Influence of Shape Effects on the Spectrum of Spin Waves in Finite Array of Ferromagnetic Pillars

  • S. A. OsokinEmail author
  • A. R. Safin
  • S. A. Nikitov


The frequency characteristics of spin waves excited in the chain of cylindrical ferromagnetic pillars are investigated. The presence of a boundary in the chain and the finite height of the pillars lead to the existence of inhomogeneity of magnetization and effective magnetic fields. Using methods of finite-difference discretization simulation we demonstrated the existence of additional resonant frequencies for the edge modes of spin waves due to the demagnetization of the pillars and dipole-dipole interaction between the pillars of the chain.


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S. A. Nikitov acknowledges support from the Government of the Russian Federation (#074-02-2018-286 for the Terahertz Spintronics laboratory of the Moscow Institute of Physics and Technology (NRU)). A.R. Safin acknowledges support from Russian Foundation for Basic Research (Grant #19-29-03015).


  1. 1.
    D. Sander, S. O. Valenzuela, D. Makarov, C. Marrows, E. Fullerton, P. Fischer, J. McCord, P. Vavassori, S. Mangin, and P. Pirro et al., J. Phys. D: Appl. Phys. 50, 363001 (2017).CrossRefGoogle Scholar
  2. 2.
    A. Roldán-Molina, A. S. Nunez, and J. Fernández-Rossier, New J. Phys. 18, 045015 (2016).ADSCrossRefGoogle Scholar
  3. 3.
    X. S. Wang, H. W. Zhang, and X. R. Wang, Phys. Rev. Appl. 9, 024029 (2018).ADSCrossRefGoogle Scholar
  4. 4.
    S. A. Nikitov, D. V. Kalyabin, I. V. Lisenkov, A. Slavin, Y. N. Barabanenkov, S. A. Osokin, A. V. Sadovnikov, E. N. Beginin, M. A. Morozova, Y. A. Filimonov, Y. V. Khivintsev, S. L. Vysotsky, V. K. Sakharov, and E. S. Pavlov, Physics-Uspekhi 58, 1002 (2015).ADSCrossRefGoogle Scholar
  5. 5.
    A. A. Nikitin, A. B. Ustinov, A. A. Semenov, A. V. Chumak, A. A. Serga, V. I. Vasyuchka, E. Lähderana, B. A. Kalinikos, and B. Hillebrands, Appl. Phys. Lett. 106, 102405 (2015).ADSCrossRefGoogle Scholar
  6. 6.
    V. Sluka, T. Schneider, R. A. Gallardo et al. (Collaboration), Nature Nanotech. 14, 02 (2019).CrossRefGoogle Scholar
  7. 7.
    V. Boucher, L.-P. Carignan, T. Kodera, C. Caloz, A. Yelon, and D. Menard, Phys. Rev. B 80, 224402 (2009).ADSCrossRefGoogle Scholar
  8. 8.
    A. M. Shutyi and D. I. Sementsov, JETP Lett. 106, 358 (2017).ADSCrossRefGoogle Scholar
  9. 9.
    Y. Barabanenkov, S. Osokin, D. Kalyabin, and S. Nikitov, Phys. Rev. B 91, 214419 (2015).ADSCrossRefGoogle Scholar
  10. 10.
    N. Locatelli, A. Hamadeh, F. Abreu Araujo, A. Belanovsky, P. Skirdkov, R. Lebrun, V. Naletov, K. Zvezdin, M. Munoz, J. Grollier, O. Klein, V. Cros, and G. Loubens, Sci. Rep. 5, 1 (2015).Google Scholar
  11. 11.
    Y. Barabanenkov, S. Osokin, D. Kalyabin, and S. Nikitov, Phys. Rev. B 94, 184409 (2016).ADSCrossRefGoogle Scholar
  12. 12.
    E. G. Galkina and B. A. Ivanov, JETP Lett. 104, 32 (2016).ADSCrossRefGoogle Scholar
  13. 13.
    I. Lisenkov, V. Tyberkevych, S. Nikitov, and A. Slavin, Phys. Rev. B 93, 214441 (2016).ADSCrossRefGoogle Scholar
  14. 14.
    M. Mruczkiewicz, M. Krawczyk, G. Gubbiotti, S. Tacchi, Y. Filimonov, D. Kalyabin, I. Lisenkov, and S. Nikitov, New J. Phys. 15, 113023 (2013).ADSCrossRefGoogle Scholar
  15. 15.
    I. Lisenkov, V. Tyberkevych, A. Slavin, P. Bondarenko, B. Ivanov, E. Bankowski, T. Meitzler, and S. Nikitov, Phys. Rev. B 90, 104417 (2014).ADSCrossRefGoogle Scholar
  16. 16.
    V. E. Demidov, S. Urazhdin, A. Zholud, A. V. Sadovnikov, and S. O. Demokritov, Appl. Phys. Lett. 105, 172410 (2014).ADSCrossRefGoogle Scholar
  17. 17.
    A. A. Awad, P. Duärrenfeld, A. Houshang, M. Dvornik, E. Iacocca, R. K. Dumas, and J. Akerman, Nature Phys. 13, 292 (2016).ADSCrossRefGoogle Scholar
  18. 18.
    A. Houshang, E. Iacocca, P. Dörrenfeld, S. R. Sani, J. Åkerman, and R. K. Dumas, Nature Nanotech. 11, 280 (2015).ADSCrossRefGoogle Scholar
  19. 19.
    A. Belanovsky, N. Locatelli, P. Skirdkov, F. Abreu Araujo, J. Grollier, K. Zvezdin, V. Cros, and A. K. Zvezdin, Phys. Rev. B 85, 10 (2012).CrossRefGoogle Scholar
  20. 20.
    A. D. Belanovsky, N. Locatelli, P. N. Skirdkov, F. Abreu Araujo, K. A. Zvezdin, J. Grollier, V. Cros, and A. K. Zvezdin, Appl. Phys. Lett. 103, 122405 (2013).ADSCrossRefGoogle Scholar
  21. 21.
    J. Torrejon, M. Riou, F. Abreu Araujo, S. Tsunegi, G. Khalsa, D. Querlioz, P. Bortolotti, V. Cros, K. Yakushiji, A. Fukushima, H. Kubota, S. Yuasa, M. Stiles, and J. Grollier, Nature 547, 428 (2017).CrossRefGoogle Scholar
  22. 22.
    D. Vodenicarevic, N. Locatelli, F. Abreu Araujo, J. Grollier, and D. Querlioz, Sci. Rep. 7, 1 (2017).CrossRefGoogle Scholar
  23. 23.
    A. Vansteenkiste, J. Leliaert, M. Dvornik, M. Helsen, F. Garcia-Sanchez, and B. van Waeyenberg, AIP Adv. 4, 107133 (2014).ADSCrossRefGoogle Scholar
  24. 24.
    M. Dvornik, P. Bondarenko, B. Ivanov, and V. Kruglyak, J. Appl. Phys. 109, 07B912 (2011).CrossRefGoogle Scholar
  25. 25.
    Y. Yin, F. Pan, M. Ahlberg, M. Ranjbar, P. Duürrenfeld, A. Houshang, M. Haidar, L. Bergqvist, Y. Zhai, R. Dumas, A. Delin, and J. Akerman, Phys. Rev. B 92, 024427 (2015).ADSCrossRefGoogle Scholar
  26. 26.
    S. A. Osokin, A. R. Safin, Y. N. Barabanenkov, and S. A. Nikitov, J. Magn. Magn. Mater 465, 519 (2018).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2019

Authors and Affiliations

  • S. A. Osokin
    • 1
    • 2
    Email author
  • A. R. Safin
    • 2
    • 3
  • S. A. Nikitov
    • 1
    • 2
    • 4
  1. 1.Moscow Institute of Physics and TechnologyState UniversityDolgoprudnyRussia
  2. 2.Kotel’nikov Institute of Radioengineering and Electronics of Russian Academy of SciencesMoscowRussia
  3. 3.National Research University “MPEI”MoscowRussia
  4. 4.Saratov State UniversitySaratovRussia

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