We report on broadband ferromagnetic resonance linewidth measurements performed on epitaxial Heusler thin films. A large and anisotropic two-magnon scattering linewidth broadening is observed for measurements with the magnetization lying in the film plane, while linewidth measurements with the magnetization saturated perpendicular to the sample plane reveal low Gilbert damping constants of $(1.5pm0.1)times 10^{-3}$, $(1.8pm0.2)times 10^{-3}$, and $<8times 10^{-4}$ for Co$_2$MnSi/MgO, Co$_2$MnAl/MgO, and Co$_2$FeAl/MgO, respectively. The in-plane measurements are fit to a model combining Gilbert and two-magnon scattering contributions to the linewidth, revealing a characteristic disorder lengthscale of 10-100 nm.
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