Proximity-Induced Superconductivity in Gd Layers on Nb: First-Principles Study with on-site Coulomb repulsion U term

Ferromagnet-superconductor (F-S) bilayers and multilayers are interesting due to competition between the ferromagnetic order and the Cooper pairs which may lead to triplet superconductivity. When the material parameters are tuned, interesting phenomena can be realized such as pi-phase Josephson junctions, superconducting spin valves, superconductor-mediated magnetic exchange coupling, and a nonmonotonic dependence of the superconducting critical temperature on the ferromagnetic film thickness. So far, these phenomena have been mostly studied by using effective models. Here, we investigate superconducting properties of one of the representative F-S bilayers, Gd films on Nb, by using the first-principles method including the band structures of Nb and Gd in the superconducting state. To consider strong correlation of Gd 4f electrons, we implement the on-site Coulomb repulsion U term into the recently developed Budapest Dirac-BdG-SKKR code in which the fully relativistic Bogoliubov-de Gennes equations are solved within the first-principles calculations based on multiple scattering theory. Our calculated superconducting properties are compared to those without the U term and the experimental data. This implementation will be useful for studies of strongly correlated superconductors.