(a) Layout of the symmetric DFL STNO consisting of four magnetic layers: two inner FLs of the thickness L and two outer pinned layers with perpendicular polarization separated by the GMR spacer of the thickness d. (b) The torques acting on the magnetization vectors of the FLs in the DFL STNO driven by the transverse bias dc current of the density J dc. The conservative torque (T P ) caused by the effective magnetic field B eff induces magnetization precession in the FLs around the normal to the STNO layers. The non-conservative spin-torques (T S ) caused by the perpendicular polarizers adjacent to each of the FLs tend to increase the precession angle, while the non-conservative torques (T D ) caused by the Gilbert damping in the FLs tend to reduce it.
(a) Numerically calculated dependences of the precession frequencies in the top and bottom FLs in a DFL STNO on the density J dc of the bias dc current, demonstrating strong hysteresis. Dynamics starts at when the bias current increases (red squares and cyan circles) and stops at when the current decreases (orange hollow squares and blue crosses). The system can be in the IPS or in the out-of-plane precessional (OPP) state. (b) Numerically calculated dependence of the frequency of an output signal f in a DFL STNO on the bias direct current density J dc. The generated frequency is equal to the sum of the precession frequencies in the FLs, . Yellow star marks a possible working point, which could be reached by using the procedure described in Sec. III C . The curves are calculated for α = 0.08, . All the other parameters of the DFL STNO are presented in Sec. II D .
Numerically calculated dependences of the current density thresholds (blue circles and line) and (red squares and line) on the different parameters of the DFL STNO. (a) The dependence of and on the Gilbert damping parameter α. (b) The dependence of and on the magnitude of the in-plane anisotropy field B A. (c) The dependence of and on the distance between the FLs d. Green stars and dashed line show the dependence of the cross-demagnetization coefficient ρ on d, ρ(d). All the curves are calculated for α = 0.08, B A = 5 mT (if other values of parameters are not mentioned specifically). All the other parameters of the DFL STNO are presented in Sec. II D .
Numerically calculated time profiles of the in-plane ( , blue curve) and out-of-plane ( , red curve) magnetization components in the top FL of the DFL STNO for different regimes of time-dependent current biasing (b, d, f). The DFL STNO is biased by a dc current density having a constant and a pulsed components and its time profile is shown by the green curve with green shading (a, c, e). Dashed horizontal lines show the levels corresponding to the higher (orange lines) and lower (violet lines) current thresholds . (a) The constant current density below the higher threshold induces only small perturbations of the IPS magnetization state (b). (c) The current density containing a constant part and a pulse of the duration 0.5 ns with the amplitude (still below the higher threshold) induces some transient dynamics, and the IPS magnetization state remains stable (d). (e) The current density containing a constant part (above the lower threshold) and a strong pulse of the duration T pulse = 0.5 ns with the amplitude (exceeding the higher threshold) induces a stable magnetization precession (f). The curves are calculated for α = 0.08, B A = 5 mT. All other parameters of the DFL STNO are presented in Sec. II D .
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