In [Nonlinearity, 1998], we set a framework for the study of antiferromagnets in a continuum approximation. Antiferromagnets are materials central in phenomena such as high temperature superconductivity. Despite of that, they typically attract much less attention than ferromagnets due to the lack of a net magnetisation and the ensuing difficulty for experimental observations.
We have systematically derived a contimuum model for a planar (2D) antiferromagnet, starting from the discrete (Heisenberg) model. This is a type of σ-model. Its static sector is similar (or identical) to that for ferromagnets. Therfore, domain walls and vortices are expected to exist in AFM for essentially the same reasons as in FM.
On the other hand, vortex dynamics in the antiferromagnetic continuum is fundamentally different than in ferromagnets. When we apply an external magnetic field, however, then the dynamics of antiferromagnetic solitons changes dramatically and it is linked to a topological number. Interestingly, this is not the same topological number (so-called, skyrmion number) as in ferromagnets. We have identified the modified topological number that is expected to affect soliton dynamics in AFM. A further study is needed in order to explore the consequencies of topology in the dynamics.
Skyrmions in antiferromagnetic materials with the Dzyaloshinskii-Moriya (DM) interaction are expected to exist for essentially the same reasons as in DM ferromagnets (FM). It is shown that skyrmions in antiferromagnets with the DM interaction can be traveling as solitary waves (see the animation) with velocities up to a maximum value that depends on the DM parameter. The energy and the linear momentum of an AFM skyrmion lead to a proper definition of its mass. We give the details of the energy-momentum dispersion of traveling skyrmions and explore their particle-like character. The skyrmion number, known to be linked to the dynamics of topological solitons in FM, is, here, unrelated to the dynamical behavior. As a result, the solitonic behavior of skyrmions in AFM is in stark contrast to the dynamical behavior of their FM counterparts. [SciPost Phys, 2020],
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The following refer to [SciPost Phys, 2020].