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Quantum Theory of Spin Wave Gap in Ultrathin Magnetic Films

  • B. Kaplan
  • R. Kaplan
Original Paper
  • 91 Downloads

Abstract

A simple quantum model is presented for the spin wave energy gap in single-layer and thin magnetic films that include both the magnetic out-of-plane and in-plane anisotropies. The films are assumed to be under the influence of the out-of-plane direction of the applied magnetic field at zero temperature. The calculated equations present a nonzero spin wave gap at zero magnetic field which is strongly affected by anisotropies. The effects of the film thickness and the role of the applied field are also examined. We discuss the results in connection with experimental data reported for nanocrystalline amorphous CoFeB films with growth-induced anisotropy.

Keywords

Magnetic anisotropy Spin wave gap Ultrathin film 

References

  1. 1.
    Bland, J.A.C., Heinrich, B.: Ultrathin Magnetic Structures. Springer, Berlin (1994)CrossRefGoogle Scholar
  2. 2.
    Schulte, O., et al.: Phys. Rev. B 52, 6480 (1995)ADSCrossRefGoogle Scholar
  3. 3.
    Hillebrands, B.: Phys. Rev. B 41, 530 (1990)ADSCrossRefGoogle Scholar
  4. 4.
    Stamps, R.L., Hillebrands, B.: Phys. Rev. B 43, 3532 (1991)ADSCrossRefGoogle Scholar
  5. 5.
    Stamps, R.L., Hillebrands, B.: Phys. Rev. B 44, 12417 (1991)ADSCrossRefGoogle Scholar
  6. 6.
    Krams, P., et al.: Phys. Rev. B 49, 3633 (1994)ADSCrossRefGoogle Scholar
  7. 7.
    Gubbiotti, G., et al.: J. Phys. C 10, 2171 (1998)Google Scholar
  8. 8.
    Kachkachi, H., Schmool, D.S.: Eur. Phys. J. B 56, 27 (2007)ADSCrossRefGoogle Scholar
  9. 9.
    Wu, C., et al.: J. Appl. Phys. 103, 07B525 (2008)Google Scholar
  10. 10.
    Tacchi, S., et al.: Surface Science 600, 4147 (2006)ADSCrossRefGoogle Scholar
  11. 11.
    Nguyen, T.M., Cottam, M.G.: Phys. Rev. B 71, 094406–1 (2005)ADSCrossRefGoogle Scholar
  12. 12.
    Manuilov, S.A., Grishin, A.M.: J. Appl. Phys. 108, 013902 (2010)ADSCrossRefGoogle Scholar
  13. 13.
    Manuilov, S.A., et al.: J. Appl. Phys. 109, 083926 (2011)ADSCrossRefGoogle Scholar
  14. 14.
    Pappas, D.P., et al.: Phys. Rev. Lett. 64, 3179 (1990)ADSCrossRefGoogle Scholar
  15. 15.
    Allenspach, R., Bischof, A.: Phys. Rev. Lett. 69, 3385 (1992)ADSCrossRefGoogle Scholar
  16. 16.
    Qiu, Z.Q., et al.: Phys. Rev. Lett. 70, 1006 (1993)ADSCrossRefGoogle Scholar
  17. 17.
    Krebs, J.J., et al.: J. Appl. Phys. 63, 3467 (1988)ADSCrossRefGoogle Scholar
  18. 18.
    Stampanoni, M., et al.: Phys. Rev. Lett. 59, 2483 (1987)ADSCrossRefGoogle Scholar
  19. 19.
    Kaplan, B., Kaplan, R.: J. Magn. Magn. Mater. 356, 95 (2014)ADSCrossRefGoogle Scholar
  20. 20.
    Kaplan, B., Kaplan, R.: J. Magn. Magn. Mater. 372, 33 (2014)ADSCrossRefGoogle Scholar
  21. 21.
    Jackson, J.D.: Mathematics for Quantum Mechanics. Dover Publications, New York (2006)Google Scholar
  22. 22.
    Holstein, T., Primakoff, H.: Phys. Rev. 58, 1098 (1940)ADSCrossRefGoogle Scholar
  23. 23.
    Gasiorowicz, S.: Quantum Physics. Wiley (1974)Google Scholar
  24. 24.
    Kittel, C.: Quantum Theory of Solids. Wiley (1987)Google Scholar
  25. 25.
    Crangle, J.: Solid State Magnetism, Edward Arnold, A division of Holder & Stouhton (1991)Google Scholar
  26. 26.
    Krams, P., et al.: Phys. Rev. Lett. 69, 3674 (1992)ADSCrossRefGoogle Scholar
  27. 27.
    Krams, P., et al.: J. Magn. Magn. Mater. 121, 483 (1992)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Secondary Science and Mathematics EducationUniversity of MersinMersinTurkey

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