Role of $4f$ states in infinite-layer NdNiO$_2$

Atomic $4f$ states have been found to be essential players in the physical behavior of lanthanide compounds, at the Fermi level $E_F$ as in the proposed topological Kondo insulator SmB$_6$, or further away as in the magnetic superconductor system ${\cal R}$Ni$_2$B$_2$C (${\cal R}$=rare earth ion) and in Y$_{1-x}$Pr$_x$Ba$_2$Cu$_3$O$_7$, where the $4f$ shell of Pr has a devastating effect on superconductivity. In hole-doped ${\cal R}$NiO$_2$, the ${\cal R}$=Nd member is found to be superconducting while ${\cal R}$=La is not, in spite of the calculated electronic structures being nearly identical. We report first principles results that indicate that the Nd $4f$ moment affects states at $E_F$ in infinite-layer NdNiO$_2$, an effect that will not occur for LaNiO$_2$. Treating 20% hole-doping in the virtual crystal approach indicates that 0.15 holes empty the $\Gamma$-centered Nd-derived electron pocket while leaving the other electron pocket unchanged; hence Ni only absorbs 0.05 holes; the La counterpart would behave similarly. However, coupling of $4f$ states to the electron pockets at $E_F$ arises through the Nd intra-atomic $4f-5d$ exchange coupling $K\approx 0.5$ eV and is ferromagnetic (FM), i.e. anti-Kondo, in sign. This interaction causes spin-disorder broadening of the electron pockets and should be included in models of the normal and superconducting states of Nd$_{0.8}$Sr$_{0.2}$NiO$_2$ The Ni moments differ by 0.2$\mu_B$ for FM and antiferromagnetic alignment (the latter are larger), reflecting some itineracy and indicating that Heisenberg coupling of the moments may not provide a quantitative modeling of Ni-Ni exchange coupling.