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The magnetization relaxation of thin ferromagnetic Ni81Fe19 films in close proximity and in direct contact with antiferromagnetic FeMn films was investigated using broadband ferromagnetic resonance. For unbiased films, a contribution to the effective-damping parameter αeff inversely proportional to the ferromagnetic film thickness is found, consistent with the presence of spin pumping. For biased films, we find a unidirectional contribution to the effective-damping parameter, which does not scale with the inverse film thickness. The unidirectional character of the magnetization relaxation is described in terms of two-magnon scattering.