Orbital and magnetic orderings in localized $t_{2g}$ systems, ${\mathrm{YTiO}}_3$ and ${\mathrm{YVO}}_3$: Comparison with a more itinerant $e_g$ system ${\mathrm{LaMnO}}_3$

The electronic structures of the narrow $t_{2g}$ band systems ${\mathrm{YTiO}}_3$ and ${\mathrm{YVO}}_3$ are studied using the generalized gradient approximation (GGA) and local-density approximation (LDA)+U method. GGA fails in reproducing the insulating nature of ${\mathrm{YTiO}}_3$ and the correct magnetic ordering of ${\mathrm{YVO}}_3.$ The LDA+U method improves the GGA results in both of the above contexts through the enhancement in the orbital polarization. These results are compared with those for the wider $t_{2g}$ band system ${\mathrm{LaVO}}_3$ and more itinerant $e_g$ system ${\mathrm{LaMnO}}_3.$ The problems of GGA and LDA+U in predicting the ground-state magnetic ordering of ${\mathrm{LaMnO}}_3$ will also be discussed.