The Symmetry Properties of Magnetoelastic Waves and the Determination of Selection Rules for Magnon-Phonon Interactions

  • Arthur P. Cracknell


Ever since the classic paper by Bouckaert, Smoluchowski and Wigner [1], group theory has been used extensively in connection with the electronic energy bands of crystalline solids. As a result of a well known theorem owing to Wigner, the wave function of an electron in a given energy band in some crystalline material must belong to, that is it must transform according to, one of the irreducible representations of the space group of the material. Consequently, the irreducible representations of the space groups have been used extensively in labelling electronic energy bands, in simplifying the forms of electronic wave functions, and in determining selection rules for processes involving electronic transitions (for references, see, e. g., the bibliography given by Bradley and Cracknell [2]). It is only much more recently that these ideas have begun to be applied to other particles or quasi-particle excitations in crystalline solids, such as phonons and magnons.


Dispersion Relation Irreducible Representation Brillouin Zone Selection Rule Spin Wave 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bouckaert, L.P., Smoluchowski, R. and Wigner, E. (1936). Phys. Rev., 50, 58.ADSMATHCrossRefGoogle Scholar
  2. 2.
    Bradley, C.J. and Cracknell, A.P. (1972). The Mathematical Theory of Symmetry in Solids: Representation Theory for Point Groups and Space Groups, (Clarendon Press, Oxford).MATHGoogle Scholar
  3. 3.
    Cowley, R.A. (1964). Phys. Rev., 134, A981.ADSCrossRefGoogle Scholar
  4. 4.
    Johnson, F.A. and Loudon, R. (1964). Proc. Roy. Soc., A281, 274.ADSGoogle Scholar
  5. 5.
    Poulet, H. (1965). J. Phys. (Paris), 26, 684.CrossRefGoogle Scholar
  6. 6.
    Maradudin, A.A. and Vosko, S.H. (1968). Rev. Mod. Phys., 40, 1.ADSCrossRefGoogle Scholar
  7. 7.
    Warren, J.L. (1968). Rev. Mod. Phys., 40, 38.ADSCrossRefGoogle Scholar
  8. 8.
    Montgomery, H. (1969). Proc. Roy. Soc., A309, 521.ADSGoogle Scholar
  9. 9.
    Loudon, R. (1968). Adv. Phys., 17, 243.ADSCrossRefGoogle Scholar
  10. 10.
    Joshua, S.J. and Cracknell, A.P. (1969). J. Phys., C2, 24.ADSGoogle Scholar
  11. 11.
    Daniel, M.R. and Cracknell, A.P. (1969). Phys. Rev., 117, 932.ADSCrossRefGoogle Scholar
  12. 12.
    Cracknell, A.P. and Joshua, S.J. (1969). Proc. Camb. Phil. Soc., 66, 493.ADSCrossRefGoogle Scholar
  13. 13.
    Cracknell, A.P. (1970). J. Phys., Met. Phys. Suppl., C3, S175.ADSGoogle Scholar
  14. 14.
    Cracknell, A.P. (1969). Lectures, Sixth Annual Winter School of Theoretical Physics, Karpacz, February 16–March 1, 1969; (1969). Rep. Prog. Phys., 32, 633.ADSCrossRefGoogle Scholar
  15. 15.
    Worlton, T.G. and Warren, J.L. (1972). Comput. Phys. Commun., 3, 88.ADSCrossRefGoogle Scholar
  16. 16.
    Dolling, G. and Cowley, R.A. (1966). Phys. Rev. Lett., 16, 683.ADSCrossRefGoogle Scholar
  17. 17.
    Jensen, J. (1971). Int. J. Mag., 1, 271.ADSGoogle Scholar
  18. 18.
    Liu, S.H. (1972). Phys. Rev. Lett., 29, 793.ADSCrossRefGoogle Scholar
  19. 19.
    Mackintosh, A.R. and Møller, H.B. (1972). Spin Waves, in Magnetic Properties of Rare Earth Metals, (ed. Elliot, R.J. Plenum Press, London), p. 187.Google Scholar
  20. 20.
    Cracknell, A.P. (1974). J. Phys., F4, 466.ADSCrossRefGoogle Scholar
  21. 21.
    Cracknell, A.P. (1973). J. Phys., C6, 1054.ADSGoogle Scholar
  22. 22.
    Montgomery, H. and Cracknell, A.P. (1973). J. Phys., C6, 3156.ADSGoogle Scholar
  23. 23.
    Wigner, E.P. (1959). Group Theory and Its Application to The Quantum Mechanics of Atomic Spectra, (Academic Press, New York).MATHGoogle Scholar
  24. 24.
    Rainford, B.D., Houmann, J.G. and Guggenheim, H.J. (1972). Neutron Inelastic Scattering 1972. Proceedings of a Symposium, Grenoble 6–10 March 1972, (IAEA, Vienna), p. 655.Google Scholar
  25. 25.
    Akhiezer, A.I., Bar’yakhtar, V.G. and Peletminskii, S.V. (1968). Spin Waves, (North-Holland, Amsterdam).Google Scholar
  26. 26.
    Montgomery, H. and Dolling, G. (1972). J. Phys. Chem. Solids, 33, 1201.ADSCrossRefGoogle Scholar
  27. 27.
    Herring, C. (1937). Phys. Rev., 52, 365.ADSCrossRefGoogle Scholar
  28. 28.
    Brinkman, W.F. and Elliott, R.J. (1966). J. Appl. Phys., 37, 1457.ADSCrossRefGoogle Scholar
  29. 29.
    Brinkman, W.F. and Elliott, R.J. (1966). Proc. Roy Soc., A294, 343.ADSGoogle Scholar
  30. 30.
    Miller, S.C. and Love, W.F. (1967). Tables of Irreducible Representations of Space Groups and Co-Representations of Magnetic Space Groups, (Pruett Press, Boulder, Colorado).Google Scholar
  31. 31.
    Altmann, S.L. and Bradley, C.J. (1965). Rev. Mod. Phys., 37, 33.MathSciNetADSCrossRefGoogle Scholar
  32. 32.
    Sedaghat, A.K. and Cracknell, A.P. (1974). Physica, 71, 615.ADSCrossRefGoogle Scholar
  33. 33.
    Koehler, W.C., Child, H.R., Nicklow, R.M., Smith, H.G., Moon, R.M. and Cable, J.W. (1970). Phys. Rev. Lett., 24, 16.ADSCrossRefGoogle Scholar
  34. 34.
    Møller, H.B., Houmann, J.G., Jensen, J., and Mackintosh, A.R. (1972). Neutron Inelastic Scattering 1972. Proceedings of a Symposium, Grenoble 6–10 March 1972, (IAEA, Vienna), p. 603.Google Scholar
  35. 35.
    Nicklow, R.M. and Wakabayashi, N. (1971). AIP Conference Proceedings, No. 5; Magnetism and Magnetic Materials, p. 1446.Google Scholar
  36. 36.
    Nicklow, R.M. and Wakabayashi, N. (1972). Neutron Inelastic Scattering. Proceedings of a Symposium, Grenoble 6–10 March 1972, (IAEA, Vienna), p. 611.Google Scholar
  37. 37.
    Dimmock, J.O. and Wheeler, R.G. (1962). Phys. Rev., 127, 391.MathSciNetADSMATHCrossRefGoogle Scholar
  38. 38.
    Katiyar, R.S. (1970). J. Phys., C3, 1087.ADSGoogle Scholar
  39. 39.
    Kittel, C. (1963). Quantum Theory of Solids, (Wiley, New York).Google Scholar
  40. 40.
    Lovesey, S.W. (1972). J. Phys., C5, 2769.ADSGoogle Scholar
  41. 41.
    Huberman, B.A. and Burstein, E. (1971). AIP Conference Proceedings, No.5: Magnetism and Magnetic Materials, p. 1350.Google Scholar

Copyright information

© Plenum Press, New York 1976

Authors and Affiliations

  • Arthur P. Cracknell
    • 1
  1. 1.Carnegie Laboratory of PhysicsUniversity of DundeeDundeeScotland

Personalised recommendations