Traveling antiferromagnetic domain walls in a magnetic field

We consider an antiferromagnet in one space dimension with easy-axis anisotropy in a perpendicular magnetic field. We study propagating domain wall solutions that can have a velocity up to a maximum $v_c$. The width of the domain wall is a non-monotonic function of the velocity and it diverges to infinity at $v_c$. Both features are in contrast to the case of the Lorentz invariant model in the absence of the field. We further study the modification of the wall profile when a Dzyaloshinskii-Moriya interaction is added. Finally, we present a propagating spiral expected to form when the system is forced at a velocity higher than the maximum velocity for domain walls and we give numerical results for the effect of the Dzyaloshinskii-Moriya interaction.