In strongly correlated electronic systems, several novel physical properties are induced by the orbital degree of freedom. In particular, orbital degeneracy near the Fermi level leads to spontaneous symmetry breaking, such as the nematic state in FeSe and the orbital ordering in several perovskite systems. Here, the novel layered perovskite material ${\mathrm{CsVF}}_4$, with a $3d^2$ electronic configuration, was systematically studied using density-functional theory and a multiorbital Hubbard model within the Hatree-Fock approximation. Our results show that ${\mathrm{CsVF}}_4$ should be magnetic, with a G-type antiferromagnetic arrangement in the $ab$ plane and weak antiferromagnetic exchange along the $c$ axis, in agreement with experimental results. Driven by the Jahn-Teller distortion in the ${\mathrm{VF}}_6$ octahedra that shorten the $c$ axis, the system displays an interesting electron occupancy $d_{xy}^1{\left(d_{xz}{d}_{yz}\right)}^1$ corresponding to the lower nondegenerate $d_{xy}$ orbital being half-filled and the other two degenerate $d_{yz}$ and $d_{xz}$ orbitals sharing one electron per site. We show that this degeneracy is broken and a novel $d_{yz}$/$d_{xz}$ staggered orbital pattern is here predicted by both the first-principles and Hubbard model calculations. This orbital ordering is driven by the electronic instability associated with degeneracy removal to lower the energy.

中文翻译：

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层状钙钛矿材料中的轨道排序

在高度相关的电子系统中，轨道的自由度诱发了几种新颖的物理性质。特别是，费米能级附近的轨道简并性导致自发对称性破坏，例如FeSe中的向列状态和几种钙钛矿系统中的轨道有序。在这里，新型的层状钙钛矿材料${\mathrm{冠状病毒}}_4$，带有 $3d^2$电子结构，使用密度泛函理论和Hatree-Fock近似中的多轨道Hubbard模型进行了系统研究。我们的结果表明${\mathrm{冠状病毒}}_4$ 应该是磁性的，在 $\mathrm{一个}b$ 沿平面和弱反铁磁交换 $C$轴，与实验结果一致。由Jahn-Teller失真的驱动${\mathrm{音频}}_6$ 八面体缩短了 $C$ 轴，系统显示出有趣的电子占有率 $d_{Xÿ}^{\mathrm{1个}}{（d_{Xž}{d}_{ÿž}）}^{\mathrm{1个}}$ 对应于较低的非简并的 $d_{Xÿ}$ 轨道半满，另两个退化 $d_{ÿž}$ 和 $d_{Xž}$每个位点共享一个电子的轨道。我们证明了这种简并性已被打破，$d_{ÿž}$/$d_{Xž}$第一原理和哈伯德模型计算都可以预测出交错的轨道模式。该轨道排序是由与简并性去除相关联的电子不稳定性所驱动，以降低能量。