Three-magnon processes in magnetic nanoelements: Quantization and localized mode effects

Three-magnon effects are known to be important for nonlinear processes in magnetic thin films. In such a process, for example, the uniform mode at a frequency omega can decay into two modes at a lower frequency omega/2. In magnetic nanoelements, there are additional concerns which do not occur in films. First, in small elements, the excitation wave vectors become a set of discrete values. This limits the availability of final states. Second, localized modes are important in nanoelements. Our study is based on micromagnetic calculations using the Landau-Lifshitz equations. We use an oscillating magnetic field at frequency omega to drive the system and to study the response over a wide range of frequencies and for a wide set of input powers. In nanoelements, the typical response occurs not exactly at omega/2 but for several frequencies which are symmetrically spaced around omega/2. This is explained by the two considerations introduced above. We study the response both as a function of the amplitude of the driving field and as a function of the driving frequency. In this way, we can study the system response both at resonance and outside of resonance.