Origin of the orbital polarization of Co$^{2+}$: a DFT+$U$ study of La$_2$CoTiO$_6$ and (LaCoO$_3$)$_1$+(LaTiO$_3$)$_1$

The unequal electronic occupation of localized orbitals (orbital polarization), and associated lowering of symmetry and degeneracy, play an important role in the properties of transition metal oxides. Here, we examine systematically the underlying origin of orbital polarization, taking as exemplar the 3$d$ manifold of Co$^{2+}$ in a variety of spin, orbital and structural phases in the double perovskite La$_2$CoTiO$_6$ and the (001) superlattice (LaCoO$_3$)$_1$+(LaTiO$_3$)$_1$ systems. Superlattices are of specific interest due to the large experimentally observed orbital polarization of their Co cations. Based on first principles calculations, we find that robust and observable orbital polarization requires symmetry reduction through the lattice structure; the role of local electronic interactions is to greatly enhance the orbital polarization.