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Assessing the correlated electronic structure of lanthanum nickelates

The series of nickel-oxide compounds LaNiO$_3$ (formal Ni$(d^7)$), La$_2$NiO$_4$ (formal Ni$(d^8)$) and LaNiO$_2$ (formal Ni$(d^9)$) is investigated by first-principles many-body, using a combination of density functional theory, self-interaction correction and dynamical mean-field theory. The characteristics of these different nickelates, in good agreement with available experimental data, is revealed by employing a compound-independent choice for the local Coulomb interactions. The dichotomy within the low-energy dominant Ni-$e_g$ sector of $\{d_{z^2},d_{x^2-y^2}\}$ kind is rising with growing Ni$(3d)$ filling across the series. An intermediate-coupling scheme for spin-polarized calculations is introduced, which leads to very weak Ni ordered moments for the infinite-layer compound LaNiO$_2$ in contrast to the robust-moment system La$_2$NiO$_4$.