Exact solutions for a ferromagnet with Dzyaloshinskii-Moriya interaction

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


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


Solid State and Materials 


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© 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

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