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We study electron states, bound to topological textures such as skyrmions anddomain walls in a N\'eel antiferromagnet. In certain limits, we find thedependence of bound states on the geometry of the texture, and estimate thebound-state contribution to its energy. This contribution proves significantcompared with the purely magnetic energy, and substantially affects theequilibrium geometry of the texture. The bound-state contribution also inducesa large shift of the transition line between the modulated and the uniformphase, extending the latter.

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