Dynamic solitons in antiferromagnets (Review Article)

A review of theoretical studies of magnetic solitons in antiferromagnets (AFM) is presented. The key concepts of AFM physics and soliton theory are discussed. An analysis of AFM nonlinear dynamics is carried out according to the unified positions on the basis of a nonlinear sigma model for the antiferromagnetic vector. The derivation of this equation and its integrals of motion are discussed considering the real AFM structure. The main focus is the study of two-parameter solitons, which are characterized by both the translational motion of the soliton center and the internal dynamics of spins inside the soliton. Solitons of various types: one-dimensional and two-dimensional, topological and without topological charge, are considered. An analysis of the AFM dynamic symmetry lowering effects, which are associated with the destruction of the Lorentz-invariant character of the sigma model, is performed. Such effects arise in the case of consistent consideration of the Dzyaloshinskii–Moriya interaction and/or the strong external magnetic field. This problem has not been discussed in monographic literature. The universality classes are established for the behavior of moving solitons.