  The non-linear parameters of spin-torque oscillators based on a synthetic
ferrimagnet free layer (two coupled layers) are computed. The analytical
expressions are compared to macrospin simulations in the case of a synthetic
ferrimagnet excited by a current spin-polarized by an external fixed layer. It
is shown that, of the two linear modes, acoustic and optical, only one is
excited at a time, and therefore the self-sustained oscillations are similar to
the dynamics of a single layer. However, the non-linear parameters values can
be controlled by the parameters of the synthetic ferrimagnet. With a strong
coupling between the two layers and asymmetric layers (different thicknesses),
it is demonstrated that the non-linear frequency shift can be reduced, which
results in the reduction of the linewidth of the power spectral density. For a
particular applied field, the non-linear parameter can even vanish; this
corresponds to a transition between a red-shift and a blue-shift frequency
dependence on the current and a linewidth reduction to the linear linewidth
value.
