Advertisement

Exact solutions for a ferromagnet with Dzyaloshinskii-Moriya interaction

  • Nicolás GrandiEmail author
  • Marcela Lagos
  • Julio Oliva
  • Aldo Vera
Regular Article
  • 18 Downloads

Abstract

On the two-dimensional non-linear Σ-model describing a ferromagnet with Dzyaloshinskii-Moriya interaction, we build three families of exact static solutions depending on a single Cartesian variable. One of them describes a clockwise helix configuration, that characterizes the ground state of the system. A second one corresponds to a counterclockwise helix, representing an excited state. These two families of solutions are parameterized by a continuous parameter that depends on the magnetic field and the Dzyaloshinskii-Moriya coupling. Finally, the third family exists only for isolated values of the same parameter, corresponding to a discrete family of Viviani curves on the target sphere. The degeneracy of the resulting spectrum suggests that an approximate symmetry may emerge at specific values of the magnetic field, at which additional solutions could then exist.

Graphical abstract

Keywords

Solid State and Materials 

References

  1. 1.
    I.E. Dzyaloshinskii, J. Exp. Theor. Phys. (U.S.S.R.) 46, 1420 (1964) Google Scholar
  2. 2.
    D.A. Yablonskii, A.N. Bogdanov, Zh. Eksp. Teor. Fiz. 95, 178 (1989) Google Scholar
  3. 3.
    A. Bogdanov, A. Hubert, J. Magn. Magn. Mater. 138, 255 (1994) ADSCrossRefGoogle Scholar
  4. 4.
    A. Bogdanov, A. Hubert, J. Magn. Magn. Mater. 195, 182 (1999) ADSCrossRefGoogle Scholar
  5. 5.
    S. Muhlbauer, B. Binz, F. Jonietz, C. Pfleiderer, A. Rosch, A. Neubauer, R. Georgii, P. Boni, Science 323, 915 (2009) ADSCrossRefGoogle Scholar
  6. 6.
    Y. Ishikawa, M. Arai, J. Phys. Soc. Jpn. 53, 2726 (1984) ADSCrossRefGoogle Scholar
  7. 7.
    B. Lebech, P. Harris, J. Skov Pedersen, K. Mortensen, C.I. Gregory, N.R. Bernhoeft, M. Jermy, S.A. Brown, J. Magn. Magn. Mater. 140–144, 119 (1995) ADSCrossRefGoogle Scholar
  8. 8.
    K. Shibata, X.Z. Yu, T. Hara, D. Morikawa, N. Kanazawa, K. Kimoto, S. Ishiwata, Y. Matsui, Y. Tokura, Nat. Nanotechnol. 8, 723 (2013) ADSCrossRefGoogle Scholar
  9. 9.
    B. Lebech, J. Bernhard, T. Freltoft, J. Phys.: Condens. Matter 1, 6105 (1989) ADSGoogle Scholar
  10. 10.
    M. Uchida, N. Nagaosa, J.P. He, Y. Kaneko, S. Iguchi, Y. Matsui, Y. Tokura, Phys. Rev. B 77, 184402 (2008) ADSCrossRefGoogle Scholar
  11. 11.
    X.Z. Yu, N. Kanazawa, Y. Onose, K. Kimoto, W.Z. Zhang, S. Ishiwata, Y. Matsui, Y. Tokura, Nat. Mater. 10, 106 (2011) ADSCrossRefGoogle Scholar
  12. 12.
    H. Wilhelm, M. Baenitz, M. Schmidt, U.K. Rößler, A.A. Leonov, A.N. Bogdanov, Phys. Rev. Lett. 107, 127203 (2011) ADSCrossRefGoogle Scholar
  13. 13.
    J. Beille, J. Voiron, M. Roth, Solid State Commun. 47, 399 (1983) ADSCrossRefGoogle Scholar
  14. 14.
    S.V. Grigoriev, V.A. Dyadkin, D. Menzel, J. Schoenes, Y.O. Chetverikov, A.I. Okorokov, H. Eckerlebe, S.V. Maleyev, Phys. Rev. B 76, 224424 (2007) ADSCrossRefGoogle Scholar
  15. 15.
    S.V. Grigoriev, D. Chernyshov, V.A. Dyadkin, V. Dmitriev, S.V. Maleyev, E.V. Moskvin, D. Menzel, J. Schoenes, H. Eckerlebe, Phys. Rev. Lett. 102, 37204 (2009) ADSCrossRefGoogle Scholar
  16. 16.
    Y. Onose, N. Takeshita, C. Terakura, H. Takagi, Y. Tokura, Phys. Rev. B 72, 224431 (2005) ADSCrossRefGoogle Scholar
  17. 17.
    I. Kézsmárki, S. Bordács, P. Milde, E. Neuber, L.M. Eng, J.S. White, H.M. Rønnow, C.D. Dewhurst, M. Mochizuki, K. Yanai, H. Nakamura, D. Ehlers, V. Tsurkan, A. Loidl, Nat. Mater. 14, 1116 (2015) ADSCrossRefGoogle Scholar
  18. 18.
    S. Seki, X.Z. Yu, S. Ishiwata, Y. Tokura, Science (New York) 336, 198 (2012) ADSCrossRefGoogle Scholar
  19. 19.
    T. Adams, A. Chacon, M. Wagner, A. Bauer, G. Brandl, B. Pedersen, H. Berger, P. Lemmens, C. Pfleiderer, Phys. Rev. Lett. 108, 237204 (2012) ADSCrossRefGoogle Scholar
  20. 20.
    G. Baskaran, Possibility of Skyrmion Superconductivity in Doped Antiferromagnet K2Fe4Se5, https://arXiv:1108.3562 (2011)
  21. 21.
    S.D. Yi, S. Onoda, N. Nagaosa, J.H. Han, Phys. Rev. B 80, 54416 (2009) ADSCrossRefGoogle Scholar
  22. 22.
    J.H. Han, J. Zang, Z. Yang, J.-H. Park, N. Nagaosa, Phys. Rev. B 82, 94429 (2010) ADSCrossRefGoogle Scholar
  23. 23.
    N. Grandi, M. Sturla, Int. J. Mod. Phys. B 32, 1850008 (2018) ADSCrossRefGoogle Scholar
  24. 24.
    F.S. Nogueira, I. Eremin, F. Katmis, J.S. Moodera, J. van den Brink, V.P. Kravchuk, Phys. Rev. B 98, 060401 (2018) ADSCrossRefGoogle Scholar
  25. 25.
    S. Gattei, On the life of Galileo: Viviani’s Historical account and other early biographies (Princeton University Press, 2019) Google Scholar
  26. 26.
    A.M. Serralunga Bardazza, Clelia Grillo Borromeo Arese: vicende private e pubbliche virtù di una celebre nobildonna nell’Italia del Settecento (Eventi & Progetti, 2005) Google Scholar
  27. 27.
    R.P. Agarwal, S.K. Sen, Creators of mathematical and computational sciences (Springer International Publishing, Cham, 2014) Google Scholar
  28. 28.
    A. Gray, Modern differential geometry of curves and surfaces with Mathematica (CRC Press, 1998) Google Scholar

Copyright information

© EDP Sciences / Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Instituto de Física de La Plata – CONICET & Departamento de Física – UNLPLa PlataArgentina
  2. 2.Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de ChileValdiviaChile
  3. 3.Departamento de Física, Universidad de ConcepciónConcepciónChile

Personalised recommendations