Goldstone Mode of Skyrmion Crystal

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription Access

Abstract

We discuss the Goldstone mode of skyrmion crystal in a model of two-dimensional ferromagnet with the Dzyaloshinskii–Moriya interaction in magnetic field. We use stereographic projection approach to construct skyrmion crystal and consider skyrmion displacement field. The small overlap of the individual skyrmion images restricts the potential energy to the interaction of nearest neighboring displacements. The closed form of the Goldstone mode dispersion is found and its dependence on the magnetic field is studied. We use semiclassical quantization to define the Green’s function and show that the propagation of displacements through the crystal changes its tensorial form from anisotropic to isotropic one at large times.

About the authors

V. E. Timofeev

Petersburg Nuclear Physics Institute, National Research Center Kurchatov Institute;St. Petersburg State University

Email: victor.timofeev@thd.pnpi.spb.ru
188300, Gatchina, Russia;199034, St. Petersburg, Russia

D. N. Aristov

Petersburg Nuclear Physics Institute, National Research Center Kurchatov Institute;St. Petersburg State University

Author for correspondence.
Email: Victor.Timofeev@thd.pnpi.spb.ru
188300, Gatchina, Russia;199034, St. Petersburg, Russia

References

  1. H. Vakili, J.-W. Xu, W. Zhou et al. (Collaboration), J. Appl. Phys. 130, 070908 (2021).
  2. Z. Yan, Y. Liu, Y. Guang, K. Yue, J. Feng, R. Lake, G. Yu, and X. Han, Phys. Rev. Appl. 44, 392001 (2011).
  3. N. S. Kiselev, A.N. Bogdanov, R. Sch¨afer, and U.K. R¨oßler, J. Phys. D: Appl. Phys. 44, 392001 (2011).
  4. F.H.D. Leeuw, R.V.D. Doel, and U. Enz, Rep. Prog. Phys. 138, 255 (1994).
  5. A.A. Thiele, Bell System Technical Journal 48, 3287 (1969).
  6. A. Bogdanov and A. Hubert, J. Magn. Magn. Mater. 138, 255 (1994).
  7. A.A. Thiele, Phys. Rev. Lett. 30, 230 (1973).
  8. M. Weißenhofer, L. R'ozsa, and U. Nowak, Phys. Rev. Lett. 127, 047203 (2021).
  9. A. Fert, N. Reyren, and V. Cros, Nat. Rev. Mater. 2, 1 (2017).
  10. S. Weißenhofer, B. Binz, F. Jonietz, C. Pfleiderer, A. Rosch, A. Neubauer, R. Georgii, and P. B¨oni, Science 323, 915 (2009).
  11. X. Z. Yu, N. Kanazawa, Y. Onose, K. Kimoto, W. Z. Zhang, S. Ishiwata, Y. Matsui, and Y. Tokura, Nat. Mater. 10, 106 (2010).
  12. X. Z. Yu, Y. Onose, N. Kanazawa, J.H. Park, J.H. Han, Y. Matsui, N. Nagaosa, and Y. Tokura, Nature 465, 901 (2010).
  13. N. Nagaosa and Y. Tokura, Nat. Nanotechnol. 8, 899 (2013).
  14. V.E. Timofeev, A.O. Sorokin, and D.N. Aristov, Phys. Rev. B 103, 094402 (2021).
  15. V.E. Timofeev, A.O. Sorokin, and D.N. Aristov, JETP Lett. 109, 207 (2019).
  16. A. Rold'an-Molina, A. S. Nunez, and J. Fern'andez- Rossier, New J. Phys. 18, 045015 (2016).
  17. M. Garst, J. Waizner, and D. Grundler, J. Phys. D: Appl. Phys. 50, 293002 (2017).
  18. A. Mook, J. Klinovaja, and D. Loss, Physical Review Research 2, 033491 (2020).
  19. V.E. Timofeev and D.N. Aristov, Phys. Rev. B 105, 024422 (2022).
  20. V.E. Timofeev and D.N. Aristov, JETP Lett. 117, 676 (2023).
  21. Y. Onose, Y. Okamura, S. Seki, S. Ishiwata, and Y. Tokura, Phys. Rev. Lett. 109, 037603 (2012).
  22. O. Petrova and O. Tchernyshyov, Phys. Rev. B 84, 214433 (2011).
  23. N. Mohanta, A.D. Christianson, S. Okamoto, and E. Dagotto, Communications Physics 3, 229 (2020).
  24. T. Schwarze, J. Waizner, M. Garst, A. Bauer, I. Stasinopoulos, H. Berger, C. Pfleiderer, and D. Grundler, Nat. Mater. 14, 478 (2015).
  25. T. Weber, D.M. Fobes, J. Waizner, P. Steffens, G. S. Tucker, M. B¨ohm, L. Beddrich, C. Franz, H. Gabold, R. Bewley, D. Voneshen, M. Skoulatos, R. Georgii, G. Ehlers, A. Bauer, C. Pfleiderer, P. B¨oni, M. Janoschek, and M. Garst, Science 375, 1025 (2022).
  26. K. L. Metlov, Phys. Rev. B 88, 014427 (2013).
  27. D.N. Aristov and A. Luther, Phys. Rev. B 65, 165412 (2002).
  28. R. Rajaraman, Solitons and instantons North Holland, Amsterdam, N.Y., Oxford (1982).

Supplementary files

Supplementary Files
Action
1. JATS XML
Download

Copyright (c) 2023 Российская академия наук