Mixed state in magnetic superconductors

The boson theory is reformulated in a form applicable to the mixed state in the rare-earth compounds, $R{\mathrm{Rh}}_4{\mathrm{B}}_4$, $R_x{\mathrm{Mo}}_6{\mathrm{S}}_8$, and $R_x{\mathrm{Mo}}_6{\mathrm{Se}}_6$. The magnetic field induced by the persistent current of vortices, and the spin magnetization magnetized by this field are self-consistently calculated. A nonuniform spin magnetization with the periodicity of a flux-line lattice appears in the crystals. The total flux which is the sum of the spin and current contributions is quantized. This quantization effects the current inversion and thus the attractive interaction between the vortices. The calculated magnetization has a tendency of becoming the type-I or type II-1 superconductor even for a large $\kappa$. The fact that $H_{c2\mathrm{}}$ is drastically depressed near the Curie or Nèel temperature explains the experiments on ${\mathrm{Dy}}_x{\mathrm{Mo}}_6{\mathrm{S}}_8$ and ${\mathrm{Er}}_x{\mathrm{Mo}}_6{\mathrm{S}}_8$.