  Motivated by the unexplored complexity of the phase diagrams for
multi-orbital Hubbard models, a three-band Hubbard model at integer fillings
(N=4) with orbital degeneracy lifted partially by crystal field splitting is
analyzed systematically in this work. By using single site dynamical mean-field
theory and rotationally invariant Gutzwiller approximation, we have computed
the full phase diagram with Coulomb interaction strength $U$ and crystal field
splitting $\Delta$. We find a large region in the phase diagram, where an
orbital selective Mott phase will be stabilized by the positive crystal field
lifting the orbital degeneracy. Further analysis indicates that the Hund's rule
coupling is essential for the orbital selective Mott phase and the transition
toward this phase is accompanied by a high-spin to low-spin transition. Such a
model may be relevant for the recently discovered pnictides and ruthenates
correlated materials.
