Collective spin-wave oscillations in finite-size ferromagnetic samples.

Abstract

A theory of collective oscillations in a system of spin waves parametrically excited by homogeneous parallel pumping in a finite-size ferromagnetic sample is developed. This theory is an extension of the well-known S theory of spin-wave collective oscillations in an infinite ferromagnetic medium for the case when the boundary conditions in a magnetic sample of finite size D are taken into account. The unstable collective oscillations in the system of parametric spin waves manifest themselves as low-frequency autooscillations of magnetization and demonstrate a variety of bifurcations and transition to chaos. We show that by introducing boundary conditions and taking into account the finite size of the sample it is possible to explain the following experimentally observed properties of spin-wave autooscillations that were not explained by the existing models of this phenomenon: (i) the difference between the threshold of parametric excitation of spin waves ${\mathit{h}}_{\mathrm{th}}$ and the threshold of autooscillations ${\mathit{h}}_{\mathrm{osc}}$; (ii) the finite value of the autooscillation frequency ${\mathit{f}}_{\mathrm{osc}}$ at the threshold of autooscillations; (iii) the dependences of the threshold ${\mathit{h}}_{\mathrm{osc}}$ and the frequency ${\mathit{f}}_{\mathrm{osc}}$ of the spin-wave autooscillations on the size of the ferromagnetic sample. The results of the theory are in good qualitative agreement with the results of experiments in which the influence of sample size on the spin-wave autooscillations was studied in yttrium iron garnet spheres.