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A phenomenological model is given for calculating magnon sideband lineshapes in the absorption spectra of antiferromagnetic crystals. The method allows an exact expression for the lineshape to be obtained when dispersion within the Brillouin zone of both the exciton energy and the exciton-magnon interaction strength is included. The effect of a substitutional spin impurity is calculated exactly, and a simple example is given which approximates the effects of an impurity on a magnon sideband in the antiferromagnetic perovskite RbMnF3 ? It is thought that the ability of the model to predict the existence of local modes and resonances justifies the simple form of the model Hamiltonians chosen. The pure crystal sideband Iineshape can also be well determined from information on the exciton dispersion and the behaviour of the exciton-magnon interaction strength within the Brillouin zone.

Extended Theory of Magnon Sideband Shapes. II. Impure Three-dimensional Antiferromagnets