Figure 1

A representative MTJ spin-torque switch. (a) The MTJ's resistance vs easy-axis-applied magnetic field. (b) The MTJ's current-voltage ($IV$) characteristics in its parallel (P), antiparallel (AP), and switching states. (c) The frequency dependence of the switching voltage position from (b). Values of calculated $E_b$ shown are in units of $k_{B}T$ with $T=300$ K. (d) The switching threshold boundary in $(V,H)$ phase space, measured by sweeping $R\left(H\right)$ loops such as shown in (a) at different junction bias voltages.Reuse & Permissions

Figure 2

The normal quantile values $S_r$ for the bit error rate (BER) of a spin-torque-driven MTJ for pulse widths of 2 (in black), 5, 50, 400, and 3200 (in cyan) ns. Shorter pulses require a higher voltage to achieve the same switching probability. Points are data, lines are guide to the eye. BER (bit-error-rate) represents cumulative nonswitching probability in unit of the apparent standard deviation $\sigma$, with zero corresponding to 50% nonswitching probability. Positive voltage is for parallel to antiparallel switching. The dashed lines indicate the location where the switching threshold and transition width are analyzed, as discussed in the text.Reuse & Permissions

Figure 3

(a) The threshold voltage $V_s$ and switching speed (defined as 1/switching time) for five MTJ devices. The threshold was defined at a probability for NOT switching of 0.006 (BER at $-2.5$$\sigma$), as shown in Fig. 2. (b) the relative switching width, as defined by the ratio of the inverse slope within $-2$ to $-3$ $\sigma$ as shown in Fig. 2 normalized to the threshold voltage at $-2.5$$\sigma$. Heavy solid lines in (b) represent the macrospin and the simple $N_a$ region subvolume excitation model's behavior in relative distribution width compared with measurement data. For both models the curves are generated using short-time asymptotes. Thus model curves should only be compared with data at the short-time limit.Reuse & Permissions

Figure 4

Junction size dependence of $E_b$(a) and $I_{c0}$(b). All shapes are approximately circular with an aspect ratio equal to 1. Open and closed circles are data from two wafers measured manually using the protocol shown in Fig. 1. One sees here that while $I_{c0}$ does appear to scale roughly with junction area, $E_b$ shows a significant zero-area intercept. (c) The spin-torque efficiency factor plotted against junction area. Most of the large size devices have spin-torque efficiency factors well below that of the macrospin model value. The deviation becomes smaller, however, as junction sizes shrink. Also shown here in gray are measurements from a much larger set of junctions on a separate wafer with about two times lower junction $RA$ and using a different measurement protocol involving fully automated on-chip CMOS-circuit-driven tests. Aside from a slope change attributable to the difference in junction $RA$, the basic scaling behavior remains the same. Part of the difference between the macrospin limit and the observed efficiency in (c) may be due to uncertainties in the estimate of $E_b$ in absolute terms, as the measurements for $E_b$ do not strictly satisfy $I/I_{c0}\ll 1$, and will suffer the problems discussed in Refs. 37 and 41. The CMOS-based measurement for $E_b$ extends only to data in millisecond duration which is shorter than that of the manually measured data, consistent with the CMOS-based data giving a lower $E_b$ and efficiency estimate on average.Reuse & Permissions

Figure 5

A side-view illustration of the $N_a$ unit subvolume excitation model structure. The free layer is assumed to fluctuate magnetically independently with $N_a$ regions, with the average size of such region being $L/\sqrt{N_a}$. The film is assumed to be sufficiently thin so the magnons perpendicular to the film surface do not participate in the dynamics of interest here. This structure gives the scaling relationships of Eq. (8).Reuse & Permissions