Electron states, bound to a texture in a N\'eel antiferromagnet

We study electron states, bound to topological textures such as skyrmions and domain walls in a N\'eel antiferromagnet. In certain limits, we find the dependence of bound states on the geometry of the texture, and estimate the bound-state contribution to its energy. This contribution proves significant compared with the purely magnetic energy, and substantially affects the equilibrium geometry of the texture. The bound-state contribution also induces a large shift of the transition line between the modulated and the uniform phase, extending the latter.