Abstract
Single-site dynamical mean-field theory is used to determine the magnetic and orbital-ordering phase diagram for a model of electrons moving on a lattice with three orbital states per site and with the fully rotationally invariant Slater-Kanamori on-site interactions. The model captures important aspects of the physics of transition-metal oxides with partially filled ${t}_{2g}$ shells and of electron-doped ${\text{C}}_{60}$. We introduce an unbiased, computationally simple, and inexpensive method for estimating the presence of two-sublattice order, determine the regimes in which spatially uniform and two-sublattice spin and orbital orderings are present and give physical arguments for the origins of the different phases. Guidelines are determined for optimizing the presence of ferromagnetism, which may be desirable in applications.
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