Effects of magnetism and doping on the electron-phonon coupling in BaFe2As2

We calculate the effect of local magnetic moments on the electron-phonon coupling in doped BaFe2As2 using the density-functional perturbation theory. We show that the magnetism enhances the total electron-phonon coupling by similar to 50%, up to lambda <= 0.35, still not enough to explain the high critical temperature, but strong enough to have a non-negligible effect on superconductivity, for instance, by frustrating the coupling with spin fluctuations and inducing order-parameter nodes. The enhancement comes not from the phonon softening but mostly from a renormalization of the electron-phonon matrix elements. We also investigate, in the rigid band approximation, the effect of doping, and find that lambda versus doping does not mirror the behavior of the density of states; while the latter decreases upon electron doping, the former does not, and even increases slightly.