Doping-dependent character and possible magnetic ordering of NdNiO$_2$

Abstract: The novel nickelate superconductors of infinite-layer type feature challenging electronic pecularities in the normal-state phase diagram with doping. Distinct many-body behavior and different dispersion regimes of the entangled ${$Ni-$d_{z^2}$, Ni-$d_{x^2-y^2}$$}$ orbital sector give rise to highly rich physics, which is here studied for the case of the NdNiO$2$ system. An analysis based on advanced realistic dynamical mean-field theory unveils that the superconducting hole-doped region is the meeting place of a (self-)doped Mott insulator from the underdoped side, and a bad Hund metal from the overdoped side. Fermi-level crossing of the Ni-$d{z^2}$ flat-band ties both regimes together to form a singular arena for unconventional superconductivity. We furthermore shed light on the intriguing problem of elusive magnetism in infinite-layer nickelates. Antiferromagnetic (AFM) order with small Ni moments is shown to be a vital competitor at low temperature. At stoichiometry, C-AFM order with ferromagnetic spin-alignment along the $c$-axis benefits from a conceivable coexistence with Kondo(-lattice) screening.