Unexpected impact of magnetic disorder on multiband superconductivity

We analyze how the magnetic disorder affects the properties of the two-band $s_{\pm}$ and $s_{++}$ models, which are subject of hot discussions regarding iron-based superconductors and other multiband systems like MgB$_2$. We show that there are several cases when the transition temperature $T_c$ is not fully suppressed by magnetic impurities in contrast to the Abrikosov-Gor'kov theory, but a saturation of $T_c$ takes place in the regime of strong disorder. These cases are: (1) the purely interband impurity scattering, (2) impurity scattering purely in one of the bands, (3) the unitary scattering limit. We show that the a transition between $s_{++}$ and $s_\pm$ states may occur with increasing magnetic disorder.