A DFT$+$DMFT study of Orbital Physics in a Spin Orbital Lattice Coupled 2$p$ Electron Mott System: KO$_{2}$

We have investigated the temperature ($T)$-dependent orbital physics in a typical spin-orbital-lattice coupled 2$p$ electron Mott system KO$_{2}$, based on the electronic structures obtained by the dynamical mean-field theory as well as the density functional theory. KO$_{2}$ consists of K$^{+}$ cations and O$_{2}^{-}$ molecule anions, and there are three electrons in the fourfold degenerate pi anti-bonding orbital of O$_{2}^{-}$ anions. Hence, the orbital degeneracy occurs in a O$_{2}^{-}$ anion with a magnetic moment. We have shown that KO$_{2}$ exhibits the orbital fluctuation phenomenon at high $T$ due to the degenerate pi anti-bonding orbital. Upon cooling, this orbital fluctuation is suppressed by the Jahn-Teller (JT) type crystal field with lowering of the crystal structure symmetry, and then the ferro-orbital (FO) ordering emerges at low $T$. This FO ordering is compatible with the experimental antiferromagnetic spin order at low $T$ in KO$_{2}$. We suggest that the suppression of the orbital fluctuation in KO$_{2}$ upon cooling is similar that in 3$d$ transition-metal oxides such as LaVO$_{3}$.