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 $3d$ manifold of ${\mathrm{Co}}^{2+}$ in a variety of spin, orbital, and structural phases in the double perovskite ${\mathrm{La}}_2{\mathrm{CoTiO}}_6$ and the (001) superlattice ${\left({\mathrm{LaCoO}}_3\right)}_1+{\left({\mathrm{LaTiO}}_3\right)}_1$ 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.

中文翻译：

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La2CoTiO6和（LaCoO3）1+（LaTiO3）1中Co2 +的轨道极化的起源：ADFT + U和DFMT研究

局部轨道的电子占有不平等（轨道极化）以及相关的对称性和简并性降低，在过渡金属氧化物的性质中起着重要作用。在这里，我们以轨道极化为例，系统地研究了轨道极化的根本成因。$3d$ 的流形 ${\mathrm{有限公司}}^{\mathrm{2个}+}$ 在双钙钛矿中的各种自旋，轨道和结构相中 ${\mathrm{啦啦}}_{\mathrm{2个}}{\mathrm{钛酸钙}}_6$ 和（001）超晶格 ${（{\mathrm{钴酸镧}}_3）}_{\mathrm{1个}}+{（{\mathrm{钛酸镧}}_3）}_{\mathrm{1个}}$系统。由于实验中观察到的Co阳离子的轨道极化较大，因此超晶格特别受关注。根据第一性原理计算，我们发现健壮且可观察到的轨道极化需要通过晶格结构减少对称性。局部电子相互作用的作用是极大地增强轨道极化。