Dynamics of domain walls in weak ferromagnets

The dynamics of domain walls in a model weak ferromagnet is shown to be governed by a suitable extension of the relativistic nonlinear sigma model to account for the Dzyaloshinskii-Moriya anisotropy and an applied magnetic field. Our analytical results are confirmed by a numerical calculation in a discrete spin model and significantly amend earlier treatments. Thus we provide a detailed description of static domain walls and subsequently study their dynamics. A virial theorem is derived that underlies the existence of a terminal state and allows a simple calculation of the mobility at low fields for both Bloch and Neel walls. We further establish the existence of a critical field above which a driven domain wall is always Neel, whereas a bifurcation takes place below the critical value where the two types of walls behave rather differently. The terminal states as well as the mobility curves are obtained for practically any strength of the applied field. Implications for the phenomenology of domain walls in orthoferrites and in rhombohedron weak ferromagnets are discussed briefly.