  Modulation of Spin Torque Oscillators (STOs) is investigated by analytically
solving the time-dependent coupled equations of an auto-oscillator. A Fourier
series solution is proposed, leading to the coefficients being determined with
a linear set of equations, from which a Nonlinear Amplitude and Frequency
Modulation (NFAM) scheme is obtained. In this framework, the NFAM features are
related to the intrinsic STO parameters, revealing a frequency-dependence of
the harmonic-dependent modulation index that allows a modulation bandwidth to
be defined for these devices. The presented results expose a rich parameter
space, where the modulation and the STO's operation conditions define the
observed modulation features. The Fourier-series representation of the time
signal is suitable for studying periodic perturbations on the auto-oscillator
equation.
