Antiferromagnetic and structural transitions in the superoxideKO2from first principles: A2p-electron system with spin-orbital-lattice coupling

${\text{KO}}_{2}$ exhibits concomitant antiferromagnetic (AFM) and structural transitions, both of which originate from the open-shell $2p$ electrons of $\text{O}_{2}{}^{\ensuremath{-}}$ molecules. The structural transition is accompanied by the coherent tilting of $\text{O}_{2}{}^{\ensuremath{-}}$ molecular axes. The interplay among the spin-orbital-lattice degrees of freedom in ${\text{KO}}_{2}$ is investigated by employing the first-principles electronic structure theory and the kinetic-exchange interaction scheme. We have shown that the insulating nature of the high-symmetry phase of ${\text{KO}}_{2}$ at high temperature $(T)$ arises from the combined effect of the spin-orbit coupling and the strong Coulomb correlation of $\text{O}\text{ }2p$ electrons. In contrast, for the low-symmetry phase of ${\text{KO}}_{2}$ at low $T$ with the tilted $\text{O}_{2}{}^{\ensuremath{-}}$ molecular axes, the band gap and the orbital ordering are driven by the combined effects of the crystal field and the strong Coulomb correlation. We have verified that the emergence of the $\text{O}\text{ }2p$ ferro-orbital ordering is essential to achieve the observed AFM structure for ${\text{KO}}_{2}$.