ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Sharaevskaya A. Y., Popov P. A., Osokin S. A. Numerical simulation of magnetostatic waves propagation in coupled meander-type magnon crystals. Izvestiya VUZ. Applied Nonlinear Dynamics, 2020, vol. 28, iss. 4, pp. 425-434. DOI: 10.18500/0869-6632-2020-28-4-425-434

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
(downloads: 197)
Article type: 
537.613, 530.182, 622.4

Numerical simulation of magnetostatic waves propagation in coupled meander-type magnon crystals

Sharaevskaya Anna Yurevna, Saratov State University
Popov P. A., Kotel'nikov Institute of Radioengineering and Electronics of Russian Academy of Sciences
Osokin S. A., Kotel'nikov Institute of Radioengineering and Electronics of Russian Academy of Sciences

Purpose of the work is to generalize the results of numerical studies for coupled magnonic meander structures in the case of the propagation of various types of magnetostatic waves in such structures. Methods. In order to solve the problems two well-known methods were used – finite elements and finite differences for coupled ferromagnetic structures. For the numerical solution with the finite element method in the magnetostatic approximation, the magnetostatic equations derived from Maxwell’s equations were used. To calculate the internal effective fields, a micromagnetic simulations were carried out using the finite difference method. Results. The features of the propagation of magnetostatic spin waves in coupled periodic complex structures in the form of two coupled meander-type magnonic crystals separated by a dielectric layer based on numerical simulation by the finite element method are studied. It is shown that the method used allows one to obtain dispersion equations for surface, forward volume and backward volume magnetostatic spin waves propagating in such structures and to reveal the main features of the dispersion characteristics of these waves. Conclusion. It is shown that, under certain conditions, forbidden bands gaps appear in the spectra due to the Bragg reflection and the complex structure of the magnonic waveguide. The width and position of these forbidden zones depends on the parameters of the magnetic films, their geometric dimensions and the direction of the constant magnetic field. The results can be utilized in creating frequency-selective devices for the selective processing of information signals in the microwave range based on magnonic crystals.


1. Kruglyak V.V., Demokritov S.O., Grundler D. Magnonoics // Journal of Physics: Applied Physics. 2010. Vol. 43, no. 26. P. 264001.

2. Chumak A.V., Vasyuchka V.I., Serga A.A., Hillebrands B. Magnon spintronics // Nature Physics. 2015. Vol. 11, no. 6. P. 453.

3. Nikitov S.A., Kalyabin D.V., Lisenkov I.V. Magnonics: A new research area in spintronics and spin wave electronics. Phys. Usp., 2015, vol. 58, p. 1002. 

4. Nikitov S.A., Tailhades P., Tsai C.S. // J. Magn. Magn. Mater. 2001. Vol. 236, no. 3. P. 320.

5. Chumak A.V., Serga A.A., Hillebrands B. Spin waves in periodic magnetic structures – mangonic crystals // Journal of Physics: Applied Physics. 2017. Vol. 50, no. 24. P. 244001.

6. Sander D., Valenzuela S.O., Makarov D. et al. The 2017 magnetism roadmap // Journal of Physics: Applied Physics. 2017. Vol. 50, no. 36. P. 363001.

7. Krawczyk M., Puszkarski H. Plane-wave theory of three-dimensional magnonic crystals // Physical Review B. 2008. Vol. 77, no. 5. 054437.

8. Graczyk P., Krawczyk M., Dhuey S. et al. Magnonics band gap and mode hybridization in continuous permalloy film induced by vertical coupling with an array of permalloy ellipses//

9. Demidov V.E., Urazhdin S., Zholud A. et al. Spin-current nano-oscillator based on nonlocal spin injection // Scientific Reports. 2015. Vol. 5. P. 8578.

10. Demidov V.E., Kostylev M.P., Rott K. et al. Excitation of short-wavelength spin waves in magnonic waveguides // Applied Physics Letters. 2011. Vol. 99, no. 8. P. 082507.

11. Spin Wave Confinement – Propagating Waves / Ed. S.O. Demokritov. Singapore: Pan Stanford Publishing Pte. Ltd., 2017.

12. Morozova M., Sharaevskaya A., Sadovnikov A. et al. Band gap formation and control in coupled periodic ferromagnetic structures // Journal of Applied. Physics. 2016. Vol. 120, no. 22. P. 223901.

13. Beginin E.N., Sadovnikov A.V., Sharaevskaya A.Y. et al. Spin wave steering in three-dimensional magnonic networks // Applied Physics Letters. 2018. Vol. 112, no. 12. P. 122404.

14. Popov P.A., Sharaevskaya A.Yu., Beginin E.N. et al. Spin wave propagation in three-dimensional magnonic crystals and coupled structures // J. Magn. Magn. Mater. 2019. Vol. 476. P. 423–427.

15. Popov P.A., Sharaevskaya A.Yu., Kalyabin D.V., Stognii A.I., Beginin E.N, Sadovnikov A.V., Nikitov S.A. Magnetostatic Spin Waves in 3D Ferromagnetic Structures // Journal of Communications Technology and Electronics. 2018. Vol. 63, no. 12. P. 1431.

16. Stancil D.D., Prabhakar A. Spin Waves. Theory and Applications. N.Y.: Springer, 2009.

17. Kabos P., Stalmachov V. Magnetostatic Waves and their Application: Springer, 1994. P. 5–37. (Chapman & Hall, 1994).

18. Damon R.W., Eschbach J. Magnetostatic modes of a ferromagnet slab // J. Phys. Chem. Solids. 1961. Vol. 19, no. 3–4. P. 308.

19. Calculated using COMSOL Multiphysics software from COMSOL, Inc.

20. Vansteenkiste A., Leliaert J., Dvornik M. et al. The design and verification of MuMax3 // AIP Advances. 2014. Vol. 4, no. 10. P. 107133.