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Quantum Theory of Spin Wave Gap in Ultrathin Magnetic Films

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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.

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References

  1. Bland, J.A.C., Heinrich, B.: Ultrathin Magnetic Structures. Springer, Berlin (1994)

    Book  Google Scholar 

  2. Schulte, O., et al.: Phys. Rev. B 52, 6480 (1995)

    Article  ADS  Google Scholar 

  3. Hillebrands, B.: Phys. Rev. B 41, 530 (1990)

    Article  ADS  Google Scholar 

  4. Stamps, R.L., Hillebrands, B.: Phys. Rev. B 43, 3532 (1991)

    Article  ADS  Google Scholar 

  5. Stamps, R.L., Hillebrands, B.: Phys. Rev. B 44, 12417 (1991)

    Article  ADS  Google Scholar 

  6. Krams, P., et al.: Phys. Rev. B 49, 3633 (1994)

    Article  ADS  Google Scholar 

  7. Gubbiotti, G., et al.: J. Phys. C 10, 2171 (1998)

    Google Scholar 

  8. Kachkachi, H., Schmool, D.S.: Eur. Phys. J. B 56, 27 (2007)

    Article  ADS  Google Scholar 

  9. Wu, C., et al.: J. Appl. Phys. 103, 07B525 (2008)

    Google Scholar 

  10. Tacchi, S., et al.: Surface Science 600, 4147 (2006)

    Article  ADS  Google Scholar 

  11. Nguyen, T.M., Cottam, M.G.: Phys. Rev. B 71, 094406–1 (2005)

    Article  ADS  Google Scholar 

  12. Manuilov, S.A., Grishin, A.M.: J. Appl. Phys. 108, 013902 (2010)

    Article  ADS  Google Scholar 

  13. Manuilov, S.A., et al.: J. Appl. Phys. 109, 083926 (2011)

    Article  ADS  Google Scholar 

  14. Pappas, D.P., et al.: Phys. Rev. Lett. 64, 3179 (1990)

    Article  ADS  Google Scholar 

  15. Allenspach, R., Bischof, A.: Phys. Rev. Lett. 69, 3385 (1992)

    Article  ADS  Google Scholar 

  16. Qiu, Z.Q., et al.: Phys. Rev. Lett. 70, 1006 (1993)

    Article  ADS  Google Scholar 

  17. Krebs, J.J., et al.: J. Appl. Phys. 63, 3467 (1988)

    Article  ADS  Google Scholar 

  18. Stampanoni, M., et al.: Phys. Rev. Lett. 59, 2483 (1987)

    Article  ADS  Google Scholar 

  19. Kaplan, B., Kaplan, R.: J. Magn. Magn. Mater. 356, 95 (2014)

    Article  ADS  Google Scholar 

  20. Kaplan, B., Kaplan, R.: J. Magn. Magn. Mater. 372, 33 (2014)

    Article  ADS  Google Scholar 

  21. Jackson, J.D.: Mathematics for Quantum Mechanics. Dover Publications, New York (2006)

    Google Scholar 

  22. Holstein, T., Primakoff, H.: Phys. Rev. 58, 1098 (1940)

    Article  ADS  Google Scholar 

  23. Gasiorowicz, S.: Quantum Physics. Wiley (1974)

  24. Kittel, C.: Quantum Theory of Solids. Wiley (1987)

  25. Crangle, J.: Solid State Magnetism, Edward Arnold, A division of Holder & Stouhton (1991)

  26. Krams, P., et al.: Phys. Rev. Lett. 69, 3674 (1992)

    Article  ADS  Google Scholar 

  27. Krams, P., et al.: J. Magn. Magn. Mater. 121, 483 (1992)

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Secondary Science and Mathematics Education, University of Mersin, Yenisehir Campus, 33169, Mersin, Turkey

    B. Kaplan & R. Kaplan

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  1. B. Kaplan
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  2. R. Kaplan
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Correspondence to B. Kaplan.

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Kaplan, B., Kaplan, R. Quantum Theory of Spin Wave Gap in Ultrathin Magnetic Films. J Supercond Nov Magn 29, 1249–1253 (2016). https://doi.org/10.1007/s10948-015-3362-5

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  • DOI: https://doi.org/10.1007/s10948-015-3362-5

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