Neodymium ions as charge reservoir in NdNiO$_2$: from lack of long range order to electron-doping-induced antiferromagnetism

We study magnetism in the electron-doped infinite-layer nickelate NdNiO$_2$. We perform an unrestricted Hartree-Fock calculation for a tight-binding model which contains both nickel and neodymium orbitals. We reproduce the self-doping effect, which is the escape of charge onto the neodymium bands. By fixing all free parameters to realistic values we find that undoped NdNiO$_2$ lies right {\it outside} the antiferromagnetic (AFM) region of the phase diagram. This is consistent with experiments, which find no long-range order in the ground state of NdNiO$_2$, yet see short-range AFM correlations and broad magnetic excitations. We also find that the self-doping effect leads to a dramatic increase in the stability of the AFM solution upon electron doping -- a behavior that is strikingly different from what is, for instance, observed in the cuprates. Finally, for smaller charge transfer energies than suggested for NdNiO$_2$, the self-doping effect may be quite strong and stabilise various stripe configurations already on the mean-field level.