  We study the Josephson current, I_J, in a junction consisting of two s-wave
superconductors that are separated by a ferromagnetic barrier possessing a
magnetic and non-magnetic scattering potential, g and Z, respectively. We
discuss the general dependence of I_J on g, Z, and the phase difference \phi
between the two superconductors. Moreover, we compute the critical current, I_c
for given g and Z, and show that it possesses two lines of non-analyticity in
the (g, Z)-plane. We identify those regions in the (g, Z)-plane where the
Josephson current changes sign with increasing temperature without a change in
the relative phase between the two superconductors, i.e., without a transition
between a 0 and \pi state of the junction. Finally, we show that by changing
the relative phase \phi, it is possible to tune the junction through a
first-order quantum phase transition in which the spin polarization of the two
superconductors' combined ground state changes from < S_z > =0 to < S_z > =1/2.
