Nonanalytic magnetization dependence of the magnon effective mass in itinerant quantum ferromagnets

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 Omega, small wave vectors k, and m-->0, the dispersion relation is found to be of the form Omega = constXm(1-alpha)k(2), with alpha=(4-d)/2 (2<d<4) for disordered systems, and alpha=(3-d) (1<d<3) for clean ones. In d=4 (disordered) and d=3 (clean), Omega proportional to m 1n(1/m)k(2). Experiments to test these predictions are proposed. [S0163-1829(98)06045-7].