Multimagnon theory of antiferromagnetic resonance relaxation

The temperature dependence of the linewidth of the antiferromagnetic resonance is shown to arise from multimagnon processes. At low temperatures a four-magnon process usually dominates. As the temperature increases towards the N\'eel temperature TN higher-order processes such as six-magnon, etc., become progressively more important. An analytic expression is derived for the n-magnon relaxation rate in the high-temperature limit. The theoretically predicted temperature and frequency dependence of the linewidth agrees quantitatively with data on MnF₂, FeF₂, GdAlO₃, Rb₂MnF₄, and K₂MnF₄, up to 0.8TN.