  Being nonlinear dynamic systems, magnetic read sensors should respond to an
excitation signal of a frequency considerably different from their natural
ferromagnetic resonance (FMR) frequencies. Because of the magnetization
dynamics' inherent nonlinear nature, the sensors' response should be measured
at the DC, excitation frequency, and its multiples (harmonics). In this paper,
we present results of such measurements, accomplished using a one-port
nonlinear vector network analyzer (NVNA), which show distinct resonances at
fractional frequencies of the free layer (FL) FMR mode. Identification of these
resonances, resulting from the nonlinear nature of the spin-torque (ST)-induced
magnetization dynamics, was performed using micromagnetic modeling. In
particular, we show that the measured DC response at the above-mentioned
fractional frequencies can be explained by a low-order nonlinearity and strong
magnetodipolar feedback between magnetic layers adjacent to an MgO barrier.
Additionally, we determined that the simulated harmonic response is strongly
enhanced by the mutual ST effect between these layers. Finally, we demonstrate
that the read sensors' nonlinear magnetization dynamics and, by extension,
their harmonic response are highly sensitive to various magnetic and ST
parameters. Thus, this study shows that using NVNA measurements in conjunction
with micromagnetic modeling can clarify the uncertainty in the definition of
these parameters.
