Origin of monoclinic distortion and its impact on the electronic properties in KO$_2$

TL;DR

This study uses density functional theory to explore how lattice distortions in KO$_2$ cause a structural transition and significantly influence its electronic properties, especially the insulating gap.

Contribution

It reveals the origin of the monoclinic distortion in KO$_2$ and demonstrates how it affects electronic structure and gap formation through lattice and electronic interactions.

Findings

Identification of a soft phonon mode leading to monoclinic distortion.

Inclusion of Coulomb interaction U opens an electronic gap.

Lattice distortion and Coulomb interactions jointly enhance the insulating gap.

Abstract

We use the density functional theory and lattice dynamics calculations to investigate the properties of potassium superoxide KO$_2$ in which spin, orbital, and lattice degrees of freedom are interrelated and determine the low-temperature phase. After calculating phonon dispersion relations in the high-temperature tetragonal $I4/mmm$ structure, we identify a soft phonon mode leading to the monoclinic $C2/c$ symmetry and optimize the crystal geometry resulting from this mode. Thus we reveal a displacive character of the structural transition with the group-subgroup relation between the tetragonal and monoclinic phases. We compare the electronic structure of KO$_2$ with antiferromagnetic spin order in the tetragonal and monoclinic phases. We emphasize that realistic treatment of the electronic structure requires including the local Coulomb interaction $U$ in the valence orbitals of the O$^-_2$ ions. The presence of the `Hubbard' $U$ leads to the gap opening at the Fermi energy in the tetragonal structure without orbital order but with weak spin-orbit interaction. We remark that the gap opening in the tetragonal phase could also be obtained when the orbital order is initiated in the calculations with a realistic value of $U$. Finally, we show that the local Coulomb interactions and the finite lattice distortion, which together lead to the orbital order via the Jahn-Teller effect, are responsible for the enhanced insulating gap in the monoclinic structure.