Double perovskites (DPs) are a large family of compounds that exhibit a wide range of properties of both fundamental and potential technological interest. Due to the presence of $3d,4d$, or $5d$ transition metal atoms with narrow ${t}_{2g}$ and ${e}_{g}$ bands in DPs, the correlation effects play an important role for the properties of these materials, leading to diverse physical phenomena, such as colossal magnetoresistance, ferroelectricity, magnetism, and superconductivity. By employing the constrained random-phase approximation within the full-potential linearized augmented-plane-wave method, we have calculated the effective on-site Coulomb interaction parameters between localized $d$ electrons in ${\mathrm{Sr}}_{2}AB{\mathrm{O}}_{6}\phantom{\rule{4pt}{0ex}}(A=\mathrm{Cr},\text{Mn},\text{Fe},\text{Co},\text{Ni}$, and $B=\mathrm{Mo},\text{W})$ DPs. We find that the correlated subspace can be defined to contain only the ${e}_{g}$ states in Ni-based compounds, leading to a simple two-band low-energy model, whereas at least an eight-orbital $(d+{t}_{2g})$ model is necessary for the other compounds. Except for Ni, the $U$ values for $A$ sites in Mo (W) based compounds are around 4 eV (4.5 eV), and they are almost independent of the $3d$ electron number, while the $U$ for Mo (W) ${t}_{2g}$ electrons slightly decreases with increasing $3d$ electron number, from 3 to 2.5 eV. Moreover, our calculations reveal that the contribution of the $3d\ensuremath{\rightarrow}3d$ channel to the total electronic screening is larger in DPs than the corresponding contribution in elementary transition metals.
Read full abstract