Abstract
The dynamic structure factor of Heisenberg magnets with weak randomness is computed. Under circumstances which are explained in detail, we find failure of hydrodynamic theory in the longitudinal structure factor due to localization of spin waves. Localization induces a power-law dependence on q and \ensuremath{\omega} for the neutron scattering line shape near magnetic Bragg spots. The exponent describing the power law is related to the correlation-length exponent of Anderson localization. Random anisotropy magnets appear to be promising candidates for experimental investigations.
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