Ferromagnetic Josephson junctions with steplike interface transparency

Within the framework of the quasiclassical Usadel equations we study the Josephson effect in superconductor-insulator-ferromagnet-superconductor (SIFS) and SIFNS (N is a normal metal) structures with a steplike transparency of the FS or NS interface. At certain parameters the steplike transparency leads to the formation of a region, where the critical current-density distribution ${J}_{C}(y)$ along the junction exhibits a damped oscillation with a sign change. This results in the formation of a $0\text{\ensuremath{-}}\ensuremath{\pi}$ nanojunction with the characteristic length of 0 and $\ensuremath{\pi}$ regions of the order of the coherence length ${\ensuremath{\xi}}_{F}$ for SIFS and ${\ensuremath{\xi}}_{N}$ for SIFNS junctions, respectively. Using several transparency steps one can create an array of nanojunctions. Such structures exhibit an unusual behavior in an external magnetic field $H$. The total critical current grows with increasing $H$ up to a certain value, which depends on the size of a single nanojunction, and has multiperiodic oscillations in the case of an array.