Parametric and Modulation Instabilities of Magnetostatic Surface Spin Waves in Ferromagnetic Films

First-order parametric instability, modulation instability and second-order instability processes for magnetostatic surface waves propagating in a pure yttrium iron garnet film are investigated in accordance with the relationship between the magnetostatic wave frequency and the internal magnetic field. The transitions from the second-order parametric instability, via the modulation instability, to the first-order parametric instability (when the magnetic field is 720 Oe and the carrier frequency varies from 3.87 to 4.39 GHz), and the transitions from the first-order parametric instability to the second-order parametric instability via the modulation instability (when the carrier frequency is 3.5 GHz and the magnetic field varies from 427 to 647 Oe) are experimentally observed and explained. Dispersion characteristics of the magnetostatic surface waves are modified by introduction of a metallic ground plane in order that the Lighthill criterion, as one of the prerequisites for onset of the modulation instability, is fulfilled in a limited frequency range. Characteristics of magnetostatic surface wave modulation instability are studied by solving the nonlinear Schrödinger equation. Dependencies of the modulation frequency induced by the modulation instability on the carrier frequency and the magnetic field are found to be consistent with experimental data.