  Spectra and spin structures of Andreev interface states and the Josephson
current are investigated theoretically in junctions between clean
superconductors (SC) with ordered interlayers. The Josephson current through
the ferromagnet-insulator-ferromagnet interlayer can exhibit a nonmonotonic
dependence on the misorientation angle. The characteristic behavior takes place
if the pi state is the equilibrium state of the junction in the particular case
of parallel magnetizations. We find a novel channel of quasiparticle reflection
(Q reflection) from the simplest two-sublattice antiferromagnet (AF) on a
bipartite lattice. As a combined effect of Andreev and Q reflections, Andreev
states arise at the AF/SC interface. When the Q reflection dominates the
specular one, Andreev bound states have almost zero energy on AF/ s-wave SC
interfaces, whereas they lie near the edge of the continuous spectrum for
AF/d-wave SC boundaries. For an s-wave SC/AF/s-wave SC junction, the bound
states are found to split and carry the supercurrent. Our analytical results
are based on a novel quasiclassical approach, which applies to interfaces
involving itinerant antiferromagnets. Similar effects can take place on
interfaces of superconductors with charge density wave materials (CDW),
including the possible d-density wave state (DDW) of the cuprates.
