Figure 1

(Color online) Dependence of the frequency $\omega ∕{\omega }_0$ generated in a magnetic nanopillar on the bias current $I∕I_{\mathrm{th}}$. Symbols—experimental data from Ref. 13 [see Fig. 1(d) in Ref. 13]. Curve 1—theoretical calculation using the standard Gilbert model [Eq. (2)]. Curves 2 and 3—theoretical calculations using the first-order nonlinear dissipation model [Eq. (6)] with $q_1=1$ (curve 2) and $q_1=3$ (curve 3). Curve 4—second-order nonlinear dissipation model with $q_1=3$ and $q_2=1$. Dashed lines show the unstable states that are not observed experimentally. External bias magnetic field $H_0∕4\pi M_0=0.35$.Reuse & Permissions

Figure 2

(Color online) Dependence of the precession angle ${\theta }_0$ on the bias current $I∕I_{\mathrm{th}}$. Parameters and notations are the same as in Fig. 1.Reuse & Permissions

Figure 3

(Color online) Main panel: dependence of the precession angle ${\theta }_0$ on the bias current $\sigma I∕I_{\mathrm{th}}$ for two models of dissipation. Angles 0° and 180° correspond to the parallel and antiparallel orientations of the magnetizations in the free and fixed layers, respectively. Arrows indicate changes in precession angle with increasing/decreasing current. Thin dashed arrows—standard Gilbert model: $\alpha \left(\xi \right)={\alpha }_G$ and thick solid arrows—first-order nonlinear dissipation model for $q_1=1$: $\alpha \left(\xi \right)={\alpha }_G(1+\xi )$. External bias magnetic field $H_0∕4\pi M_0=1.4$. Inset: dependence of the precession frequency $\omega ∕{\omega }_0$ in the nonlinear dissipation model on the bias current for the same parameters as in the main panel.Reuse & Permissions

Figure 4

(Color online) Phase diagram of possible dynamical states in an in-plane magnetized nanopillar. White areas correspond to the region where no stable precessional states are possible, light gray areas show the regions where both stable precessional and stable stationary states coexist, and dark gray areas show the regions where the only stable states are the precessional states. Solid lines show boundaries between dynamical states. Left panel: standard Gilbert model $\alpha \left(\xi \right)={\alpha }_G$ and right panel: first-order nonlinear dissipation model for $q_1=3$: $\alpha \left(\xi \right)={\alpha }_G(1+3\xi )$. Thick vertical line shows the interval of bias magnetic field in which a state, interpreted as a stable precessional state, was observed in Ref. 12 [see Fig. 3(d) in Ref. 12].Reuse & Permissions