Interplay of orbitally polarized and magnetically ordered phases in doped transition metal oxides

We investigate the magnetic instabilities of the two-dimensional model of interacting e_g electrons for hole doping away from two electrons per site in the mean-field approximation. In particular, we address the occurrence of orbitally polarized states due to the inequivalent orbitals, and their interplay with ferromagnetic and antiferromagnetic spin order. The role played by the Hund's exchange coupling J_H and by the crystal field orbital splitting E_z in stabilizing one of the competing phases is discussed in detail.