Josephson tunnel junctions with the strong ferromagnetic alloy $Fe_{0.75}Co_{0.25}$ as the barrier material were studied. The junctions were prepared with high quality down to a thickness range of a few monolayers of Fe-Co. An oscillation length of $xi_{F2}approx 0.79:{rm {nm}}$ between 0 and $pi$-Josephson phase coupling and a very short decay length $xi_{F1}approx 0.22:{rm {nm}}$ for the amplitude of the superconducting pair wave function in the Fe-Co layer were determined. The rapid damping of the pair wave function inside the Fe-Co layer is caused by the strong ferromagnetic exchange field and additional magnetic pair breaking scattering. Josephson junctions with Fe-Co barriers show a significantly increased tendency towards magnetic remanence and flux trapping for larger thicknesses $d_{F}$.
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