Effect of the interface transparency and ferromagnetic thickness on the critical temperature of NbN/Gd/NbN hybrid structure

Abstract

We have investigated the variation of the critical temperature (Tc) in the NbN/Gd/NbN system in the dirty limit under the cumulative effect of ferromagnetic thickness (df) and the SF interface transparency by solving the linearized Usadel equations analytically in the Matsubara Greens function technique and the following trends in the Tc(df) curves were observed. (a) Non-monotonic decrease of Tc with the ferromagnetic thickness df for higher interface transparency. (b) Reentrant behavior of Tc for smaller values of the interface transparency. (c) Monotonous behavior of Tc for extremely low interface transparency. It was also found that the transition into the π−phase in NBN/Gd/NbN system with small interface transparency is unrelated to the oscillations of the superconducting critical temperature in the F-layer. The critical temperature has a non-monotonous dependency when it switches between 0−π phases.