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In ferromagnets which nonuniformities are beyond the linearized spin waves, there is a nonlinear q2 contribution to damping [see arXiv:0803.2175 (unpublished)] which has a different physical origin, related to the longitudinal spin-current fluctuations.
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Although both σ and χ are in principle tensors in transverse spin space, they are proportional to δab in axially symmetric systems; hence we use scalar notation.
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