Effective Coulomb interaction in transition metals from constrained random-phase approximation

Abstract

The effective on-site Coulomb interaction (Hubbard $U$) between localized $d$ electrons in 3$d$, 4$d$, and 5$d$ transition metals is calculated employing a parameter-free realization of the constrained random-phase approximation using Wannier functions within the full-potential linearized augmented-plane-wave method. The $U$ values lie between 1.5 and 5.7 eV and depend on the crystal structure, spin polarization, $d$ electron number, and $d$ orbital filling. On the basis of the calculated $U$ parameters, we discuss the strength of the electronic correlations and the instability of the paramagnetic state toward the ferromagnetic one for 3$d$ metals.