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Dudko G. M., Khivintsev Y. V., Sakharov V. K., Kozhevnikov A. V., Vysotskii S. L., Seleznev M. E., Filimonov Y. A. Micromagnetic modeling of self-focusing effect of backward volume magnetostatic waves in iron-yttrium garnet films. Izvestiya VUZ. Applied Nonlinear Dynamics, 2021, vol. 29, iss. 2, pp. 302-316. DOI: 10.18500/0869-6632-2021-29-2-302-316

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537.562.2; 537.862

Micromagnetic modeling of self-focusing effect of backward volume magnetostatic waves in iron-yttrium garnet films

Dudko Galina Mihajlovna, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Khivintsev Y. V., Saratov State University
Sakharov Valentin Konstantinovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Kozhevnikov Aleksandr Vladimirovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Vysotskii S. L., Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Seleznev M. E., Saratov State University
Filimonov Y. A., Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences

 Abstract. Topic. Micromagnetic modeling of the propagation of backward volume magnetostatic waves (MSBVW) beams, excited by an antenna, placed in the center of yttrium iron garnet (YIG) film, has been carried out. Aim. To explore MSBVWbeam focusing with an increase in the amplitude of the exciting field at the antenna under conditions when only four-magnon (4M) processes are allowed for the MSBVW. Methods. The problem was solved using micromagnetic modeling by the finite-difference method solving the Landau–Lifshitz equation using the OOMMF software package. Results. It is shown that, depending on the position of the signal frequency in the MSBVW spectrum, an increase in the amplitude of the input signal above a certain threshold can lead to both the effect of wave beam focusing due to the development of modulation instability and the spatiotemporal chaotization of the amplitude distribution in the beam due to 4M decay processes. Changing of MSBVW-beam instability character at the frequency variation is associated with a change in the angular spectrum width of the beam and interaction between MSBVW and so-called «width» modes of the film. The obtained results can be used to analyze the effects of the propagation of nonlinear spin waves in YIG film waveguides.

  1. Vashkovskii AV, Stal’makhov AV, Shakhnazaryan DG. Formation, reflection, and refraction of magnetostatic wave beams. Soviet Physics Journal. 1988;31(11):908–915. DOI: 10.1007/BF00893543.
  2. Vashkovskii AV, Stalmakhov AV, Tulukin VA, Shakhnazaryan DG. On the possibility of applying the methods of geometric optics to the creation of devices on magnetostatic waves. Soviet Journal of Communications Technology and Electronics. 1990;35(12):2606–2610 (in Russian).
  3. Vashkovskii AV, Stalmakhov AV, Sharaevskii YP. Magnetostatic Waves in Microwave Electronics. Saratov State University; 1993. 312 p (in Russian).
  4. Nikitov SA, Kalyabin DV, Lisenkov IV, Slavin AN, Barabanenkov YN, Osokin SA, Sadovnikov AV, Beginin EN, Morozova MA, Sharaevsky YP, Filimonov YA, Khivintsev YV, Vysotsky SL, Sakharov VK, Pavlov ES. Magnonics: a new research area in spintronics and spin wave electronics. Phys. Usp. 2015;58(10):1002–1028. DOI: 10.3367/UFNe.0185.201510m.1099.
  5. Csaba G, Papp A, and Porod W. Spin-wave based realization of optical computing primitives. J. Appl. Phys. 2014;115(17):17C741. DOI: 10.1063/1.4868921.
  6. Toedt JN, Mundkowski M, Heitmann D, Mendach S, Hansen W. Design and construction of a spin-wave lens. Sci. Rep. 2016;6(1):33169. DOI: 10.1038/srep33169.
  7. Dzyapko O, Borisenko IV, Demidov VE, Pernice W, Demokritov SO. Reconfigurable heat-induced spin wave lenses. Appl. Phys. Lett. 2016;109(23):232407. DOI: 10.1063/1.4971829.
  8. Grafe J, Decker M, Keskinbora K, Noske M, Gawronski P, Stoll H, Back CH, Goering EJ, ¨ Schutz G. X-Ray microscopy of spin wave focusing using a Fresnel zone plate. Phys. Rev. B. ¨ 2020;102:024420. DOI: 10.1103/PhysRevB.102.024420.
  9. Whitehead NJ, Horsley SAR, Philbin TG, Kruglyak VV. A Luneburg lens for spin waves. Appl. Phys. Lett. 2018;113(21):212404. DOI: 10.1063/1.5049470.
  10. Madami M, Khivintsev Y, Gubbiotti G, Dudko G, Kozhevnikov A, Sakharov V, Stal’makhov A, Khitun A, Filimonov Y. Nonreciprocity of backward volume spin wave beams excited by the curved focusing transducer. Appl. Phys. Lett. 2018;113(5):152403. DOI: 10.1063/1.5050347.
  11. Dudko GM, Kozhevnikov AV, Saharov VK, Stalmahov AV, Filimonov YA, Khivintsev YV. Calculation of focusing spin wave transducers using the method of micromagnetic simulation. Izvestiya of Saratov University. New series. Series: Physics. 2018;18(2):92–102 (in Russian). DOI: 10.18500/1817-3020-2018-18-2-92-102.
  12. Albisetti E, Tacchi S, Silvani R, Scaramuzzi G, Finizio S, Wintz S, Rinaldi C, Cantoni M, Raabe J, Carlotti G, Bertacco R, Riedo E, Petti D. Optically inspired nanomagnonics with nonreciprocal spin waves in synthetic antiferromagnets. Adv. Mater. 2020;32(9):1906439. DOI: 10.1002/adma.201906439.
  13. Annenkov AY, Gerus SV, Lock EH. Superdirectional beam of surface spin wave. Europhysics Letters. 2018;123(4):44003.DOI: 10.1209/0295-5075/123/44003.
  14. Demidov VE, Demokritov SO, Birt D, O’Gorman B, Tsoi M, Li X. Radiation of spin waves from the open end of a microscopic magnetic-film waveguide. Phys. Rev. B. 2009;80(1):014429. DOI: 10.1103/PhysRevB.80.014429.
  15. Schneider T, Serga AA, Chumak AV, Sandweg CW, Trudel S, Wolff S, Kostylev MP, Tiberkevich VS, Slavin AN, Hillebrands B. Nondiffractive subwavelength wave beams in a medium with externally controlled anisotropy. Phys. Rev. Lett. 2010;104(19):197203. DOI: 10.1103/PhysRevLett.104.197203.
  16. Davies CS, Sadovnikov AV, Grishin SV, Sharaevskii YP, Nikitov SA, Kruglyak VV. Generation of propagating spin waves from regions of increased dynamic demagnetising field near magnetic antidots. Appl. Phys. Lett. 2015;107(16):162401. DOI: 10.1063/1.4933263.
  17. Gieniusz R, Ulrichs H, Bessonov VD, Guzowska U, Stognii AI, Maziewski A. Single antidot as a passive way to create caustic spin-wave beams in yttrium iron garnet films. Appl. Phys. Lett. 2013;102(10):102409. DOI: 10.1063/1.4795293.
  18. Divinskiy B, Thiery N, Vila L, Klein O, Beaulieu N, Ben Youssef J, Demokritov SO, Demidov VE. Sub-micrometer near-field focusing of spin waves in ultrathin YIG films. Appl. Phys. Lett. 2020;116(6):062401. DOI: 10.1063/1.5131689.
  19. Gruszecki P, Kasprzak M, Serebryannikov AE, Krawczyk M, Smigaj W. Microwave excitation of ´ spin wave beams in thin ferromagnetic films. Sci. Rep. 2016;6(1):22367. DOI: 10.1038/srep22367.
  20. Madami M, Gubbiotti G, Khivintsev YV, Dudko GM, Sakharov VK, Kozhevnikov AV, Filimonov YA, Khitun AG. Spin waves interference under excitation by focusing transducers: logic and signal processing. Semiconductors. 2020;54(12):1716–1720. DOI: 10.1134/S1063782620120192.
  21. Heussner F, Serga AA, Bracher T, Hillebrands B, Pirro P. A switchable spin-wave signal splitter ¨ for magnonic networks. Appl. Phys. Lett. 2017;111(12):122401. DOI: 10.1063/1.4987007.
  22. Papp A, Porod W, Csurgay ´ AI, Csaba G. Nanoscale spectrum analyzer based on spin-wave ´ interference. Sci. Rep. 2017;7(1):9245. DOI: 10.1038/s41598-017-09485-7.
  23. Demidov VE, Kostylev MP, Rott K, Krzysteczko P, Reiss G, and Demokritov SO. Generation of the second harmonic by spin waves propagating in microscopic stripes. Phys. Rev. B. 2011;83(5): 054408. DOI: 10.1103/PhysRevB.83.054408.
  24. Zvezdin AK, Popkov AF. Contribution to the nonlinear theory of magnetostatic spin waves. Sov. Phys. JETP. 1983;57(2):350–355.
  25. Boyle JW, Nikitov SA, Boardman AD, Booth JG, Booth K. Nonlinear self-channeling and beam shaping of magnetostatic waves in ferromagnetic films. Phys. Rev. B. 1996;53(18):12173–12181. DOI: 10.1103/PhysRevB.53.12173.
  26. Bauer M, Mathieu C, Demokritov SO, Hillebrands B, Kolodin PA, Sure S, Dotsch H, Grimalsky V, ¨ Rapoport Yu, Slavin AN. Direct observation of two-dimensional self-focusing of spin waves in magnetic films. Phys. Rev. B. 1997;56(14):R8483. DOI: 10.1103/PhysRevB.56.R8483.
  27. Bauer M, Buttner O, Demokritov SO, Hillebrands B, Grimalsky V, Rapoport Yu, Slavin AN. ¨ Observation of spatiotemporal self-focusing of spin waves in magnetic films. Phys. Rev. Lett. 1998;81(17):3769. DOI: 10.1103/PhysRevLett.81.3769.
  28. Buttner O, Bauer M, Demokritov SO, Hillebrands B, Kostylev MP, Kalinikos BA, Slavin AN. ¨ Collisions of spin wave envelope solitons and self-focused spin wave packets in yttrium iron garnet films. Phys. Rev. Lett. 1999;82(21):4320–4323. DOI: 10.1103/PhysRevLett.82.4320.
  29. Donahue M, Porter D. Object Oriented Micro Magnetic Framework (OOMMF). Interagency Report NISTIR 6376, National Institute of Standards and Technology, Gaithersburg, MD; Sept. 1999. 897 p. Access mode:
  30. Dudko GM, Filimonov YA. Numerical investigation of the phenomena of self-action of limited beams of backward volume magnetostatic waves in ferromagnetic films. Izvestiya VUZ. Applied Nonlinear Dynamics. 1999;7(2–3):17–28 (in Russian).
  31. Pramanik T, Roy U, Tsoi M, Register LF, Banerjee SK. Micromagnetic simulations of spin-wave normal modes and the spin-transfer-torque driven magnetization dynamics of a ferromagnetic cross. J. Appl. Phys. 2014;115(17):17D123. DOI: 10.1063/1.4863384.
  32. Schultheiss K, Verba R, Wehrmann F, Wagner K, Korber L, Hula T, Hache T, K ¨ akay A, Awad AA, ´ Tiberkevich V, Slavin AN, Fassbender J, and Schultheiss H. Excitation of whispering gallery magnons in a magnetic vortex. Phys. Rev. Lett. 2019;122(9):097202. DOI: 10.1103/PhysRevLett.122.097202.
  33. Mohseni M, Kewenig M, Verba R, Wang Q, Schneider M, Heinz B, Kohl F, Dubs C, Lagel B, ¨ Serga AA, Hillebrands B, Chumak AV, Pirro P. Parametric generation of propagating spin-waves in ultra thin yttrium iron garnet waveguides. Physica Status Solidi (RRL) – Rapid Research Letters. 2020;14(4):2000011. DOI: 10.1002/pssr.202000011.
  34. Dudko GM, Khivintsev YV, Sakharov VK, Kozhevnikov AV, Vysotskii SL, Seleznev ME, Filimonov YA, Khitun AG. Micromagnetic modeling of nonlinear interaction of lateral magnetostatic modes in cross-shaped structures based on waveguides from iron yttrium garnet films. Izvestiya VUZ. Applied Nonlinear Dynamics. 2019;27(2):39–60 (in Russian). DOI: 10.18500/0869-6632-2019-27-2-39-60.
  35. Kalinikos BA, Slavin AN. Theory of dipole-exchange spin wave spectrum for ferromagnetic films with mixed exchange boundary conditions. J. Phys. C: Solid State Phys. 1986;19(35): 7013–7033. DOI: 10.1088/0022-3719/19/35/014.
  36. O’Keeffe TW, Patterson RW. Magnetostatic surface-wave propagation in finite samples. J. Appl. Phys. 1978;49(9):4886–4895. DOI: 10.1063/1.325522.
  37. Dvornik M. Numerical investigations of spin waves at the nanoscale. PhD thesis. University of Exeter; 2011. P. 58–79. DOI: 10036/3304.