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

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The effects of a paramagnetic normal state on the superconducting Ginzburg-Landau (GL) equations, the interphase surface energy ${\ensuremath{\sigma}}_{\mathrm{ns}}$ and the intermediate-state critical field ${B}_{\mathrm{cI}}$ of thin films in a perpendicular field are calculated. For a linear $H(B)$ relation, the scaling of ${\ensuremath{\lambda}}_{L}$ into $\frac{{\ensuremath{\lambda}}_{L}}{{(1+4\ensuremath{\pi}\ensuremath{\chi})}^{\frac{1}{2}}}$ introduced by Tachiki et al. is adequate for the GL equations and ${\ensuremath{\sigma}}_{\mathrm{ns}}$ but not for ${B}_{\mathrm{cI}}$. For a nonlinear $H(B)$ relation, as might occur for spontaneous ferromagnetism or for fields large enough that the magnetization saturates, neither the GL equations nor ${\ensuremath{\sigma}}_{\mathrm{ns}}$, 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}$.