  We calculate the dc supercurrent through a Josephson tunnel junction
consisting of an antiferromagnetic (AF) interlayer sandwiched between two
d-wave superconductors (d). Such d/AF/d 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 dSC leads include subdominant
magnetic correlations. In this case induced magnetism near the interface can
strongly diminish the critical current for 110 oriented junctions whereas no
suppression is obtained 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.
