Parametersκ1,κ2, andκ3in magnetic superconductors

The parametrization to describe the magnetic properties of superconductors, ${\kappa }_1\mathrm{}\left(t\right)\mathrm{}{\kappa }_2\mathrm{}\left(t\right)\mathrm{}$, and ${\kappa }_3\mathrm{}\left(t\right)\mathrm{}$, is extended to the case of magnetic superconductors in such a way that the effects of average polarization are subtracted. In this extension, ${\kappa }_1\mathrm{}\left(t\right)\mathrm{}$, ${\kappa }_2\mathrm{}\left(t\right)\mathrm{}$ approach the same value $\kappa$ in the limit $t\to 1$. It was shown that when the electromagnetic interplay is the main mechanism in the magnetic superconductors, ${\kappa }_1\mathrm{}\left(t\right)\mathrm{}$, ${\kappa }_2\mathrm{}\left(t\right)\mathrm{}$ [and ${\kappa }_3\mathrm{}\left(t\right)\mathrm{}$] are related to the nonmagnetic ${\kappa }_1\mathrm{}\left(t\right)\mathrm{}$ 's by the simple scaling rule near the critical temperature. In this case, it is also shown that the magnetization curve can be obtained by a suitable scaling of fields and $\kappa$ from the nonmagnetic ones. Especially, types of the magnetization curve are classified not in terms of $\kappa$ but in terms of the the scaled ${\kappa }^{\prime }$ {$\equiv \frac{\kappa }{{[1+4\mathrm{}\pi \chi \mathrm{}(t\left)\right]}^{\frac{1}{2}}}$, where $\chi \mathrm{}\left(t\right)\mathrm{}$ is the static spin susceptibility} near the critical-temperature region. Several relations related to the magnetic properties are also presented. The practical usefulness of our formulation lies in the fact that it presents a simple way of obtaining the magnetization curves of magnetic superconductors from those of nonmagnetic ones.