Theory of spin-wave instability thresholds for ultrathin ferromagnetic films under parallel pumping

Abstract

A microscopic, or Hamiltonian-based, theory is developed to study the spin-wave instability thresholds for the parametric processes occurring in ultrathin ferromagnetic films under conditions of parallel pumping with a microwave field. Most previous work has focused on spheres or films with dimensions of order several microns or more, and the theoretical interpretation has been in terms of macroscopic (continuum) methods. At smaller size scales, as in ultrathin films with thickness less than about 100 nm, the discreteness of the quantized spin waves and their spatial distributions become modified, making it more appropriate (particularly for the nonlinear dynamics) to employ a microscopic or Hamiltonian-based approach with a lattice of effective spins interacting with one another through the magnetic dipole-dipole and exchange interactions. This work utilizes a similar microscopic approach, but with the effects of microwave pumping included, to calculate the spin-wave instability thresholds for the bands of quantized spin waves in ultrathin films with the saturation magnetization parallel to their surface. Magnetic materials with different ratios of the exchange to dipole-dipole strengths are considered, taking examples for relatively strong, intermediate, and weak exchange. In the case of parallel pumping it is found that the shape of the typical ``butterfly curve,'' as conventionally obtained with macroscopic samples of YIG, becomes modified in these ultrathin films due to the occurrence of several quantized spin-wave bands and their spatial properties.