Abstract
We have investigated the temperature ($T$)-dependent evolution of orbital states in a typical spin-orbital-lattice-coupled $2p$ electron Mott system $\mathrm{K}{\mathrm{O}}_{2}$, based on the electronic structures obtained by the dynamical mean-field theory as well as the density functional theory. We have shown that $\mathrm{K}{\mathrm{O}}_{2}$ exhibits the orbital fluctuation feature at high $T$ due to degenerate ${\ensuremath{\pi}}_{g}^{*}$ orbitals. Upon cooling, the orbital fluctuation is suppressed by the Jahn-Teller-type crystal field that becomes stronger with the lowering of structural symmetry, and then the ferro-orbital (FO) ordering emerges at low $T$. This FO ordering feature distinguishes $\mathrm{K}{\mathrm{O}}_{2}$ from $\mathrm{Rb}{\mathrm{O}}_{2}$ and $\mathrm{Cs}{\mathrm{O}}_{2}$ in that the latter two seem to have antiferro-orbital orderings at low $T$, indicating that the underlying physics is different between them. We propose that the suppression of the orbital fluctuation in $\mathrm{K}{\mathrm{O}}_{2}$ can be observed by thermal-conductivity measurement, as observed in spin-orbital-lattice-coupled $3d$ transition-metal oxides such as $\mathrm{LaV}{\mathrm{O}}_{3}$.
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