Interplay between Zhang-Rice singlets and high-spin states in a model for doped NiO$_2$ planes

TL;DR

This study investigates the competition between Zhang-Rice singlets and high-spin triplet states in doped NiO$_2$ planes, revealing how charge-transfer energy and interatomic interactions influence the ground state and superconductivity mechanisms.

Contribution

It provides a detailed analysis of how charge-transfer energy and Ni-O interactions determine the local electronic states in doped NiO$_2$ layers, highlighting the importance of multiple orbitals and correlations.

Findings

Crossover from Zhang-Rice singlets to triplet states with increasing charge-transfer energy.

Smaller charge-transfer energy favors triplet ground states when Ni-O repulsion is considered.

Oxygen orbitals are less spectral weight at high energies for large charge-transfer energy.

Abstract

Superconductivity found in doped NdNiO$_2$ is puzzling as two local symmetries of doped NiO$_2$ layers compete, with presumably far-reaching implications for the involved mechanism: a cuprate-like regime with Zhang-Rice singlets {\cblue is replaced by local triplet states at realistic values of charge-transfer energy, which would suggest a rather different superconductivity scenario from high-$T_c$ cuprates}. We address this competition by investigating Ni$_4$O$_8$ clusters with periodic boundary conditions in the parameter range relevant for the superconducting nickelates. With increasing value of charge-transfer energy we observe upon hole doping the expected crossover from the cuprate regime dominated by Zhang-Rice singlets to the local triplet states. We find that smaller charge-transfer energy $\Delta$ is able to drive this change of the ground state character when realistic values for nickel-oxygen repulsion $U_{dp}$ are taken into account. For large values of the charge-transfer energy, oxygen orbitals are less important than in superconducting cuprates as their spectral weight is found only at rather high excitation energies. However, a second Ni($3d$) orbital can easily become relevant, with either the $xy$ or the $3z^2-r^2$ orbitals contributing in addition to the $x^2-y^2$ orbital {\cblue to the formation of triplet states. In addition,} our result that $U_{dp}$ (acting between Ni and O) favors onsite triplets implies that correlation effects beyond purely onsite interactions should be taken into account when obtaining effective two-band models.