  Using the Density Matrix Renormalization Group and two-leg ladders, we
investigate an electronic two-orbital Hubbard model including plaquette
diagonal hopping amplitudes. Our goal is to search for regimes where charges
added to the undoped state form pairs, presumably a precursor of a
superconducting state.For the electronic density $\rho=2$, i.e. the undoped
limit, our investigations show a robust $(\pi,0)$ antiferromagnetic ground
state, as in previous investigations. Doping away from $\rho=2$ and for large
values of the Hund coupling $J$, a ferromagnetic region is found to be stable.
Moreover, when the interorbital on-site Hubbard repulsion is smaller than the
Hund coupling, i.e. for $U'<J$ in the standard notation of multiorbital Hubbard
models, our results indicate the coexistence of pairing tendencies and
ferromagnetism close to $\rho=2$. These results are compatible with previous
investigations using one dimensional systems. Although further research is
needed to clarify if the range of couplings used here is of relevance for real
materials, such as superconducting heavy fermions or pnictides, our theoretical
results address a possible mechanism for pairing that may be active in the
presence of short-range ferromagnetic fluctuations.
