Quenching of magnetism in NaO₂ due to electrostatic interaction induced partial orbital ordering

The transport properties of sodium superoxide (NaO₂) are governed by the transfer of charge between O₂^- complexes. Although it goes through a plethora of structural phase transitions, its electronic and magnetic ground state remains shrouded in mystery. In this work, we perform first-principles density functional theory (DFT) calculations to understand the relationship between electronic structure and the reason for the non-observation of an antiferromagnetic (AFM) ground state in NaO₂ vis-a-vis in KO₂. In the cubic phase, uniform < Na-O-Na bond angles result in high symmetry and hence degeneracy in the O-2p orbitals. The freely rotating O₂^- molecules result in orbital degeneracy and hence paramagnetism at room temperature. Although the degeneracy between the bonding and anti-bonding orbitals of O₂ dimers is lifted in the pyrite phase, the degeneracy between σ (σ^*) and π (π^*) states is still maintained and hence orbital degeneracy is partially lifted as the dimers are restricted to four directions now. The O-π^* states are localized in such a manner that results in a substantial magnetic moment in the π^*-orbital. The < O-Na-O bond angle (= 180°) in the c-axis facilitates a superexchange mechanism and thereby the system should be AFM in the pyrite phase. In the marcasite phase, the O-atoms are aligned parallel in alternative planes. The preservation of degeneracy among the two π^* orbitals leading to only long-range orbital ordering negates any chance of quasi-one-dimensional AFM spin chains in NaO₂. The difference in magnetic ground states of NaO₂ and KO₂ arises due to the difference in the electrostatic repulsion between electrons of Na⁺ and K⁺ ions with the O₂^- dimers.