Orbital and magnetic order in the two-orbital Hubbard model

We examine the orbital and magnetic order of the two-orbital Hubbard model within dynamical mean-field theory. The model describes the low-energy physics of a partially filled ${e}_{g}$ band as can be found in some transition metal compounds. The model shows antiferromagnetic as well as ferromagnetic phases. For stabilizing ferromagnetism we find that Hund's coupling is particularly important. Quarter filling represents a very special situation in the phase diagram, where the coupling of spin, charge, and orbital degrees of freedom are involved. Exactly at quarter filling we find a metal insulator transition (MIT) between two almost fully polarized ferromagnetic states. This MIT can be tuned by changing the local interaction strength and seems to be a first order transition at zero temperature. Apart from these ferromagnetic states we were also able to stabilize antiferromagnetic and charge ordered phases at quarter filling, depending on the interaction parameters.