Ferromagnetic resonance (FMR) was used to investigate the static and dynamic magnetic properties of carbon-doped Mn5Ge3 (C$_{0.1}$ and C$_{0.2}$) thin films grown on Ge(111). The temperature dependence of magnetic anisotropy shows an increased perpendicular magneto-crystalline contribution at 80K with an in-plane easy axis due to the large shape contribution. We find that our samples show a small FMR linewidth (corresponding to an intrinsic magnetic damping parameter $alpha$=0.005), which is a measure of the spin relaxation and directly related with the magnetic and structural quality of the material. In the perpendicular-to-plane geometry, the FMR linewidth shows a minimum at around 200K for all the samples, which seems to be not correlated to the C-doping. The magnetic relaxation parameters have been determined and indicate the two-magnon scattering as the main extrinsic contribution. We observe a change in the main contribution from scattering centres in Mn5Ge3C0.2 at low temperatures, which could be related to the minimum in linewidth.
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