Number of modes governing spin-wave turbulence

The Landau–Lifschitz equations describe the time evolution of magnetization in classical ferromagnets and are of basic importance for the understanding of magnetism. It is shown that, under quite general conditions, dissipative forms of these equations have attracting sets which are finite dimensional in a suitable sense. It follows from these results that, after an initial transient period, only a finite number of spin-wave modes contribute to the spin-wave instabilities responsible for the chaotic behavior recently found in ferromagnetic resonance, in both the tranverse and parallel pumping versions.