Physics of the Solid State

, Volume 60, Issue 12, pp 2460–2470 | Cite as

Features of Spin Waves Focusing in Ferromagnets

  • S. M. BakharevEmail author
  • S. P. Savchenko
  • A. P. Tankeev

Abstract—Features of focusing spin waves in ferromagnets with magnetic moment exchange interaction with the closest neighbors and second neighbors are explored. It is shown that in the long-wave approximation, no spin wave focusing occurs: it is observed only in the wavevectors in the second half of the Brillouin zone (at aq ≥ π/2, where a is the lattice constant, q is the value of wavevector). Additionally, it is shown that magnons in such system are focused along directions [110], and are defocused in directions [100]. It is found that the external magnetic field and the magnetic anisotropy field do not cause changes in directions of magnon focusing. When the parameter of exchange interaction with the second neighbors near directions [110] and [111] is negative, magnons form a caustic, near which the intensity of the spin-wave field surges.



The study was accomplished within the state quota, topic Spin AAAAA18-118020290104-2, and project no. 32- within the Program of Basic Research of the Presidium of the Russian Academy of Sciences, under the Contract with the Ministry of Education and Science of Russia 14.Z50.31.0025, and supported by the Russian Foundation for Basic Research, project no. 18-32-00139 mol_a.


  1. 1.
    B. Taylor, H. J. Maris, and C. Elbaum, Phys. Rev. Lett. 23, 416 (1969).ADSCrossRefGoogle Scholar
  2. 2.
    B. Taylor, H. J. Maris, and C. Elbaum, Phys. Rev. B 3, 1462 (1971).ADSCrossRefGoogle Scholar
  3. 3.
    J. P. Wolfe, Imaging Phonons. Acoustic Wave Propagation in Solids (Cambridge Univ. Press, New York, 1998).CrossRefGoogle Scholar
  4. 4.
    H. J. Maris, J. Acoust. Soc. Am. 50, 812 (1971).ADSCrossRefGoogle Scholar
  5. 5.
    Cz. Jasiukiewicz, T. Paszkiewicz, and D. Lehmann, Z. Phys. B: Condens. Matter 96, 213 (1994).ADSCrossRefGoogle Scholar
  6. 6.
    E. Held, W. Klein, and R. P. Huebener, Z. Phys. B: Condens. Matter 75, 223 (1989).ADSCrossRefGoogle Scholar
  7. 7.
    O. Büttner, M. Bauer, S. O. Demokritov, B. Hillebrands, Yu. S. Kivshar, V. Grimalsky, Yu. Rapoport, M. P. Kostylev, B. A. Kalinikos, and A. N. Slavin, J. Appl. Phys. 87, 5088 (2000).ADSCrossRefGoogle Scholar
  8. 8.
    V. E. Demidov, S. O. Demokritov, K. Rott, P. Krzysteczko, and G. Reiss, Appl. Phys. Lett. 91, 252504 (2007).ADSCrossRefGoogle Scholar
  9. 9.
    V. Veerakumar and R. E. Camley, Phys. Rev. B 74, 214401 (2006).ADSCrossRefGoogle Scholar
  10. 10.
    V. Veerakumar and R. E. Camley, Phys. Rev. B 81, 174432 (2010).ADSCrossRefGoogle Scholar
  11. 11.
    J. J. Bible and R. E. Camley, Phys. Rev. B 95, 224412 (2017).ADSCrossRefGoogle Scholar
  12. 12.
    C. S. Davies, A. V. Sadovnikov, S. V. Grishin, Yu. P. Sharaevskii, S. A. Nikitov, and V. V. Kruglyak, Appl. Phys. Lett. 107, 162401 (2015).ADSCrossRefGoogle Scholar
  13. 13.
    R. Gieniusz, H. Ulrichs, V. D. Bessonov, U. Guzo-wska, A. I. Stognii, and A. Maziewski, Appl. Phys. Lett. 102, 102409 (2013).ADSCrossRefGoogle Scholar
  14. 14.
    E. A. Turov, Physical Properties of Magnetically Ordered Crystals (Akad. Nauk SSSR, Moscow, 1963) [in Russian].Google Scholar
  15. 15.
    A. G. Every, Phys. Rev. B 24, 3456 (1981).ADSCrossRefGoogle Scholar
  16. 16.
    J. Philip and K. S. Viswanathan, Phys. Rev. B 17, 4969 (1978).ADSCrossRefGoogle Scholar
  17. 17.
    M. Lax and V. Narayanamurti, Phys. Rev. B 22, 4876 (1980).ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    G. A. Northrop and J. P. Wolfe, Phys. Rev. B 22, 6196 (1980).ADSCrossRefGoogle Scholar
  19. 19.
    I. I. Kuleyev, S. M. Bakharev, I. G. Kuleyev, and V. V. Ustinov, Phys. Status Solidi 59, 1600263 (2017).Google Scholar
  20. 20.
    I. I. Kuleev, S. M. Bakharev, I. G. Kuleev, and V. V. Ustinov, Phys. Met. Metallogr. 118, 10 (2017).ADSCrossRefGoogle Scholar
  21. 21.
    J. Smit and H. P. J. Wijn, Ferrites (Philips Technical Library, Eindhoven, 1959).Google Scholar
  22. 22.
    F. H. de Leeuw, R. van den Doel, and V. Enz, Rep. Prog. Phys. 43, 691 (1980).ADSCrossRefGoogle Scholar
  23. 23.
    T. O’Dell, Ferromagnetodynamics: The Dynamics of Magnetic Bubbles, Domains, and Domain Walls (Wiley, Chichester, 1981).CrossRefGoogle Scholar
  24. 24.
    Ch. Kittel, Quantum Theory of Solids (Wiley, New York, 1963; Nauka, Moscow, 1967).Google Scholar
  25. 25.
    Ferromagnetic Resonance, Collection of Articles, Ed. by S. V. Vonsovskii (GIFML, Moscow, 1961) [in Russian].Google Scholar
  26. 26.
    A. V. Pogorelov, Differential Geometry (Nauka, Moscow, 1974; Noordhoff, Groningen, 1959).Google Scholar
  27. 27.
    V. I. Arnol’d, Catastrophe Theory (Nauka, Moscow, 1990; Springer, Berlin, Heidelberg, 1984).Google Scholar
  28. 28.
    V. Cherepanov, I. Kolokolov, and V. L’vov, Phys. Rep. 229, 81 (1993).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • S. M. Bakharev
    • 1
    Email author
  • S. P. Savchenko
    • 1
  • A. P. Tankeev
    • 1
    • 2
  1. 1.Mikheev Institute of Metal Physics, Ural Branch, Russian Academy of SciencesYekaterinburgRussia
  2. 2.Ural Federal University Named after the First President of Russia B.N. YeltsinYekaterinburgRussia

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