Figure 1

An overview plot of the measured efficiencies of spin-torque switchable MTJs of different sizes. (a) The dependence of observed efficiency $\kappa$ vs junction size. Here the parallel-state conductance $G_p$ is used to represent the junction area, with an averaged junction resistance-area product ranging between 5 and 20 $\Omega$$\mu {\text{m}}^2$. Junctions are all of circular shape. (b) The same set of devices showing the efficiency vs junction's MR. The two dashed lines are comparisons to Eq. (3) with $\alpha =0.005$ (upper) and $0.015$ (lower).Reuse & Permissions

Figure 2

Size dependence of junction properties. Here for most devices [except the relatively large ones marked in gray pentagons in (a)–(c)], the size of the actual junction is confirmed post-transport measurement with cross-section transmission electron microscopy (TEM) images. (a) The dependence of thermal activation energy on junction area, showing the initial rise followed by saturation at larger junction area. Note that the initial rise does not follow a simple linear area dependence with zero intercept but rather there is a significant intercept at zero device area. (b) The dependence of $E_b$ on the diameter of junction, showing a large region of nearly linear dependence with zero intercept before reaching saturation $E_b$ (Refs. 6, 7, 8, 9) as indicated by line (3). (c) The dependence of switching current on junction area showing the expected linear dependence with zero intercept. (d) The dependence of spin-torque efficiency $\kappa =E_b/I_{c0}$ on junction area. The gray scale represents the actual measured resistance-area product $\text{RA}$ of the junction. It shows that the effect of $\text{RA}$ on $\kappa$ is minor compared to $\kappa$'s very strong size dependence.Reuse & Permissions

Figure 3

A sketch of the various model predictions of thermal activation energy vs disk diameter $a$ compared with experimental observations. Here $d$ is the disk thickness. $E_{b,MS}$ is the macrospin energy barrier, $E_{b,DW}$ is the energy barrier for a domain-wall-like object sweeping across the disk, $E_{b,\mathrm{saturated}}\approx 4\pi A_{ex}d$ is the subvolume related saturation activation energy (Refs. 6, 7, 8, 9). The gray curve illustrates our experimentally observed behavior. The inset shows the energy maximum state of a domain-wall-like object sweeping across the disk. The gray scale represents the polar angle of ${\mathbf{n}}_m$ with disk-film normal ${\mathbf{e}}_z={\mathbf{e}}_x\times {\mathbf{e}}_y$. The choice of $K_{pma}$ here, and the related relationship between the macrospin branch and the experimental curve is only for illustrating the difference in trend. Scaling relations with “$\sim$” symbols are only crude estimates, while those with “$=$” are exact predictions. A more quantitative comparison is given by the model calculation presented in Fig. 2.Reuse & Permissions