Spin-wave Instability Theory for Ferromagnetic Nanostructures

A microscopic, or Hamiltonian-based, theory is outlined for studying the spin-wave instability thresholds of the parametric processes occurring in ferromagnetic nanostructures under conditions of pumping with a microwave eld. Most previous work has concentrated on spheres or lms with dimensions of order several μm or more, with the theoretical interpretation being made in terms of macroscopic (or continuum) methods. At smaller length scales, as in ultrathin lms and nanowires with thickness or lateral dimensions less than about 100 nm, the discreteness of the quantized spin waves and their spatial distributions become modi ed, making it more appropriate to employ a microscopic approach to the nonlinear dynamics with a lattice of e ective spins interacting through the magnetic dipole dipole and exchange interactions. E ects of microwave pumping (in either the parallel or perpendicular con guration) are incorporated in calculations for the instability thresholds of the quantized spin-wave bands in di erent nanostructures and materials.