Origin of orbital polarization in transition metal oxides: the case of Co²⁺

The degree of broken orbital degeneracy, which can be represented by the term \emph{orbital polarization}, can play a crucial role in the electronic and magnetic properties of transition metal oxides. Since spin, lattice, and orbital degrees of freedom are entangled, the fundamental origin and systematic understanding of the conditions leading to strong orbital polarization is lacking. Recently, we observed the strong orbital polarization of Co²⁺ in LaCoO₃+LaTiO₃ (LCO+LTO) superlattice [1]. The orbital polarization of Co is particularly interesting, since Co²⁺ ion has multiple spin states and t_2g or e_g character is determined by these spin states. Here we systematically study the origin of the strong orbital polarization of Co²⁺ by considering the various structural phases of (LCO)₁+(LTO)₁ superlattice and La₂CoTiO₆. While the symmetry reduction by forming a superlattice is the sufficient condition to break degeneracy of the e_g bands for the low-spin state, the polarization is greatly enhanced by Coulomb U. The sign of the e_g polarization depends on U, local octahedral distortion, and strain. For the high-spin state, the origin of the orbital polarization of t_2g bands is similar to e_g case.
[1] S. Lee, A. T. Lee et al., Phys. Rev. Lett. 123, 117201 (2009)