Current-Induced Switching of Perpendicularly Magnetized Magnetic Layers Using Spin Torque from the Spin Hall Effect

We show that in a perpendicularly magnetized $\mathrm{Pt}/\mathrm{Co}$ bilayer the spin-Hall effect (SHE) in Pt can produce a spin torque strong enough to efficiently rotate and switch the Co magnetization. We calculate the phase diagram of switching driven by this torque, finding quantitative agreement with experiments. When optimized, the SHE torque can enable memory and logic devices with similar critical currents and improved reliability compared to conventional spin-torque switching. We suggest that the SHE torque also affects current-driven magnetic domain wall motion in $\mathrm{Pt}/\mathrm{\text{ferromagnet}}$ bilayers.

Figure 1

(a), (b) Current-induced switching in a $\mathrm{Pt}/\mathrm{Co}/{\mathrm{AlO}}_x$ sample at room temperature in the presence of a small, fixed in-plane magnetic field $B_y$ with (a) $B_y=10\mathrm{mT}$ and (b) $B_y=-10\mathrm{mT}$. (c) Top view of the sample ($50\mu \mathrm{m}$ scale bar). (d) $R_H$ as a function of $B_{\mathrm{ext}}$ perpendicular to the sample plane. (e) Illustration of the torques exerted by the external field ${\overrightarrow{B}}_{\mathrm{ext}}$, the anisotropy field ${\overrightarrow{B}}_{\mathrm{an}}$, and the SHE torque ${\overrightarrow{\tau }}_{\mathrm{ST}}$ for positive current, when ${\overrightarrow{B}}_{\mathrm{ext}}$ and $M$ are in the $yz$ plane. The dashed arrows show the direction of electron flow for positive current.

Figure 2

(a) Predictions for current-induced magnetic switching within the macrospin model. (b) Illustration of the tilted magnetic states that are stable in the absence of a current when a fixed in-plane magnetic field (left) $B_y>0$ or (right) $B_y<0$ is applied. The tilt angle is exaggerated compared to Figs. 1a, 1b. Current-induced switching depends on the sign of ${\tau }_{\mathrm{ST}}^0$ as shown. (c) $R_H$ vs $B_{\mathrm{ext}}$, measured during coherent rotation for $I=\pm 12\mathrm{mA}$, when the magnetic field is in the $yz$ plane at $\beta =4°$. (d) Points: measured values of $B_{-}(\theta )-B_{+}(\theta )$ and $[B_{-}(\theta )+B_{+}(\theta )]/2$ as defined in the text, determined from the data in (c). Lines: fits to the macrospin model to determine ${\tau }_{\mathrm{ST}}^0(I)$ and $B_{\mathrm{an}}^0(I)$. (e) ${\tau }_{\mathrm{ST}}^0/I$ measured for different values of $I$. (f) $R_H$ as a function of the applied field when $B_{\mathrm{ext}}$ is applied along the $x$ direction, for $I=\pm 10\mathrm{mA}$. The curves are indistinguishable, allowing us to set a limit on the in-plane Rashba field.

Figure 3

(a), (b) SPD calculated in the zero-temperature macrospin model for (a) $B_{\mathrm{ext}}$ applied along the $y$ axis and (b) $B_y$ fixed at $0.2B_{\mathrm{an}}^0$ with $B_z$ varied continuously. Switching boundaries for the $\{m_z=\uparrow /\downarrow ,m_x=0\}$ states (solid lines) . Limits of stability for the $m_x\ne 0$ states (dashed lines). (c), (d) SPD determined experimentally by (c) sweeping $I$ for fixed values of $B_{\mathrm{ext}}$ along the $y$ axis, and (d) fixing $B_y=40\mathrm{mT}$ and sweeping $B_z$. The solid lines in (c) and (d) represent switching boundaries calculated using the modified Stoner-Wohlfarth model. In all panels, the symbol $\uparrow$ means $m_z>0$ and $\downarrow$ means $m_z<0$, not $m_z=\pm 1$.