Spin Wave Resonance Frequency in the Bilayer Ferromagnetic Film

  • Shu-Hui Zhang
  • Jian-hong Rong
  • Huan Wang
  • Dong Wang
  • Lei Zhang
Original Paper


The dependence of spin wave resonance (SWR) frequency on the surface anisotropy, the interlayer and interfacial coupling, the ferromagnetic layer thickness and the external magnetic field in the bilayer ferromagnetic film have been investigated by using the linear spin wave approximation and Green’s function technique. We find that the SWR frequency of the ferromagnetic bilayer films are shifted to higher values corresponding to those of above factors, respectively. The mode of the energetically highest can be controlled by the interfacial coupling, the thickness and the symmetry of the film. The SWR frequency of mode number m = 1 is almost flat except for applied magnetic field. Analytical details and the validity of the method are shown and discussed.


Spin wave resonance Surface anisotropy Interlayer and interfacial coupling 



The work was supported by the National Natural Science Foundation of China under Grant No. 11072104, and by the Science and Technology Research Projects in Colleges and Universities of Inner Mongolia of China under Grant Nos. NJZY16014 and NJZY13072, and by the Nature Science Foundation of Inner Mongolia of China under Grant No. 2012MS110.


  1. 1.
    Ikeda, K., Kobayashi, K., Ohta, K., Kondo, R., Suzuki, T., Fujimoto, M.: IEEE Trans. Magn. 39, 3057 (2003)ADSCrossRefGoogle Scholar
  2. 2.
    Qiu, R.K., Ma, F.J., Zhang, Z.D.: J. Magn. Magn. Mater. 394, 454 (2015)ADSCrossRefGoogle Scholar
  3. 3.
    Lassri, M., Salhi, H., Moubah, R., Lassri, H.: Bull. Mater. Sci. 39, 4 (2016)CrossRefGoogle Scholar
  4. 4.
    Qiu, R.K., Cai, W.: J. Magn. Magn. Mater. 436, 68 (2017)ADSCrossRefGoogle Scholar
  5. 5.
    Abe, M., Shames, A.I., Matsushita, N., Shimada, Y.: IEEE Trans. Magn. 39, 3142 (2003)ADSCrossRefGoogle Scholar
  6. 6.
    Han, Z., Li, D., Liu, X.G., Geng, D.Y., Li, J., Zhang, Z.D.: J. Phys. D: Appl. Phys. 42, 055008 (2009)ADSCrossRefGoogle Scholar
  7. 7.
    Naito, Y., Suetake, K.: IEEE Trans. Microw. Theory Tech. 19, 65 (1971)ADSCrossRefGoogle Scholar
  8. 8.
    Kim, D.Y., Chung, Y.C., Kang, T.W., Kim, H.C.: IEEE Trans. Magn. 32, 555 (1996)ADSCrossRefGoogle Scholar
  9. 9.
    Snoek, J.L.: Nature 160, 90 (1947)ADSCrossRefGoogle Scholar
  10. 10.
    Zhang, Z., Zhou, L., Wigen, P.E.: Phys. Rev. B 50, 6094 (1994)ADSCrossRefGoogle Scholar
  11. 11.
    Chen, J.W., Tang, D.M., Zhang, B.S., Tilley, D.R.: J. Phys. Condens. Matter 19, 346227 (2007)CrossRefGoogle Scholar
  12. 12.
    Qiu, R.K., Song, P.P., Zhang, Z.D.: J. Magn. Magn. Mater. 321, 3031 (2009)ADSCrossRefGoogle Scholar
  13. 13.
    Puszkarki, H., Tomczak, P.: Sci. Rep. 4, 6135 (2014)ADSCrossRefGoogle Scholar
  14. 14.
    Qiu, R.K., Huang, A.D., Li, D., Zhang, Z.D.: J. Phys. D: Appl. Phys. 44, 415002 (2011)CrossRefGoogle Scholar
  15. 15.
    Chai, G.Z., Yang, Y.C., Zhu, J.Y., Lin, M., Sui, W.B., Guo, D.W., Li, X.L., Xue, D.S.: Appl. Phys. Lett. 96, 012505 (2010)ADSCrossRefGoogle Scholar
  16. 16.
    Wang, Z.K., Feng, E., Wang, W.W., Ma, Z., Liu, Q.F., Wang, J.B., Xue, D.S.: J. Alloys Compd. 543, 197 (2012)CrossRefGoogle Scholar
  17. 17.
    Baek, J.S., Park, Y.J., Kim, Y.Y., Lim, W.Y.: IEEE Trans. Magn. 35, 5 (1999)CrossRefGoogle Scholar
  18. 18.
    Lassri, H., Ouahmane, H., Berrada, A., Kaabouchi, A., Dinia, A., Krishnan, R.: J. Magn. Magn. Mater. 272, E973 (2004)ADSCrossRefGoogle Scholar
  19. 19.
    Ren, Y.H., Wu, C., Gong, Y., Pettiford, C., Sun, N.X.: J. Appl. Phys. 105, 07D304 (2009)CrossRefGoogle Scholar
  20. 20.
    Chai, G.Z., Xue, D.S., Fan, X.L., Li, X.L., Guo, D.W.: Appl. Phys. Lett. 93, 152516 (2008)ADSCrossRefGoogle Scholar
  21. 21.
    Greve, H., Pochstein, C., Takele, H., Zaporojtchenko, V., Faupel, F., Gerber, A., Frommberger, M., Quandt, E.: Appl. Phys. Lett. 89, 242501 (2006)ADSCrossRefGoogle Scholar
  22. 22.
    Yang, X., Gong, L.Q., Wei, J.Q., Qiao, L., Wang, T., Li, F.S.: J. Phys. D: Appl. Phys. 43, 215002 (2010)ADSCrossRefGoogle Scholar
  23. 23.
    Cottam, M.G., Slavin, A.N.: Linear and Nonlinear Spin Waves in Magnetic Films and Superlattices. World Scientific, Singapore (1994)CrossRefGoogle Scholar
  24. 24.
    Kruglyak, V.V., Davies, C.S., Tkachenko, V.S., Gorobets, O.Y., Gorobets, Y.I., Kuchko, A.N.: J. Phys. D: Appl. Phys. 50, 094003 (2017)ADSCrossRefGoogle Scholar
  25. 25.
    Grünberg, P., Barnas, J., Saurenbach, F., Fuss, J.A., Wolf, A., Vohl, M.: J. Magn. Magn. Mater. 93, 58 (1991)ADSCrossRefGoogle Scholar
  26. 26.
    Vohl, M., Wolf, J.A., Grünberg, P., Spörl, K., Weller, D., Zeper, B.: J. Magn. Magn. Mater. 93, 403 (1991)ADSCrossRefGoogle Scholar
  27. 27.
    Wang, Z.J., Mitsudo, S., Watanabe, K., Awaji, S., Saito, K., Fujimori, H., Motokawa, M.: J. Magn. Magn. Mater. 176, 127 (1997)ADSCrossRefGoogle Scholar
  28. 28.
    de Sousa, M.A., Pelegrini, F., Alayo, W., Quispe-Marcatoma, J., Baggio-Saitovitch, E.: Physica B: Condens. Matter. 450, 167 (2014)ADSCrossRefGoogle Scholar
  29. 29.
    Kaplan, B., Kapian, R.: J. Supercond. Nov. Magn. 29, 124953 (2016)Google Scholar
  30. 30.
    Khivintsev, Y.V., Reisman, L., Lovjoy, J., Adam, R., Schneider, C.M., Camley, R.E., Celinski, Z.J.: J. Appl. Phys. 108, 023907 (2010)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Inner Mongolia Key Lab of Nanoscience and Nanotechnology and School of Physical Science and TechnologyInner Mongolia UniversityHohhotPeople’s Republic of China
  2. 2.College of ScienceInner Mongolia Agricultural UniversityHohhotPeople’s Republic of China

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