Analysis of spin density wave conductivity spectra of iron pnictides in the framework of density functional theory

The optical conductivity of LaFeAsO, BaFe$_2$As$_2$, SrFe$_2$As$_2$, and EuFe$_2$As$_2$ in the spin-density wave (SDW) state is investigated within density functional theory (DFT) in the framework of spin-polarized generalized gradient approximation (GGA) and GGA+U. We find a strong dependence of the optical features on the Fe magnetic moments. In order to recover the small Fe magnetic moments observed experimentally, GGA+$U_{\rm eff}$ with a suitable choice of negative on-site interaction $U_{\rm eff}=U-J$ was considered. Such an approach may be justified in terms of an overscreening which induces a relatively small U compared to the Hund's rule coupling J, as well as a strong Holstein-like electron-phonon interaction. Moreover, reminiscent of the fact that GGA+$U_{\rm eff}$ with a positive $U_{\rm eff}$ is a simple approximation for reproducing a gap with correct amplitude in correlated insulators, a negative $U_{\rm eff}$ can also be understood as a way to suppress magnetism and mimic the effects of quantum fluctuations ignored in DFT calculations. With these considerations, the resulting optical spectra reproduce the SDW gap and a number of experimentally observed features related to the antiferromagnetic order. We find electronic contributions to excitations that so far have been attributed to purely phononic modes. Also, an orbital resolved analysis of the optical conductivity reveals significant contributions from all Fe 3d orbitals. Finally, we observe that there is an important renormalization of kinetic energy in these SDW metals, implying that the effects of correlations cannot be neglected.