Superconducting Transition Temperature in Heterogeneous Ferromagnet-Superconductor Systems

We study the shift of the the superconducting transition temperature $T_c$ in ferromagnetic-superconducting bi-layers and in a superconducting film supplied a square array of ferromagnetic dots. We find that the transition temperature in these two cases change presumably in opposite direction and that its change is not too small. We extend these results to multilayer structures. We predict that rather small external magnetic field $\sim 10$ Oe can change the transition temperature of the bilayer by 10% .