Ginzburg-Landau equations, interphase surface energy, and the intermediate state of superconductors with a paramagnetic normal state

The effects of a paramagnetic normal state on the superconducting Ginzburg-Landau (GL) equations, the interphase surface energy ${\sigma }_{\mathrm{ns}}$ and the intermediate-state critical field $B_{\mathrm{cI}}$ of thin films in a perpendicular field are calculated. For a linear $H\left(B\right)\mathrm{}$ relation, the scaling of ${\lambda }_L$ into $\frac{{\lambda }_L}{{(1+4\mathrm{}\pi \chi )}^{\frac{1}{2}}}$ introduced by Tachiki et al. is adequate for the GL equations and ${\sigma }_{\mathrm{ns}}$ but not for $B_{\mathrm{cI}}$. For a nonlinear $H\left(B\right)\mathrm{}$ relation, as might occur for spontaneous ferromagnetism or for fields large enough that the magnetization saturates, neither the GL equations nor ${\sigma }_{\mathrm{ns}}$, nor $B_{\mathrm{cI}}$, can be obtained by scaling the nonmagnetic case. These results should be applicable to magnetic superconductors such as Er${\mathrm{Rh}}_4$ ${\mathrm{B}}_4$.