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Fermi surface nesting and possibility of orbital ordering in FeO

We study FeO, a Mott insulator in GGA and GGA+U approximations. In the GGA we find a multi-band metallic state with remarkable inter-band nesting between two $t_{2g}$ bands of Fermi surface, which signals possible instability towards an orbital ordered insulating phase. Such broken symmetry state, although has lower energy than the underlying homogeneous metallic state, but the gap magnitude is less than the experimentally observed optical gap. Therefore we incorporate the calculated value of on-site Coulomb repulsion U on orbital ordered state. We find that symmetry breaking and Coulomb correlations cooperate together to stabilize the system and give an insulating orbital ordered state, with the gap magnitude very close to the experimental value. We propose this method as a possible indication of orbital ordering in LDA and GGA calculations. We check our method with known examples of LiVO$_2$ and LaMnO$_3$.