O. Jaoul, Doctoral Thesis, Univ. de Paris-Sud (1974).Google Scholar
  60. 28.
    A. K. Majumdar and L. Berger, Phys. Rev. B 7: 4203 (1973).ADSCrossRefGoogle Scholar
  61. 29.
    A. Friederich and A. Fert, Phys. Rev. B 13: 397 (1976).ADSCrossRefGoogle Scholar
  62. A. Fert and A. Friederich, A.I.P. Conf. Proc. 24: 466 (1975).ADSCrossRefGoogle Scholar
  63. 30.
    L. Berger, Phys. Rev. 177: 790 (1969).ADSCrossRefGoogle Scholar
  64. R. V. Coleman, A.I.P. Conf. Proc. 29: 520 (1975).ADSCrossRefGoogle Scholar
  65. 31.
    J. Smit, Physica 21: 877 (1955).ADSCrossRefGoogle Scholar
  66. 32.
    S. K. Lyo, Phys. Rev. B 8:1185 (1973).ADSCrossRefGoogle Scholar
  67. 33.
    J. N. Chazalviel, Phys. Rev. B 11: 3918 (1975).ADSCrossRefGoogle Scholar
  68. 34.
    C. M. Hurd, Contemp. Phys. 16: 517 (1975).ADSCrossRefGoogle Scholar
  69. 35.
    B. Chakraborty and P. B. Allen, Phys. Rev. Letters 42: 736 (1979).ADSCrossRefGoogle Scholar
  70. 36.
    S. C. Miller and N. Ashby, Phys. Rev. Letters 29: 740 (1972).ADSCrossRefGoogle Scholar
  71. 37.
    J. Picht, Ann. Physik 3:433 (1929).ADSMATHCrossRefGoogle Scholar
  72. J. Picht, Physik Z. 30: 905 (1929).Google Scholar
  73. 38.
    F. Goos and H. Hänchen, Ann. Physik 1:333 (1947).ADSCrossRefGoogle Scholar
  74. F. Goos and H. Hänchen, Ann. Physik 5:521 (1949).Google Scholar
  75. 39.
    F. I. Federov, Dokl. Akad. Nauk SSSR 105: 465 (1955).MathSciNetGoogle Scholar
  76. 40.
    C. Imbert, Phys. Rev. D 5: 787 (1972).ADSCrossRefGoogle Scholar
  77. C. Imbert, C. R. Acad. Sci. (Paris) B267:1401 (1968).Google Scholar
  78. 41.
    B. Velicky, S. Kirkpatrick and H. Ehrenreich, Phys. Rev. 175: 747 (1968).ADSCrossRefGoogle Scholar
  79. S. Kirkpatrick, B. Velicky, N. D. Lang and H. Ehrenreich, J. Appl. Phys. 40: 1283 (1969).ADSCrossRefGoogle Scholar
  80. 42.
    H. Ashworth, D. Sengupta, G. Schnakenberg, L. Shapiro, and L. Berger, Phys. Rev. 185: 792 (1969).ADSCrossRefGoogle Scholar
  81. 43.
    L. Berger, Physica 91B:31 (1977).Google Scholar
  82. 44.
    H. D. Drew and R. E. Doezema, Phys. Rev. Letters 28: 1581 (1972).ADSCrossRefGoogle Scholar
  83. K. Y. Yu, C. R. Helms, W. E. Spicer, and P. W. Chye, Phys. Rev. B 15: 1629 (1977).ADSCrossRefGoogle Scholar
  84. 45.
    P. Oelhafen, E. Hauser, H. J. Güntherodt, and K. H. Bennemann, Phys. Rev. Letters 43: 1134 (1979).ADSCrossRefGoogle Scholar
  85. 46.
    R. C. O’Handley and L. Berger, Inst. Phys. Conf. Ser. (London) 39:477 (1978).Google Scholar
  86. R. C. O’Handley, Phys. Rev. B 18: 2577 (1978).ADSCrossRefGoogle Scholar
  87. 47.
    W. Felsch, Z. f. Angew. Physik 29: 217 (1970).Google Scholar
  88. 48.
    G. Bergmann, Z. Physik B25:255 (1976).ADSGoogle Scholar
  89. G. Bergmann, Solid State Comm. 18:897 (1976).MathSciNetADSCrossRefGoogle Scholar
  90. G. Bergmann and P. Marquardt, Phys. Rev. B 18:326 (1978).ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1980

Authors and Affiliations

  • L. Berger
    • 1
  • G. Bergmann
    • 2
  1. 1.Physics DepartmentCarnegie-Mellon UniversityPittsburghUSA
  2. 2.Institut für FestkörperforschungJülichWest Germany

Personalised recommendations