ferromagnetism in a realistic two-band model:: A slave boson study.

Using a slave boson representation of multi-band Hubbard models, we investigate a two-band model relevant to layered perovskites in the vicinity of half-filling. Beside the strong influence of the Hund's rule coupling, we obtain that the phase diagram separates into two regions: a weak to moderate coupling region where the effective mass is weakly renormalized, and a strong coupling regime where it is strongly renormalized. The transition between these two regimes is very sharp. It takes place in a (vanishingly) small domain. A ferromagnetic instability in only found in the strongly correlated regime, and is triggered by the Hund's rule coupling. The results are compared to La-doped layered ruthenates.