Intertwined charge and spin instability of La3Ni2O7

Research on nickel-based superconductors has progressed from infinite-layer LaNiO₂ to finite-layer La₆Ni₅O₁₂, and most recently to the Ruddlesden-Popper phase La₃Ni₂O₇, which was found to exhibit onset of superconductivity at ∼80 K under a pressure of ∼16 GPa. Using density functional calculations and multi-orbital, multi-atom cluster exact diagonalization that includes local exchange and Coulomb interactions, here we analyze the pressure dependent low-energy electronic states of the Ni₂O₉ cluster, relevant for the bilayer phase of La₃Ni₂O₇. We quantify the various possible spin states and the exchange and superexchange mechanisms of the Ni₂O₉ cluster are quantified through the involvement of the \({\rm{Ni}}-3d_{3z^2-r^2}\) orbitals and the atomic Hund’s rule exchange, the apical bridging O-2p_z orbitals, and the orbitals involved in the formation of local Zhang-Rice singlet like states. We find that the leading configurations contributing to the cluster ground-states both for nominal valence and also with local charge fluctuations, do not involve occupation of the apical oxygen; instead, they favor the formation of in-plane Zhang-Rice singlet-like states between an O ligand hole and the Ni \(3d_{z^2-y^2}\) orbital. We also highlight two possible charge and spin ordered states suggested by our cluster results, that are nearly degenerate at all relevant pressures within our modeling.