Intertwined charge and spin instability of La$_3$Ni$_2$O$_7$

TL;DR

This study investigates the electronic and magnetic properties of La$_3$Ni$_2$O$_7$ under pressure, revealing intertwined charge and spin instabilities, with a focus on low-energy states and potential superconductivity mechanisms.

Contribution

The paper provides a detailed analysis of the pressure-dependent electronic states and spin configurations of La$_3$Ni$_2$O$_7$ using advanced computational methods, highlighting the role of in-plane Zhang-Rice singlets.

Findings

In-plane Zhang-Rice singlet states dominate the ground state.

Two nearly degenerate charge and spin ordered states are identified.

Pressure influences the balance between different spin and charge configurations.

Abstract

Research on nickel-based superconductors has progressed from infinite-layer LaNiO$_2$ to finite-layer La$_{6}$Ni$_{5}$O$_{12}$, and most recently to the Ruddlesden-Popper phase La$_3$Ni$_2$O$_7$, which was found to exhibits onset of superconductivity at $\sim$80\,K under a pressure of $\sim$16\,GPa. Unlike the superconductivity mainly driven by the $d_{x^2-y^2}$ orbital in infinite-layer nickelates, the Ni-$d_{z^2}$ and O-2$p$ orbitals contribute significantly to the low energy states and potentially to the superconducting electron pairing mechanism of La$_3$Ni$_2$O$_7$. Employing density functional calculations and multi-orbital multi-atom cluster exact diagonalization including local exchange and Coulomb interactions, here we analyze the pressure dependent low-energy electronic states of the Ni$_2$O$_9$ cluster, relevant for the bilayer phase of La$_3$Ni$_2$O$_7$. The various possible spin states and the exchange and superexchange mechanisms of the Ni$_2$O$_9$ cluster are quantified via the involvement of the 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 contributiong 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 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 modelling.