Dynamics of Dzyaloshinskii Domain Walls for Ferrimagnets with Compensation of Angular Momentum

Dzyaloshinskii domain walls in chiral ferrimagnets, with a violation of spatial inversion symmetry due to Dzyaloshinskii–Moriya interaction, are studied theoretically. The dynamics of domain walls with non-small velocity is investigated by means of qualitative and numerical analysis of the sigma-model equation, generalized for accounting for chiral interactions and not complete compensation of sublattice angular momenta. Domain wall critical velocity, the maximal velocity that the domain wall can move, its energy and linear momentum are determined. Domain wall dispersion relation, the dependence of the energy on the linear momentum, is constructed. Forced motion of domain walls with accounting for weak dissipation processes is investigated by means of collective variable approach. We found quite a complicated picture of the dynamics of domain walls in chiral ferrimagnet that can be of interest for general theory of magnetic solitons and useful for applications. In addition to the increasing of the critical velocity of the domain wall when approaching angular momentum compensation point, which is the well-known sequence of the exchange enhancement effect, even the qualitative picture of domain wall states is changing. The main difference is that a few different types of domain walls appear, forming a sequence of states with a characteristic complication of the wall structure (formation of cluster domain walls) together with an increase in their energy. Both factors, the exchange enhancement of the limiting domain wall velocity and the destruction of integrability, turn out to be important here. In particular, the critical velocities of cluster domain walls, as well as the maximal values of their linear momenta, appear to be higher (sometimes, a few times higher) than for standard domain walls. This effect is absent for domain walls, known for non-integrable models of ferromagnets. The presence of cluster domain walls can be of interest for the problem, how to increase the maximal velocity of motion for domain walls.