Field modulation of the critical current in magnetic Josephson junctions

The dependence of the critical current of a simple Josephson junction on the applied magnetic field is well known and, for a rectangular junction, gives rise to the classic 'Fraunhofer' modulation with periodic zeros at the fields that introduce a flux quantum into the junction region. Much recent work has been performed on Josephson junctions that contain magnetic layers. The magnetization of such layers introduces additional flux into the junction and, for large junction areas or strong magnetic materials, can significantly distort the modulation of the critical current and strongly suppress the maximum critical current. The growing interest in junctions that induce odd-frequency triplet pairing in a ferromagnet, and the need to make quantitative comparisons with theory, mean that a full understanding of the role of magnetic barriers in controlling the critical current is necessary. This paper analyses the effect of magnetism and various magnetic configurations on Josephson critical currents; the overall treatment applies to junctions of general shape, but the specific cases of square and rectangular junctions are considered.