Thin highly textured Fe$_{mathrm{1+x}}$Co$_{mathrm{2-x}}$Si ($0 leq$ x $leq 1$) films were prepared on MgO (001) substrates by magnetron co-sputtering. The magneto-optic Kerr effect (MOKE) and ferromagnetic resonance (FMR) measurements were used to investigate the composition dependence of the magnetization, the magnetic anisotropy, the gyromagnetic ratio and the relaxation of the films. The effective magnetization for the thin Fe$_{mathrm{1+x}}$Co$_{mathrm{2-x}}$Si films, determined by FMR measurements, are consistent with the Slater Pauling prediction. Both MOKE and FMR measurements reveal a pronounced fourfold anisotropy distribution for all films. In addition we found a strong influence of the stoichiometry on the anisotropy as the cubic anisotropy strongly increases with increasing Fe concentration. The gyromagnetic ratio is only weakly dependent on the composition. We find low Gilbert damping parameters for all films with values down to $0.0012pm0.00012$ for Fe$_{1.75}$Co$_{1.25}$Si. The effective damping parameter for Co$_2$FeSi is found to be $0.0018pm 0.0004$. We also find a pronounced anisotropic relaxation, which indicates significant contributions of two-magnon scattering processes that is strongest along the easy axes of the films. This makes thin Fe$_{mathrm{1+x}}$Co$_{mathrm{2-x}}$Si films ideal materials for the application in STT-MRAM devices.
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