We derive an effective-mass electron Hamiltonian for a Néel antiferromagnet in the presence of a smooth texture of the staggered magnetization. For certain locations of electron band extrema, the texture produces a peculiar and anomalously strong spin-orbit coupling of the scale ℏv/L, with v the Fermi velocity and L the relevant length scale of the texture. For a skyrmion texture, this coupling generates electron bound states, whose energy scale is given by the gap Δ in the electron spectrum. With dopant carriers, such bound states turn the skyrmion into a charged particle, that can be manipulated by electric field.
