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 d F of the F layer at which the 0- π transitions occur. For certain values of d , F a 0- π transition can even be achieved by changing only the N layer thickness. We use our model to fi t experimental data of SIFS and SINFS tunnel junctions.