3D analytical model of skyrmion-like structures in an antiferromagnet with DMI

Abstract

The purpose of the research is the construction of the analytical model for description of a number of topological objects in a two-sublattice antiferromagnet with uniaxial magnetic anisotropy and Dzyaloshinskii-Moriya interaction (DMI) including vortices, antivortices, skyrmions, antiskyrmions, skyrmioniums and their bound states, which are the exact dynamic solutions of the nonlinear Landau-Lifshitz equations. “Relativistic contraction” of skyrmion-like topological object size in the direction of motion is demonstrated for “subcritical” case when its velocity is less than spin wave velocity in antiferromagnet. Lorentz-like “supercritical” transformation are found for skyrmion-like magnetic structures moving with velocity greater than spin wave velocity in antiferromagnet. In particular, the results of the analytical model are applied for an antiferromagnet in the form of cylindrical nanoshell; in this case, there are more than one solution of the nonlinear Landau-Lifshitz equations for the same boundary and initial conditions. It means that vortices, skyrmions, skyrmioniums and their bound states represent the ground state and the excited states in an antiferromagnetic cylindrical nanoshell. The particular cases of the exact static solutions of the nonlinear Landau-Lifshitz equations include the well-known one-dimensional solutions such as Bloch domain, Neel domain wall, Shirobokov domain structure, antiferromagnetic vortices, two-dimensional Belavin-Polyakov soliton, three-dimensional Hodenkov soliton and target type soliton. The results of this paper can be used for further development of theory of the antiferromagnetic soliton and skyrmion physics. Besides, the exact dynamic solutions of the nonlinear Landau-Lifshitz equations can serve as the reference solutions for testing the results of micromagnetic simulations.