Josephson effect in thin-film superconductor/insulator/superconductor junctions with misaligned in-plane magnetic fields

We study a tunnel junction consisting of two thin-film s-wave superconductors separated by a thin, insulating barrier in the presence of misaligned in-plane exchange fields. We find an interesting interplay between the superconducting phase difference and the relative orientation of the exchange fields, manifested in the Josephson current across the junction. Specifically, this may be written I-J(C)=(I-0+I-m cos phi)sin Delta theta, where I-0 and I-m are constants, and phi is the relative orientation of the exchange fields, while Delta theta is the superconducting phase difference. Similar results have recently been obtained in other superconductor-insulator-superconductor junctions coexisting with helimagnetic or ferromagnetic order. We calculate the superconducting order parameter self-consistently, and investigate quantitatively the effect which the misaligned exchange fields constitute on the Josephson current, to see if I-m may have an appreciable effect on the Josephson current. It is found that I-0 and I-m become comparable in magnitude at sufficiently low temperatures and fields close to the critical value, in agreement with previous work. From our analytical results, it then follows that the Josephson current in the present system may be controlled in a well-defined manner by a rotation of the exchange fields on both sides of the junction. We discuss a possible experimental realization of this proposition.