Magnetization fluctuation renormalization of single magnon energies

We have suggested1 that the dependence on magnetic disorder of certain properties of itinerant ferromagnets is best studied by first computing them in the presence of a spatially slowly varying magnetization density, and then functionally averaging the magnetization. We report self‐consistent rpa calculations of single particle and spin wave energies and damping in the presence of such a magnetization modulation, or arbitrary amplitdue. The average energy gap is proportional to the population difference of suitably defined up‐ and down‐spin bands. The gap, and also the local magnetization magnitude, do not decrease in proportion to the average magnetization, but as the mean square gradient of the magnetization direction. At wave vectors large compared to those dominant in the background, the spin wave stiffness also contains a term proportional to this gradient squared. The coefficient is positive fr parabolic bands in the strong limit. These results are consitent with the observed insensitivity of band s...