  We calculate the persistent currents in
$S-F_{\uparrow}F_{\uparrow[\downarrow]}-S$ structures (S denotes the
superconductor in a closed ring geometry, F the ferromagnet in a two
dimensional geometry, and the arrows the alignment of exchange field) as a
function of the applied magnetic flux, self consistently by solving the
Bogoliubov-de Gennes equations within the two dimensional Hubbard model. The
local current shows a sign change i.e. a 0 to $\pi$ transition in the parallel
alignment of the magnetizations and it does not change sign in antiparallel
alignment.
