Josephson effect in superconducting junctions with different types of magnetic barrier between the superconductors

Microscopic theory of the DC Josephson effect in S-MB-S junctions (S is a bulk superconductor) with different types of magnetic barrier (MB) is developed. The junctions with MB determined by uniformly polarized exchange field in a ferromagnetic layer (F) and also with MB created by FNF or FIF structures (N is a normal metal, I is an insulating layer) for different mutual orientation of the exchange field in the F layers (parallel to the F/S interfaces) are investigated. The conditions of the transition from the conventional, '0-type', to the π-type of junctions are studied. It is shown that such transition may occur with variation of temperature or due to applying the external magnetic field. The cases of ballistic and diffusive electron transport are investigated. For ballistic junctions the effect of pairbreaking in the S electrodes on the Andreev discrete states and on the supercurrent is studied. The effect of the critical current enhancement due to the presence of the exchange field in the F layer(s) is investigated