The effect of normal and insulating layers on 0-π transitions in Josephson junctions with a ferromagnetic barrier

Using the Usadel approach, we provide a formalism that allows us to calculate the critical current density of 21 different types of Josephson junctions (JJs) with a ferromagnetic (F) barrier and additional insulating (I) or/and normal (N) layers inserted between the F layer and superconducting (S) electrodes. In particular, we obtain that in SFS JJs, even a thin additional N layer between the S layer and F layer may noticeably change the thickness dF of the F layer at which the 0-π transitions occur. For certain values of dF, a 0-π transition can even be achieved by changing only the N layer thickness. We use our model to fit experimental data of SIFS and SINFS tunnel junctions.