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 Ni-3d3z2−r2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rm{Ni}}-3d_{3z^2-r^2}$$\end{document} orbitals and the atomic Hund’s rule exchange, the apical bridging O-2pz 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 3dz2−y2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3d_{z^2-y^2}$$\end{document} 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.