Josephson effects in d-wave superconductor junctions with magnetic interlayers

We calculate the dc supercurrent through a Josephson tunnel junction consisting of an antiferromagnetic or ferromagnetic interlayer sandwiched between two d-wave superconductors (d). Such junctions exhibit a rich dependence of the Josephson current on the interlayer parameters, including the possibility of 0-pi transitions with varying temperature or interlayer thickness. Furthermore, we study d/I/d junctions when the d-wave superconductor leads include subdominant magnetic correlations. Induced magnetism near the interface can strongly diminish the critical current for 110 oriented junctions whereas no suppression exists for the 100 orientation. This may help resolve a long-standing puzzle of the critical current versus grain boundary angle in high-T(c) superconductors.