Mixed states in ferromagnetic superconductors

A detailed study of the mixed state of the ferromagnetic rare-earth compounds $R{\mathrm{Rh}}_4{\mathrm{B}}_4$, $R_x{\mathrm{Mo}}_6{\mathrm{S}}_8$, and $R_x{\mathrm{Mo}}_6{\mathrm{Se}}_6$ is presented. The saturation effect of the magnetic moments is taken into account. Depending on the parameters, there are many types of phase transitions between the type-II/2, type-II/1, and type-I mixed states and the paramagnetic Meissner state, ferromagnetic Meissner state, spin-periodic Meissner state, and the self-induced vortex state. It is predicted that the magnetization can exhibit a variety of unusual modes.