Noninteracting Band Model for Dielectric Screening in Transition Metals: Application to Paramagnetic Nickel

The static dielectric function is studied for a transition metal on the basis of a model band structure with noninteracting $s$ and $d$ bands. The free-electron approximation is used for electrons in the $s$ band, while a simplified tight-binding scheme is used for the $d$ electrons. Explicit expressions are obtained for the intraband and interband contributions to the dielectric function. The model is applied to calculate the static dielectric function for paramagnetic nickel for ${\mathrm{}\left(3d\right)\mathrm{}}^9{\mathrm{}\left(4s\right)\mathrm{}}^1$ and ${\mathrm{}\left(3d\right)\mathrm{}}^{9.4}{\mathrm{}\left(4s\right)\mathrm{}}^{0.6}$ configurations along the three principal symmetry directions [100], [110], and [111]. The contributions due to the intraband and interband transitions are compared: It is found that the major contribution to the dielectric function is due to the intraband transitions.