Pattern formation due to spin-wave instabilities: Squares, hexagons, and quasiperiodic patterns

We study dissipative patterns caused by spin-wave instabilities in insulating ferromagnetic films which are driven by out-of-plane parallel pumping. Using a multiple-scale perturbation method, we derive amplitude equations for magnetostatic modes with wavelengths much larger than the film thickness, and study the stability of solutions with constant amplitudes. The main result is that the only stable patterns are squares, hexagons, and quasiperiodic patterns based on three standing waves. Quantitative results strongly support the suggestion that these patterns should be experimentally observable by means of Faraday rotation.