Pressure and doping effects on the electronic structure and magnetism of the single-layer nickelate La$_2$NiO$_4$
La$_2$NiO$_4$ is a prototypical member of the Ruddlesden-Popper nickelate series that offers a valuable reference point for elucidating the key ingredients behind the intriguing properties of these systems. However, the structural and electronic properties of La$_2$NiO$_4$ under pressure and doping remain surprisingly underexplored. Here, we investigate these properties using density-functional-theory calculations. We find that its tetragonal $I4/mmm$ structure can be stabilized, not only under pressure, but also at ambient pressure via the partial substitution of La with Ba. In both cases, we find a pronounced magnetostructural interplay that manifests, in particular, as anomalies in the lattice-parameter evolution with composition, deviating from Vegard's law. Moreover, we show that the combined effects of Ba substitution and pressure leads to qualitative changes in the electronic structure towards the formal $d^{7.5}$ configuration of the superconducting bilayer nickelates. Further, while La$_2$NiO$_4$ can undergo a insulator-metal transition with pressure retaining G-type antiferromagnetic order, La$_{1.5}$Ba$_{0.5}$NiO$_4$ exhibits metallic behavior with an enhanced competition between different magnetic states. Our results thus offer new insights into the interplay of structure, doping, and magnetism across the Ruddlesden-Popper nickelate series.