Goldstone Mode of Skyrmion Crystal
- Authors: Timofeev V.E.1,2, Aristov D.N.1,2
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Affiliations:
- Petersburg Nuclear Physics Institute, National Research Center Kurchatov Institute
- St. Petersburg State University
- Issue: Vol 118, No 5-6 (9) (2023)
- Pages: 455-461
- Section: Articles
- URL: https://vestnik.nvsu.ru/0370-274X/article/view/663110
- DOI: https://doi.org/10.31857/S1234567823180118
- EDN: https://elibrary.ru/WWXBLC
- ID: 663110
Cite item
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
- H. Vakili, J.-W. Xu, W. Zhou et al. (Collaboration), J. Appl. Phys. 130, 070908 (2021).
- Z. Yan, Y. Liu, Y. Guang, K. Yue, J. Feng, R. Lake, G. Yu, and X. Han, Phys. Rev. Appl. 44, 392001 (2011).
- N. S. Kiselev, A.N. Bogdanov, R. Sch¨afer, and U.K. R¨oßler, J. Phys. D: Appl. Phys. 44, 392001 (2011).
- F.H.D. Leeuw, R.V.D. Doel, and U. Enz, Rep. Prog. Phys. 138, 255 (1994).
- A.A. Thiele, Bell System Technical Journal 48, 3287 (1969).
- A. Bogdanov and A. Hubert, J. Magn. Magn. Mater. 138, 255 (1994).
- A.A. Thiele, Phys. Rev. Lett. 30, 230 (1973).
- M. Weißenhofer, L. R'ozsa, and U. Nowak, Phys. Rev. Lett. 127, 047203 (2021).
- A. Fert, N. Reyren, and V. Cros, Nat. Rev. Mater. 2, 1 (2017).
- S. Weißenhofer, B. Binz, F. Jonietz, C. Pfleiderer, A. Rosch, A. Neubauer, R. Georgii, and P. B¨oni, Science 323, 915 (2009).
- X. Z. Yu, N. Kanazawa, Y. Onose, K. Kimoto, W. Z. Zhang, S. Ishiwata, Y. Matsui, and Y. Tokura, Nat. Mater. 10, 106 (2010).
- X. Z. Yu, Y. Onose, N. Kanazawa, J.H. Park, J.H. Han, Y. Matsui, N. Nagaosa, and Y. Tokura, Nature 465, 901 (2010).
- N. Nagaosa and Y. Tokura, Nat. Nanotechnol. 8, 899 (2013).
- V.E. Timofeev, A.O. Sorokin, and D.N. Aristov, Phys. Rev. B 103, 094402 (2021).
- V.E. Timofeev, A.O. Sorokin, and D.N. Aristov, JETP Lett. 109, 207 (2019).
- A. Rold'an-Molina, A. S. Nunez, and J. Fern'andez- Rossier, New J. Phys. 18, 045015 (2016).
- M. Garst, J. Waizner, and D. Grundler, J. Phys. D: Appl. Phys. 50, 293002 (2017).
- A. Mook, J. Klinovaja, and D. Loss, Physical Review Research 2, 033491 (2020).
- V.E. Timofeev and D.N. Aristov, Phys. Rev. B 105, 024422 (2022).
- V.E. Timofeev and D.N. Aristov, JETP Lett. 117, 676 (2023).
- Y. Onose, Y. Okamura, S. Seki, S. Ishiwata, and Y. Tokura, Phys. Rev. Lett. 109, 037603 (2012).
- O. Petrova and O. Tchernyshyov, Phys. Rev. B 84, 214433 (2011).
- N. Mohanta, A.D. Christianson, S. Okamoto, and E. Dagotto, Communications Physics 3, 229 (2020).
- T. Schwarze, J. Waizner, M. Garst, A. Bauer, I. Stasinopoulos, H. Berger, C. Pfleiderer, and D. Grundler, Nat. Mater. 14, 478 (2015).
- 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).
- K. L. Metlov, Phys. Rev. B 88, 014427 (2013).
- D.N. Aristov and A. Luther, Phys. Rev. B 65, 165412 (2002).
- R. Rajaraman, Solitons and instantons North Holland, Amsterdam, N.Y., Oxford (1982).
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