The spin-wave dispersion relation in both clean and disordered itinerant quantum ferromagnets is calculated. It is found that effects akin to weak-localization physics cause the frequency of the spin waves to be a nonanalytic function of the magnetization m. For low frequencies Ω, small wave vectors k, and m→0, the dispersion relation is found to be of the form Ω=const x m1-αk2, with α = (4-d)/2 (2 < d < 4) for disordered systems, and α = (3-d) (1 < d < 3) for clean ones. In d = 4 (disordered) and d = 3 (clean), Ωαm ln (1/m) k2. Experiments to test these predictions are proposed.
D. Belitz et al., "Nonanalytic Magnetization Dependence of the Magnon Effective Mass in Itinerant Quantum Ferromagnets," Physical Review B - Condensed Matter and Materials Physics, vol. 58, no. 21, pp. 14155-14158, American Physical Society (APS), Dec 1998.
The definitive version is available at https://doi.org/10.1103/PhysRevB.58.14155
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