Abstract
The influence of multiple elastic scattering on the magnon parametric excitation in low-dimensional magnets is studied. The multiple-scattering results in the strong backscattering of magnons. This backscattering can interfere with the parametric excitation because both phenomena involve pairs of magnons with opposite momenta. It is shown that the influence of the backscattering on the threshold of parametric excitation in two-dimensional systems is proportional to the logarithm of the size, even if it exceeds the inelastic mean free path. The possibilities of experimental observation of the effect are discussed.
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