Spin-wave Theory for the Magnetic Damping in Microwave Nano-Oscillators

Here we present a calculation for the linewidth of the spin-wave that is generated when a spin valve nanostructure is traversed by a high-density spin-polarized direct current. In this case, the magnetization excitations are considered to be standing spin-wave modes interacting through the four-magnon processes. We obtain an analytic expression for the effective nonlinear dissipation rate of a magnetic spin-torque nano-oscillator, taking into account a nonlinear phenomenological model of magnetic dissipation and the natural nonlinear contributions due to the demagnetizing fields. The calculation is applied for the general case of the external magnetic field applied in an arbitrary direction.