Figure 1

(a) Schematic of the MTJ nanopillar with layer thicknesses given in nm. (b) Measured bias dependence of the MTJ conductance in the parallel ($G_{\mathrm{P}}$) and antiparallel ($G_{\mathrm{AP}}$) states. Also shown are the average conductance $G_0$ and the inverse time-averaged resistance $⟨R{⟩}^{-1}$ for the indicated external in-plane field. (c) Examples of trajectories followed by the free-layer magnetization on the sphere, and the distributions of the sample plane crossing angles at a nonzero temperature. We use spherical coordinates $\theta$ and $\phi$, where $\theta$ is the polar angle defined with respect to the sample plane normal $\widehat{z}$ and $\phi$ is the azimuthal angle defined with respect to the P state direction $\widehat{x}$. (d) A time-domain resistance trace $R(t)$ whose maxima and minima are used to reconstruct the sample plane crossing distributions.Reuse & Permissions

Figure 2

Plane crossing probability distributions ${\rho }_c(\phi )$ measured at several values of the bias current for $H=500$ Oe applied at ${\phi }_H=120°$. Also shown are distributions calculated from macrospin and micromagnetic simulations as well as by the Fokker-Planck approach described in the text. The macrospin distributions have been shifted towards $\phi =0$ by $0.03\pi$ as a visual aid. This shift is an artifact of the macrospin approximation [28]. The inset shows the magnitude of the FLT extracted (using both macrospin fitting and the Stoner-Wohlfarth model described in the text) from the current-induced shifts of the equilibrium angles.Reuse & Permissions

Figure 3

(a) Measured PSDs delivered to a $50\Omega$ load along with macrospin and micromagnetic simulation results ($I$ in steps of 0.1 mA). (b) Effective energies $E_{\mathrm{eff}}(\phi ,I)$ and corresponding crossing probability distributions ${\rho }_c(\phi )$. (c) Frequencies (solid lines) and generated electrical powers (dotted lines) of the macrospin conservative orbits. (d) Comparison of (offset) PSDs from macrospin simulations and the effective energy approach given by Eq. (7).Reuse & Permissions