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Antiferromagnetic insulating state in layered nickelates at half-filling

We provide a set of computational experiments based on \textit{ab initio} calculations to elucidate whether a cuprate-like antiferromagnetic insulating state can be present in the phase diagram of the low-valence layered nickelate family (R$_{n+1}$Ni$_n$O$_{2n+2}$, R= rare-earth, $n=1-\infty$) in proximity to half-filling. It is well established that at $d^9$ filling the infinite-layer ($n=\infty$) nickelate is metallic, in contrast to cuprates wherein an antiferromagnetic insulator is expected. We show that for the Ruddlesden-Popper (RP) reduced phases of the series (finite $n$) an antiferromagnetic insulating ground state can naturally be obtained instead at $d^9$ filling, due to the spacer RO$_2$ fluorite slabs present in their structure that block the $c$-axis dispersion. In the $n=\infty$ nickelate, the same type of solution can be derived if the off-plane R-Ni coupling is suppressed. We show how this can be achieved if a structural element that cuts off the $c$-axis dispersion is introduced (i.e. vacuum in a monolayer of RNiO$_2$, or a blocking layer in multilayers formed by (RNiO$_2$)$_1$/(RNaO$_2$)$_1$).