Limiting velocity and dispersion law of domain walls in ferrimagnets close to the spin compensation point

The motion of domain walls in GdFeCo-type ferrimagnets near the point of compensation of sublattice spins $s_1$ and $s_2$, when the effects of the exchange increase in the limiting wall velocity take place, is theoretically studied. The energy $E$ and momentum $P$ of the wall are determined and the dispersion relation $E = E(P)$ is derived. It is found that some walls become unstable at a sufficiently small decompensation value $s_1-s_2<\nu_c(s_1+s_2)$, $\nu_c\ll1$, and the dispersion relation $E(P)$ has an end point at some finite momentum. At $s_1-s_2>\nu_c(s_1+s_2)$, this dispersion relation, as well as that for ferromagnets, is periodic.