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Phenomenological Theory of Magnetic Ordering: Importance of Interactions with the Crystal Lattice

  • Chapter
Magnetic Properties of Rare Earth Metals

Abstract

The diverse, and sometimes exotic, magnetic behavior of the rare earth elements and their alloys as observed in the past fifteen or so years is basically understood in terms of a very simple physical picture. The key element of this picture is that one makes a sharp distinction between localized, magnetic, 4f electrons and outer-shell conduction electrons; and one takes the magnetic system for these metals as a lattice of localized tripositive rare earth ions (divalent for Eu) with moments corresponding to the unfilled 4f shells. (The ionic moment is quite well given by the application of Hund’s rules so that in general, J, the total spin plus orbital angular momentum, is treated as a good quantum number for the magnetic system of tripositive ions.) This lattice of localized ions, with their corresponding localized moments, is then immersed in a sea of conduction electrons to which each rare-earth atom contributes its three outer electrons. This picture is excellent for the heavy rare earth metals(1, 2) (gadolinium through thulium), and is reasonably good for most of the light rare earths. (The most complex behavior in the rare earth series, requiring concepts beyond those of this simple picture, is found for the end members, cerium and ytterbium.)

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References

  1. Elliott, R. J., in Magnetism (G. T. Rado and H. Suhl, eds). Academic Press, New York (1965), Vol. IIA, p. 385.

    Google Scholar 

  2. Cooper, B. R., in Solid State Physics ( F. Seitz, D. Turnbull and H. Ehrenrecih, eds). Academic Press, New York (1968), Vol. 21, p. 393.

    Google Scholar 

  3. Kaplan, T. A. and Lyons, D. H. Phys. Rev., 129, 2072 (1963).

    Article  Google Scholar 

  4. Specht, F. Phys. Rev., 162, 389 (1967).

    Article  CAS  Google Scholar 

  5. Elliott, R. J. Phys. Rev., 124, 346 (1961).

    Article  CAS  Google Scholar 

  6. Yosida, K. and Miwa, H. J. Appl. Phys., 32, 8S (1961)

    Google Scholar 

  7. Miwa, H. and Yosida, K. Progr. Theoret. Phys., (Kyoto) 26, 693 (1961).

    Article  CAS  Google Scholar 

  8. Kaplan, T. A. Phys. Rev., 124, 329 (1961).

    Article  CAS  Google Scholar 

  9. Brinkman, W. F. and Elliott, R. J. Proc. Roy. Soc., 294A, 343 (1966)

    Article  CAS  Google Scholar 

  10. Brinkman, W. F. J. Appl. Phys. 38, 939 (1967).

    Article  CAS  Google Scholar 

  11. Bjerrum Moller, H. and Gylden Houmann, J. C. Phys. Rev. Letters, 16, 737 (1966).

    Article  Google Scholar 

  12. Evenson, W. E. and Liu, S. H. Phys. Rev., 178, 783 (1969).

    Article  CAS  Google Scholar 

  13. Yoshinori, A. J. Phys. Soc. Japan, 14, 807 (1959).

    Article  CAS  Google Scholar 

  14. Villain, J. J. Phys. Chem. Solids, 11, 303 (1959).

    Article  CAS  Google Scholar 

  15. Herpin, A., Meriel, P. and Villain, J. Comps. Rend., 249, 1334 (1959).

    CAS  Google Scholar 

  16. Herpin, A. and Meriel, P. Compt. Rend., 251, 1450 (1960).

    Google Scholar 

  17. Kaplan, T. A. Phys. Rev„ 116, 888 (1959).

    Article  CAS  Google Scholar 

  18. Nagamiya, T., in Solid State Physics ( F. Sitez, D. Turnbull, and H. Ehrenreich, eds). Academic Press, New York (1967), Vol. 20, p. 306.

    Google Scholar 

  19. Enz, U. J. Appl. Phys., 32, 22S (1961).

    Article  Google Scholar 

  20. Cooper, B. R. Proc. Phys. Soc. (London), 80, 1225 (1962).

    Article  CAS  Google Scholar 

  21. Goodings, D. A. J. Appl. Phys., 39, 887 (1968).

    Article  CAS  Google Scholar 

  22. Miwa, H. Proc. Phys. Soc. (London), 85, 1197 (1965).

    Article  CAS  Google Scholar 

  23. Elliott, R. J. and Wedgwood, F. A. Proc. Phys. Soc. (London), 84, 63 (1964).

    Article  CAS  Google Scholar 

  24. de Gennes, P. G. and Saint James, D. Solid State Comm., 1, 62 (1963).

    Article  CAS  Google Scholar 

  25. Cooper, B. R. Phys. Rev., 169, 281 (1968).

    Article  CAS  Google Scholar 

  26. Feron, J. L. Thesis, University of Grenoble, 1969 (unpublished).

    Google Scholar 

  27. Callen, H. B. and Callen, E. J. Phys. Chem. Solids, 27, 1271 (1966).

    Article  CAS  Google Scholar 

  28. Cooper, B. R., Elliott, R. J., Nettel, S. J. and Suhl, H. Phys. Rev., 127, 57 (1962).

    Article  CAS  Google Scholar 

  29. Shirane, G. and Pickart, S. J. J. Appl. Phys., 37, 1032 (1966).

    Article  CAS  Google Scholar 

  30. Millhouse, A. H. Ph.D. Thesis, Virginia Polytechnic Institute, Sept. 1969.

    Google Scholar 

  31. Fisher, E. S. and Dever, D. Trans. AIME, 239, 48 (1967).

    CAS  Google Scholar 

  32. Rosen, M. and Klimker, H. Phys. Rev., BI, 3748 (1970).

    Google Scholar 

  33. Clark, A. E., DeSavage, B. F. and Bozorth, R. Phys. Rev., 138, A216 (1965).

    Article  Google Scholar 

  34. Rhyne, J. J. and Legvold, S. Phys. Rev., 138, A507 (1965).

    Article  Google Scholar 

  35. Rhyne, J. J. and Clark, A. E. J. Appl. Phys., 38, 1379 (1968).

    Article  Google Scholar 

  36. Koehler, W. C., Cable, J. W., Child, H. R., Wilkinson, M. K. and Wollan, W. O. Phys. Rev., 158, 450 (1967).

    Article  CAS  Google Scholar 

  37. Herpin, A. and Meriel, P. J. Phys. Radium, 22, 337 (1961).

    Article  CAS  Google Scholar 

  38. Enz, U. Physica, 26, 698 (1960).

    Article  CAS  Google Scholar 

  39. Nagamiya, T., Nagata, K. and Kitano, Y. Progr. Theoret. Phys. (Kyoto), 27, 1253 (1962).

    Article  Google Scholar 

  40. Nagamiya, T. J. Appl. Phys., 33, 1029 (1962).

    Article  CAS  Google Scholar 

  41. Kitano, Y. and Nagamiya, T. Prlgr. Theoret. Phys. (Kyoto), 31, 1 (1964).

    Article  Google Scholar 

  42. Cooper, B. R. and Elliott, R. J. Phys. Rev., 131, 1043. (1963). Erratum: Phys. Rev., 153, 654 (1967).

    Article  Google Scholar 

  43. Cooper, B. R. Phys. Rev. Letters, 19, 900 (1967).

    Article  CAS  Google Scholar 

  44. These values of Tv and Tc are taken from the magnetization measurements of Behrendt et al. (D. R. Behrendt, S. Legvold and F. H. Spedding, Phys. Rev.,109, 1544 (1958) and differ slightly from the values found by electrical resistivity measurements in Chapter 7.

    Google Scholar 

  45. Koehler, W. C. J. Appl. Phys., 37, 1076 (1965).

    Google Scholar 

  46. Wilkinson, M. K., Koehler, W. C., Wollan, E. O. and Cable, J. W. J. Appl. Phys., 32, 485 (1961).

    Article  Google Scholar 

  47. Darnell, F. J. Phys. Rev., 132, 128 (1963).

    Article  CAS  Google Scholar 

  48. Callen, E. and Callen, H. B. Phys. Rev., 139, A455 (1965).

    Article  Google Scholar 

  49. Liu, S. H., Behrendt, D. R., Legvold, S. and Good, Jr, R. H. Phys. Rev., 116, 1464 (1959).

    Article  CAS  Google Scholar 

  50. Mackintosh, A. R. 1970 NATO Advanced Summer Institute on Magnetism of Rare Earth Materials, Alta Lake, British Columbia, August, 1970.

    Google Scholar 

  51. Bjerrum Moller, H., Gylden Houmann, J. C. and Mackintosh, A. R. Phys. Rev. Letters, 19, 312 (1967).

    Article  Google Scholar 

  52. Bjerrum Moller, H., Nielsen, M. and Mackintosh, A. R. Les Elements des Terres Rares. (Proceedings of the Grenoble Conference May, 1969) Colloques Intern du CNRS, No 180, Tome II, page 277.

    Google Scholar 

  53. Nicklow, R. M. J. Appl. Phys., 42, 1672 (1971).

    Article  CAS  Google Scholar 

  54. Turov, E. A. and Shavrov, V. G. Fiz. Tverd. Tela, 7, 217 (1965).

    CAS  Google Scholar 

  55. Nielsen, M., Bjerrum Moller, H. and Mackintosh, A. R. J. Appl. Phys., 41, 1174 (1970).

    Article  CAS  Google Scholar 

  56. Sievers, A. J. J. Appl. Phys., 41, 980 (1970).

    Article  CAS  Google Scholar 

  57. Wagner, T. K. and Stanford, J. L. Phys. Rev., 184, 505 (1969).

    Article  CAS  Google Scholar 

  58. Trammell, G. T. J. Appl. Phys., 31, 3625 (1960).

    Article  Google Scholar 

  59. Trammell, G. T. Phys. Rev., 131, 932 (1963).

    Article  CAS  Google Scholar 

  60. Bleaney, B. Proc. Roy. Soc. (London), A276, 19 (1963).

    Google Scholar 

  61. Cooper, B. R. Phys. Rev., 163, 144 (1967).

    Google Scholar 

  62. Wang, Y.-L. and Cooper, B. R. Phys. Rev., 172, 539 (1968).

    Article  CAS  Google Scholar 

  63. Wang, Y.-L. and Cooper, B. R. Phys. Rev., 185, 696 (1969).

    Article  CAS  Google Scholar 

  64. Cooper, B. R. J. Appl. Phys., 40, 1344 (1969).

    Article  CAS  Google Scholar 

  65. Bleaney, B. Proc. Roy. Soc. (London), A276, 39 (1963).

    Google Scholar 

  66. Rainford, B. D. and Wedgwood, F. A. 1969 (unpublished).

    Google Scholar 

  67. Johansson, T., Lebech, B., Nielsen, M., Bjerrum Moller, H. and Mackintosh, A. R., Phys. Rev. Letters, 25, 524 (1970).

    Article  CAS  Google Scholar 

  68. Bucher, E., Chu, C. W., Maita, J. P., Andres, K., Cooper, A. S., Buehler, E. and Nassau, K. Phys. Rev. Letters, 22, 1260 (1969).

    Article  CAS  Google Scholar 

  69. Child, H. R., Wilkinson, M. K., Cable, J. W., Koehler, W. C. and Wollan, E. O. Phys. Rev., 131, 922 (1963).

    Article  CAS  Google Scholar 

  70. Busch, G. J. Appl. Phys., 38, 1386 (1967).

    Article  CAS  Google Scholar 

  71. Vogt, O. and Cooper, B. R. J. Appl. Phys., 39, 1202 (1968)

    Article  CAS  Google Scholar 

  72. Cooper, B. R. and Vogt, O. Phys. Rev., BI, 1211 (1970).

    Google Scholar 

  73. Junod, P., Menth, A. and Vogt, O. Phys. Kondens. Materie, 8, 323 (1969).

    CAS  Google Scholar 

  74. Cooper, B. R. and Vogt, O. Phys. Rev., BI, 1218 (1970).

    Google Scholar 

  75. Stutius, W. Phys. Kondens. Materie, 9, 341 (1969).

    CAS  Google Scholar 

  76. Cable, J. W., Moon, R. M., Koehler, W. C. and Wollan, E. O. Phys. Rev. Letters, 12, 553 (1964).

    Article  CAS  Google Scholar 

  77. Bucher, E., Andres, K., Maita, J. P. and Hull, Jr., G. W. Hely. Phys. Acta, 41, 723 (1968).

    CAS  Google Scholar 

  78. Lee, K. N., Bachmann, R., Geballe, T. H. and Maita, J. P., Phys. Rev., B2, 4580 (1970).

    Article  Google Scholar 

  79. Buschow, K. H. J. and Fast, J. F. Z. Physik. Chem., Neue Folge, 50, 1 (1966).

    Article  CAS  Google Scholar 

  80. Cooper, B. R. Hely. Physica Acta, 41, 750 (1968).

    CAS  Google Scholar 

  81. de Wijn, H. W., van Diepen, A. M. and Buschow, K. H. J., Phys., Rev. B1, 4203 (1970).

    Article  Google Scholar 

  82. Moon, R. M., Cable, J. W. and Koehler, W. C. J. Appl. Phys., 35, 1041 (1964).

    Article  CAS  Google Scholar 

  83. Tsuchida, T. and Wallace, W. E. J. Chem. Phys., 43, 2087 (1965).

    Article  CAS  Google Scholar 

  84. Tsuchida, T. and Wallace, W. E. J. Chem. Phys., 43, 2885 (1965).

    Article  CAS  Google Scholar 

  85. Busch, G. and Vogt, O. Phys. Letters, 20, 152 (1966).

    Article  CAS  Google Scholar 

  86. Wang, Y. L. and Cooper, B. R., Phys. Rev., B2, 2607 (1970).

    Article  Google Scholar 

  87. Stevens, K. H. W. Rev. Mod. Phys., 25, 166 (1953).

    Article  CAS  Google Scholar 

  88. Van Vleck, J. H. Rev. Mat. Fis. Teor. (Tueuman, Argentina), 14, 189 (1962).

    Google Scholar 

  89. Levy, P. M. Phys. Rev. Letters, 20, 1366 (1968).

    Article  Google Scholar 

  90. Elliott, R. J. and Thorpe, M. F. J. Appl. Phys., 39, 802 (1968).

    Article  CAS  Google Scholar 

  91. Birgeneau, R. J., Hutchings, M. T., Baker, J. M. and Riley, J. D. J. Appl. Phys., 40, 1070 (1969).

    Article  CAS  Google Scholar 

  92. Cooper, B. R. and Vogt, O., J. de Physique, 32, C1–1026 (1971).

    Article  Google Scholar 

  93. Cooper, B. R., Jacobs, I. S., Graham, C. D. and Vogt, O., J. de Physique, 32, C1–359 (1971).

    Article  Google Scholar 

  94. Griffith, J. S. Phys. Rev., 132, 316 (1963).

    Article  Google Scholar 

  95. Bozorth, R. M. and Van Vleck, J. H. Phys. Rev., 118, 1493 (1960).

    Article  CAS  Google Scholar 

  96. Bogoliubov, N. N. and Tiablikov, S. Ia. Izv. Akad. Nauk. SSSR Ser Fiz., 21, 849 (1957).

    Google Scholar 

  97. Grover, B. Phys. Rev., 140, A1944 (1965).

    Article  Google Scholar 

  98. Pink, D. A. J. Phys., Cl, 1246 (1968).

    Google Scholar 

  99. Stevens, K. W. H., in Magnetism ( G. T. Rado and H. Suhl, eds). Academic Press, New York (1963), Vol. I, p. 1.

    Google Scholar 

  100. Callen, H. B. Phys. Rev., 130, 890 (1963).

    Article  Google Scholar 

  101. Elliott, R. J. and Pfeuty, P., private communication (1969)

    Google Scholar 

  102. Elliott, R. J., Pfeuty, P. and Wood, C. Phys. Rev. Letters, 25, 443 (1970).

    Article  Google Scholar 

  103. Kitano, Y., abstract (in Japanese) for talk presented at the joint annual meeting of the Physical and Applied Physical Societies of Japan, 1969. Translation provided by the Japanese Liaison Office of the General Electric Research and Development Center.

    Google Scholar 

  104. Hsieh, Y. Y. and Blume, M., private communication, 1970.

    Google Scholar 

  105. Lea, K. R., Leask, M J. M. and Wolf, W. P. J. Phys. Chem. Solids, 23, 1381 (1962)

    Article  CAS  Google Scholar 

  106. Cooper, B. R., Jacobs, I. S., Fedder, R. C., Kouvel, J. S. and Schumacher, D. P. J. Appl. Phys., 37, 1384 (1966).

    Article  CAS  Google Scholar 

  107. Cooper, B. R. Phys. Letters, 22, 24 (1966).

    Article  CAS  Google Scholar 

  108. Parkinson, D. H., Simon, F. E. and Spedding, F. H. Proc. Roy. Soc. (London), 207A, 137 (1951).

    Article  CAS  Google Scholar 

  109. Lock, J. M. Proc. Phys. Soc. (London), B70, 566 (1957).

    Article  Google Scholar 

  110. Dreyfus, B., Goodman, B. B., Lacaze, A. and Trolliet, G. Comps. Rend., 253, 1764 (1961).

    CAS  Google Scholar 

  111. Dempsey, C. W., Gordon, J. E. and Soller, T. Bull. Am. Phys. Soc., 7, 309 (1962).

    Google Scholar 

  112. Lounasmaa, O. V. Phys. Rev., 133, A211 (1964).

    Article  Google Scholar 

  113. Matthias, B. T., Geballe, T. H., Andres, K., Corengwit, E., Hull, G. W., and Maita, J. P. Science, 159, 530 (1968)

    Article  Google Scholar 

  114. Geballe, T. H., Matthias, B. T., Andres, K., Maita, J. P., Cooper, A. S. and Corengwit, E. Science, 160, 1443 (1968).

    Google Scholar 

  115. Menth, A., Buehler, E. and Geballe, T. H. Phys. Rev. Letters, 22, 295 (1969).

    Article  CAS  Google Scholar 

  116. Geballe, T. H., Menth, A., Buehler, E. and Hull, G. W. J. Appl. Phys., 41, 904 (1970)

    Article  CAS  Google Scholar 

  117. Birgeneau, R. J., Bucher, E., Passell, L., Price, D. L. and Turberfield, K. C. J. Appl. Phys., 41, 900 (1970).

    Article  CAS  Google Scholar 

  118. Turberfield, K. C., Passell, L., Birgeneau, R. J. and Bucher, E. J. Appl. Phys., 42, 1746 (1971).

    Article  CAS  Google Scholar 

  119. Birgeneau, R. J., Bucher, E., Passell, L. and Turberfield, K. C. Phys. Rev., B4, 718 (1971).

    Article  Google Scholar 

  120. Cable, J. W., Collins, M. F. and Woods, A. D. B. Proc. 6th Rare Earth Research Conference, Gatlinburg, Tenn. (May 3–5, 1967 ), page 297.

    Google Scholar 

  121. Holden, T. M., Powell, B. M., and Woods, A. D. B. J. Appl. Phys., 39, 457 (1968).

    Article  CAS  Google Scholar 

  122. Woods, A. D. B. Canadian J. of Physics, 46, 1499 (1968).

    Article  CAS  Google Scholar 

  123. Uhrich, D. L. and Barnes, R. G. Phys. Rev., 164, 428 (1967).

    Article  CAS  Google Scholar 

  124. Hirst, L. L., Williams, G., Griffiths, D. and Coles, B. R. J. Appl. Phys., 39, 844 (1968).

    Article  CAS  Google Scholar 

  125. Williams, G. and Hirst, L. L. Phys. Rev., 185, 407 (1970).

    Article  Google Scholar 

  126. Griffiths, D. and Coles, B. R. Phys. Rev. Letters, 16, 1093 (1966).

    Article  CAS  Google Scholar 

  127. Sugawara, T. and Soga, R. J. Phys. Soc. Japan, 18, 1102 (1963).

    Article  CAS  Google Scholar 

  128. Nagasawa, H. and Sugawara, T. J. Phys. Soc. Japan, 23, 701 (1967).

    Article  CAS  Google Scholar 

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  1. General Electric Research and Development Center, Schenectady, New York, 12301, USA

    Bernard R. Cooper

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    R. J. Elliott

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Cooper, B.R. (1972). Phenomenological Theory of Magnetic Ordering: Importance of Interactions with the Crystal Lattice. In: Elliott, R.J. (eds) Magnetic Properties of Rare Earth Metals. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-5691-3_2

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