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We find a nearly linear dependence of the interface-related Gilbert damping enhancement $\\Delta\\alpha$ on the heavy-metal spin-sink layer thicknesses t$_\\textrm{N}$ in direct-contact Ni$_{81}$Fe$_{19}$/(Pd, Pt) junctions, whereas an exponential dependence is observed when Ni$_{81}$Fe$_{19}$ and (Pd, Pt) are separated by \\unit[3]{nm} Cu. 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