ON THE THRESHOLD OF PARAMETRIC-INSTABILITY OF SPIN-WAVES IN A FILM WITH A ROUGH-SURFACE

The threshold of parametric excitation of spin waves in a ferrite film with a rough surface is calculated. The influence of the surface on the threshold is twofold: (i) the normal component of the wave vector of a spin wave is quantized and (ii) surface roughnesses scatter a spin wave elastically. The elastic scattering conserves energy of spin waves and mixes phases of spin waves with different wave vectors. The threshold of parametric excitation h(th) depends on the relationship between the film thickness d and the mean free path l. The threshold in a thick film (d >> l) is close to that in an unbounded sample of ferromagnet h(th0): (h(th)/h(th0)2 = 1 + (pi-l/d)2. In a thin film (d << l) the threshold is close to that in a randomly inhomogeneous ferromagnet (h(th)/h(th0)2 approximately gamma-s/gamma, where gamma is the spin-wave damping and gamma-s is the frequency of elastic scattering of spin waves on surface roughnesses.