Calculation of the Gilbert damping matrix at low scattering rates in Gd

In rare-earth metals the magnetization dynamics is determined by the interplay between the magnetization M-4f of localized 4f electrons and the magnetization m of delocalized 5d6sp valence electrons, whereby both subsystems can deliver angular momentum to the lattice, thus producing damping. It is shown within the framework of a phenomenological version of the s-f model that the effective Gilbert damping parameter for M-4f(t) is given by alpha(eff)(4f) = alpha(4f)+alpha(5d6sp)/(1+M-4f/m), where alpha(4f) is a direct 4f contribution and alpha(5d6sp) describes the Gilbert damping for the valence magnetization. By a combination of the ab initio density-functional electron theory with the breathing Fermi-surface model it is shown that for a [0001] orientation of the magnetization the indirect valence contribution to alpha(eff)(4f) is comparable to the damping parameter of Co (which is considerably smaller than the one of Ni). Measurements of the damping at low temperatures and for Gd samples with high purity are required to figure out whether there is a considerable larger direct contribution alpha(4f).