Hund-driven local-itinerant duality of Eu-4$f$ electrons in infinite-layer nickelates

Abstract

Recent discovery of reentrant superconductivity and elevated $T_c$ in Eu-substituted infinite-layer nickelates raises a critical question concerning the nature of Eu-4$f$ states and their potential interaction with Ni-$d$ electrons. Here we combine density functional theory with the dynamical mean-field theory (DFT+DMFT) calculations to investigate the valence and magnetic properties of Eu-ions in the nickelate 112 structure, explicitly treating the Coulomb repulsion in both Ni-3$d$ and Eu-4$f$ shells. We find a three-regime evolution of the Eu-4$f$ configuration driven by its Hund's rule coupling $J_{\rm H}$. The magnetic and mixed-valence Eu ionic state inferred by experiments only occurs for moderate $J_{\rm H}$, with coexisting local moments and strongly correlated $j=7/2$ quasiparticles, in contrast to the nonmagnetic state at small $J_{\rm H}$ and the fully spin-polarized divalent state at large $J_{\rm H}$. This local-itinerant duality arises from an effectively hole-doped orbital-selective Mott state induced by the intra-4$f$ charge transfer between $j=5/2$ and $7/2$ manifolds. It not only explains the origin of the mixed-valence and local moment behaviors of the Eu-ions observed experimentally, but also predicts low-energy 4$f$ quasiparticles that may hybridize with the Ni-3$d$ electrons and contribute to the elevated $T_c$. Our work provides a basis for understanding the unusual ferromagnetic and superconducting properties of Eu-substituted infinite-layer nickelates.