Hysteresis regime in the operation of a dual-free-layer spin-torque nano-oscillator with out-of-plane counter-precessing magnetic moments

We studied the operation of a dual-free-layer (DFL) spin-torque nano-oscillator (STNO) and demonstrated that in a practically interesting regime when the magnetizations of the two free layers (FLs) precess in opposite directions along large-angle out-of-plane trajectories, thus doubling the generation frequency, the operation of the DFL STNO is strongly hysteretic as a function of a bias dc current. The stable magnetization dynamics starts at a rather large magnitude of the bias dc current density $Jdc>Jthhigh$ when the bias current is increased, but the regime of stable counter-precession of the FLs persists till rather low magnitudes of the bias dc current density $Jthlow<Jdc<Jthhigh$ when the bias current is decreased. This hysteresis is caused by the dipolar coupling between the FLs, and is especially pronounced for small distances between the FLs and the small magnetic damping in them. The discovered hysteretic behavior of the DFL STNO implies the possibility of application of a strong initial pulse of the bias current (greater than the upper threshold $Jthhigh$ of the stable dynamics) and subsequent reduction of the bias current to a working point (⁠$Jthlow<Jdc<Jthhigh$⁠) corresponding to the required output frequency $f(Jdc)$⁠. The obtained results are important for the practical development of DFL STNOs with optimized operation characteristics.