Long-wavelength magnetic excitations in randomly anisotropic ferromagnets

A semiclassical Green's function method is used for studying long-wavelength spin wave excitations in amorphous ferromagnetic alloys with randomly orientated single-ion anisotropy. The dispersion law and the density of states of such excitations are calculated both by a Green's function truncation procedure and numerically using a Monte Carlo technique to generate the ground state of the system. Both procedures yield a gap in the excitation spectrum which increases monotonically with the anisotropy constant and is somewhat smaller than the gap in the related crystalline ferromagnet. In addition, the density of states of the spin wave excitations, as calculated numerically, shows the possible existence of localised states in the gap region.