Analytical and Micromagnetic Study of Nonlinear Amplitude Modulation in Spintronic Modulators

A previous universal model of "combined" frequency-amplitude nonlinear modulation has been used to describe the spin-wave dynamics observed in spin-transfer oscillators. In that case, it was shown that it is not possible to obtain a pure frequency modulation process because the strict nonlinear relationship existing between the characteristic parameters of the oscillator yields a non-negligible amplitude modulation process to take place simultaneously. Here, we demonstrate that there exists a particular configuration in which a spin-torque oscillator behaves as a "pure" nonlinear amplitude modulator. For the case of a nano-contact geometry, for example, such a condition implies the usage of an external out-of-plane bias field directed along the critical angle at which the frequency tunability coefficient T = partial derivative f/partial derivative I vanishes. In all those cases in which this coefficient is not zero, the previous combined process takes place. The phenomenon is first analyzed by developing an analytical model which describes the structure of the frequency spectrum of a nonlinearly amplitude modulated signal. Results of this approach are finally compared with those of micromagnetic investigations, carried out in time and frequency domains, deriving an excellent agreement.