Skip to main content
SpringerLink
Log in

Spin Waves

  • Chapter
Magnetic Properties of Rare Earth Metals

Abstract

In this chapter, we will review the knowledge which has been accumulated over the last few years on spin waves in the rare earth metals, and describe the way in which this information may be interpreted to elucidate the magnetic interactions which give rise to their characteristic magnetically ordered structures. Most of the discussion will be concerned with the hcp heavy rare earths, since the magnetic excitations in the light rare earths, which are complicated by strong crystal field effects, have not yet been extensively studied. Recent measurements on praseodymium will, however, be briefly described. The great majority of the information which has been obtained about the dispersion relations for the spin wave quanta, or magnons, has resulted from inelastic neutron scattering experiments since these allow, in principle and often even in practice, the determination of the magnon energy at any point in the Brillouin zone, as well as providing much valuable additional information about magnon interactions. An important supplementary technique is provided by the absorption of electromagnetic waves, which, however, only determines the magnon energies at certain high symmetry points within the zone. In addition, some information may be obtained from the low-temperature thermodynamic and transport properties, although the number of explicit features of the magnon dispersion relations which can be deduced from them is extremely limited. However, they do provide a useful check on the consistency of the measured or calculated magnon spectrum.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Liu, S. H., Phys. Rev., 121, 451 (1961).

    Article  CAS  Google Scholar 

  2. Ruderman, M. A. and Kittel, C., Phys. Rev., 96, 99 (1954)

    Article  CAS  Google Scholar 

  3. Kasuya, T., Prog. T.eor. Phys. (Kyoto), 16, 45 (1956)

    Article  Google Scholar 

  4. Yosida, K., Phys. Rev., 106, 893 (1957).

    Article  Google Scholar 

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

    Article  Google Scholar 

  6. Kasuya, T. and Lyons, D. H., J. Phys. Soc. Japan, 21, 287 (1965).

    Google Scholar 

  7. Levy, P. M., Solid State Commun., 7, 1813 (1969)

    Article  CAS  Google Scholar 

  8. See Chapters 1 and 2.

    Google Scholar 

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

    CAS  Google Scholar 

  10. English trans.: Soviet Phys. Solid State, 7, 166 (1965).

    Google Scholar 

  11. Lindgârd, P. A. J. de Physique, 32, CI-238 (1971)

    Google Scholar 

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

    Article  Google Scholar 

  13. Koehler, W. C., Child, H. R., Nicklow, R. M., Smith, H. G., Moon, R. M., and Cable, J. W., Phys. Rev. Letters, 24, 16 (1970).

    Article  CAS  Google Scholar 

  14. Holstein, T. D. and Primakoff, H., Phys. Rev., 58, 1098 (1940);

    Article  Google Scholar 

  15. Brooks, M. S. S., Phys. Rev., BI, 2257 (1970)

    Google Scholar 

  16. Goodings, D. A. and Southern, B. W., Can. J. Phys. 49, 1157 (1971).

    Google Scholar 

  17. Niira, K., Phys. Rev., 117, 129 (1960).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  19. Cracknell, A. P., J. Phys. C, 3, S175 (1970).

    Article  CAS  Google Scholar 

  20. See e.g. Lomer, W. M. and Low, G. G., in Thermal Neutron Scattering ( P. A. Egelstaff, Ed.). ( Academic Press, London, 1965 ), p. 2.

    Google Scholar 

  21. Brooks, M. S. S., Goodings, D. A., and Ralph, H. I., J. Phys. C, 1, 132 (1968).

    Article  Google Scholar 

  22. Trammell, G. T., Phys. Rev., 92, 1387 (1953); see also Lovesey, S. W. and Rimmer, D. E., Rep. Frog. Phys., 32, 333 (1969).

    Google Scholar 

  23. Steinsvoll, O., Shirane, G., Nathans, R., Blume, M., Alperin, H. A., and Pickart, S. J., Phys. Rev., 161, 499 (1967).

    Article  CAS  Google Scholar 

  24. Lindgârd, P. A., Kowalska, A., and Laut, P., J. Phys. Chem. Solids, 28, 1357 (1967).

    Article  Google Scholar 

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

    Article  Google Scholar 

  26. Moller, H. Bjerrum, Houmann, J. C. G., and Mackintosh, A. R., J. Appl. Phys., 39, 807 (1968)

    Article  Google Scholar 

  27. Moller, H. Bjerrum, in Neutron Inelastic Scattering ( IAEA, Vienna, 1968 )

    Google Scholar 

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

    Article  CAS  Google Scholar 

  29. Moller, H. Bjerrum, Nielsen, M., and Mackintosh, A. R., in Les Eléments des Terres Rares ( CNRS, Paris, 1970 ), Vol. II, p. 277.

    Google Scholar 

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

    Article  CAS  Google Scholar 

  31. Nicklow, R. M., Wakabayashi, N., Wilkinson, M. K., and Reed, R. E., Phys. Rev. Letters, 26, 140 (1971).

    Article  CAS  Google Scholar 

  32. Moller, H. Bjerrum, Houmann, J. C. G., Nielsen, M., and Mackintosh, A. R., (to be published).

    Google Scholar 

  33. Lindgârd, P. A., (private communication).

    Google Scholar 

  34. Stringfellow, M. W. and Windsor, C. G., Proc. Phys. Soc., 92, 408 (1967).

    Article  CAS  Google Scholar 

  35. Houmann, J. C. G., Solid State Commun., 6, 479 (1968).

    Article  Google Scholar 

  36. Cooper, B. R. Phys. Rev., 169, 281 (1968); Lindgârd, P. A. J. de Physique, 32, CI-238 (1971).

    Google Scholar 

  37. Nielsen, M., Moller, H. Bjerrum, Lindgârd, P. A., and Mackintosh, A. R., Phys. Rev. Letters, 25, 1451 (1970).

    Article  CAS  Google Scholar 

  38. Mackintosh, A. R., Phys. Letters, 4, 140 (1963).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  40. Rossol, F. C. and Jones, R. V., J. Appl. Phys., 37, 1227 (1966)

    Article  CAS  Google Scholar 

  41. Bagguley, D. M. S. and Liesegang, J., Proc. Roy. Soc., A300, 497 (1967).

    Article  CAS  Google Scholar 

  42. Marsh, H. S. and Sievers, A. J., J. Appl. Phys., 40, 1563 (1969)

    Article  CAS  Google Scholar 

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

    Google Scholar 

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

    Article  CAS  Google Scholar 

  45. Wagner, T. K. and Stanford, J. L., Phys. Rev., Bl, 4488 (1970).

    Google Scholar 

  46. Feron, J. L., Hug, G., and Pauthenet, R., in Les Eléments des Terres Rares (CNRS, Paris, 1970), Vol. II, p. 19; see also Chapter 4.

    Google Scholar 

  47. Callen, H. B. and Callen, E., J. Phys. Chem. So.ids, 27, 1271 (1966).

    Article  CAS  Google Scholar 

  48. Brooks, M. S. S., Phys. Rev., Bl, 2257 (1970)

    Google Scholar 

  49. Kasuya, T., in Magnetism (G. T. Rado and H. Suhl, eds.). (Academic Press, New York 1966), Vol. IIB, p. 215.

    Google Scholar 

  50. Moller, H. Bjerrum, Thesis, University of Copenhagen (1968).

    Google Scholar 

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

    Article  Google Scholar 

  52. Baryakhtar, V. G. and Maleev, S. V., Fiz. Tverd. Tela, 5, 1175 (1963).

    CAS  Google Scholar 

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

    Article  Google Scholar 

  54. Nicklow, R. M., Mook, H. A., Smith, H. G., Reed, R. E., and Wilkinson, M. K., J. Appl. Phys., 40, 1452 (1969).

    Article  CAS  Google Scholar 

  55. Nicklow, R. M., Houmann, J. C. G., and Mook, H. A., (to be published).

    Google Scholar 

  56. Stringfellow, M. W., Holden, T. M., Powell, B. M., and Woods, A. D. B., J. Phys. C, 2, S189 (1970).

    Article  Google Scholar 

  57. Elliott, R. J. and Lange, R. V., Phys. Rev., 152, 235 (1966).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  59. Sherrington, D., (to be published).

    Google Scholar 

  60. Elliott, R. J., (private communication).

    Google Scholar 

  61. Woods, A. D. B., Holden, T. M., and Powell, B. M. Phys. Rev. Letters, 19, 908 (1967)

    Article  CAS  Google Scholar 

  62. Nicklow, R. M., Wakabayashi, N., Wilkinson, M. K., and Reed, R. E. Phys. Rev. Letters (1971)

    Google Scholar 

  63. Holden, T. M., Powell, B. M., Stringfellow, M. W., and Woods, A. D. B. J. Appl. Phys., 41, 1176 (1970).

    Article  CAS  Google Scholar 

  64. Nagamiya, T., Nagata, K., and Kitano, Y., Frog. Theor. Phys. (Kyoto), 31, 1 (1964).

    Article  Google Scholar 

  65. Cooper, B. R. and Elliott, R. J., Phys. Rev., 131, 1043 (1963)

    Article  CAS  Google Scholar 

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

    Google Scholar 

  67. Rossol, F. C., Thesis, Harvard University ( 1966 ); Liesegang, J., Thesis, Oxford University (1966).

    Google Scholar 

  68. Brooks, M. S. S., Goodings, D. A., and Ralph, H. I., J. Phys. C, 2, 1596 (1968).

    Article  Google Scholar 

  69. Hegland, D. E., Legvold, S., and Spedding, F. H., Phys. Rev., 131, 158 (1963)

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  71. Lounasmaa, O. V. and Sundström, L. J., Phys. Rev., 150, 399 (1966).

    Article  CAS  Google Scholar 

  72. Houmann, J. C. G. and Nicklow, R. M. Phys. Rev., Bl, 3943 (1970).

    Google Scholar 

  73. Elliott, R. J. and Stern, H., in Inelastic Scattering of Neutrons ( IAEA, Vienna, 1961 ), p. 61.

    Google Scholar 

  74. Dyson, F. J., Phys. Rev., 102, 1217 (1956)

    Article  Google Scholar 

  75. Bloch, M., Phys. Rev. Letters, 9, 286 (1962).

    Article  Google Scholar 

  76. Tyablikov, S. V., Ukr. Math. Zh., 11, 287 (1959);

    Article  Google Scholar 

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

    Article  Google Scholar 

  78. Kascheev, V. N. and Krivoglaz, M. A., Fiz. Tverd. Tela, 3, 3167 (1961).

    Google Scholar 

  79. Nielsen, M. and Moller, H. Bjerrum, Acta Cryst., A25, 547 (1969).

    Article  Google Scholar 

  80. Jensen, J. Intern. J. Magnetism, 1, 271 (1971).

    CAS  Google Scholar 

  81. Mason, W. P., Phys. Rev., 96, 302 (1954).

    Article  CAS  Google Scholar 

  82. Wolfram, T. and Callaway, J., Phys. Rev., 130, 2207 (1963).

    Google Scholar 

  83. Blackman, J. A., J. Phys. Chem. Solids, 31, 1573 (1970).

    Article  CAS  Google Scholar 

  84. Kasuya, T., Prog. T.eor. Phys. (Kyoto), 16, 45 (1956).

    Google Scholar 

  85. Kasuya, T., Prog. T.eor. Phys. (Kyoto), 22, 227 (1959).

    Google Scholar 

  86. Mannari, I., Prog. Theor. Phys. (Kyoto), 22, 335 (1959).

    Google Scholar 

  87. Brun, T. O., (1965-unpublished).

    Google Scholar 

  88. Sze, N. H., Rao, K. V., and Meaden, G. T., J. Low Temp. Phys, 1, 563 (1969).

    Article  CAS  Google Scholar 

  89. Mackintosh, A. R. and Spanel, L. E., Solid State Commun., 2, 383 (1964).

    Article  CAS  Google Scholar 

  90. Koehler, W. C., Cable, J. W., Wilkinson, M. K., and Wollan, E. O., Phys. Rev., 151, 414 (1966).

    Article  CAS  Google Scholar 

  91. See Mackintosh, A. R. J. de Physique, 32, C1–482 (1971).

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  93. Parkinson, D. A., Simon, F. E., and Spedding, F. H., Proc. Roy. Soc., A207, 137 (1951).

    Article  CAS  Google Scholar 

  94. Johansson, T., Lebech, B., Nielsen, M., Bjerrum Moller, H. and Mackintosh, A. R. Phys. Rev. Letters, 25, 524 (1970); Johansson, T., J. de Physique, 32, C1–372 (1971).

    Article  Google Scholar 

  95. Trammell, G. T., J. Appl. Phys., 31, 362S (1960).

    Article  Google Scholar 

  96. Rainford, B. D. and Houmann, J. C. G. Phys. Rev. Letters, 26, 1254 (1971).

    Article  CAS  Google Scholar 

  97. Bjerrum Moller, H., Houmann, J. C. G., Jensen, J. and Mackintosh, A. R. in Neutron Inelastic Scattering (IAEA, Vienna, to be published) have studied the anisotropy of the exchange in terbium by measuring the magnetic field dependence of the magnon energy, as a function of q in the c-direction. They find that, if the exchange is written as in (5.45), with a different parameter multiplying each Cartesian component, its isotropic and anisotropic components have the same order of magnitude.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. H.C. Ørsted Institute, University of Copenhagen, Denmark

    A. R. Mackintosh

  2. Atomic Energy Commission Research Establishment, Risø, Roskilde, Denmark

    H. Bjerrum Møller

Authors
  1. A. R. Mackintosh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. Bjerrum Møller
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Theoretical Physics, University of Oxford, Parks Road, Oxford, England

    R. J. Elliott

Rights and permissions

Reprints and permissions

Copyright information

© 1972 Springer Science+Business Media New York

About this chapter

Cite this chapter

Mackintosh, A.R., Møller, H.B. (1972). Spin Waves. In: Elliott, R.J. (eds) Magnetic Properties of Rare Earth Metals. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-5691-3_5

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-5691-3_5

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4757-5693-7

  • Online ISBN: 978-1-4757-5691-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation