Electric-field control of field-free spin-orbit torque switching via laterally modulated Rashba effect in Pt/Co/AlOx structures

Abstract

Spin-orbit coupling effect in structures with broken inversion symmetry, known as the Rashba effect, facilitates spin-orbit torques (SOTs) in heavy metal/ferromagnet/oxide structures, along with the spin Hall effect. Electric-field control of the Rashba effect is established for semiconductor interfaces, but it is challenging in structures involving metals owing to the screening effect. Here, we report that the Rashba effect in Pt/Co/AlO_x structures is laterally modulated by electric voltages, generating out-of-plane SOTs. This enables field-free switching of the perpendicular magnetization and electrical control of the switching polarity. Changing the gate oxide reverses the sign of out-of-plane SOT while maintaining the same sign of voltage-controlled magnetic anisotropy, which confirms the Rashba effect at the Co/oxide interface is a key ingredient of the electric-field modulation. The electrical control of SOT switching polarity in a reversible and non-volatile manner can be utilized for programmable logic operations in spintronic logic-in-memory devices.

Fig. 1. Electrical control of field-free SOT switching in Pt/Co/AlO_x/TiO2 samples.

a Schematic of the gate voltage-induced lateral symmetry breaking. Gate voltage difference (ΔV_G) induces an electric-field modulation along the y-direction, creating additional lateral symmetry-breaking. With a charge current along x-direction, this lateral symmetry-breaking generates out-of-plane spin–orbit fields (red arrows); field-like effective field ($B_{\mathrm{FLT}}^z$), and damping-like effective field ($B_{\mathrm{DLT}}^z$). Those result in additional SOTs (z-SOT) in direction of $\mathbf{m}\times \mathbf{z}$ by $B_{\mathrm{FLT}}^z$ and $\mathbf{m}\times \left(\mathbf{m}\times \mathbf{z}\right)$ by $B_{\mathrm{DLT}}^z$, where $\mathbf{m}$ is located in y-z plane. The blue arrows indicate the in-plane spin–orbit fields ($B_{\mathrm{FLT}}^y$ and $B_{\mathrm{DLT}}^y$) induced by symmetry-breaking along the z-direction. b Schematic illustration of the Hall-bar device with two side gates and the sample structure of Pt/Co/AlO_x/TiO₂, where the inset shows the optical microscopic image. c Current-induced SOT switching for ΔV_G = 0 (V_G,L = V_G,R = 0 V). B_x = 20 mT. d, e Field-free spin–orbit torque switching for ΔV_G > 0 (V_G,L = +8 V, V_G,R = 0 V) (d) and the ΔV_G < 0 (V_G,L = 0 V, V_G,R = +8 V) (e). 8 V corresponds to the electric field of 2.5 MV/cm. Here, the blue (or red) dot arrows indicate from up-to-down (or down-to-up) switching direction.

Fig. 2. Harmonic spin–orbit torque measurements in Pt/Co/AlO_x/TiO2 samples.

a Schematic for the measurement configuration. The second harmonic Hall resistances $\left(R_{\mathrm{xy}}^{2\mathrm{\omega }}\right)$ for an a.c. current I_ac are measured while rotating the sample in the plane (azimuthal angle $\phi$) under an external field B_ext. b The $R_{\mathrm{xy}}^{2\mathrm{\omega }}$ versus $\phi$ curves for the TiO₂ samples with four different V_G combinations and B_ex = 3 T, where the single standard deviation uncertainty of the harmonic Hall voltage measurements is ±0.15 μV, which is included as error bars in the figures. Here, (+,+), (−,−), (+,−), and (−,+) denote (V_G,L = V_G,R = +8 V), (V_G,L = V_G,R = −8 V), (V_G,L = +8 V and V_G,R = −8 V), and (V_G,L = −8 V and V_G,R = +8 V), respectively. c–e The extracted $\phi$-dependent components of $R_{\mathrm{xy}}^{2\omega }$; $\mathrm{c}\mathrm{os}\phi$ component (c), $\left(2{\cos }^3\phi -\cos \phi \right)$ component (d), and $\cos 2\phi$ component (e). f–h Each $\phi$-dependent component plotted as a function of 1/B_eff (or 1/B_ext), where the error bars are due to the uncertainty of the fitting of the $R_{xy}^{2\omega }$ versus $\phi$ curves to Eq. (1); $\cos \phi$ component versus 1/B_eff (f), $\left(2{\cos }^3\phi -\cos \phi \right)$ component versus 1/B_ext (g), and $\cos 2\phi$ component versus 1/B_ext (h).

Fig. 3. Electric-field control of the field-free switching in Pt/Co/AlO_x/ZrO2 samples.

a Current-induced SOT switching for ΔV_G = 0 (B_x = 20 mT). b, c Field-free SOT switching for ΔV_G > 0 (b) and ΔV_G < 0 (c). Here, the blue (or red) dot arrows indicate from up-to-down (or down-to-up) switching direction.

Fig. 4. Voltage-induced variation of the potential barrier and field-like torque.

a, b I–V characteristics in the Ta (10 nm)/Co (10 nm)/AlO_x (2 nm)/TiO₂ (5 nm)/Ru (20 nm) (a) and Ta (10 nm)/Co (10 nm)/AlO_x (2 nm)/ZrO₂ (5 nm)/Ru (20 nm) tunnel junctions (b) depending on pre-biased gate voltages V_G corresponding to ±2.5 MV/cm. The inset corresponds to schematic drawing of the lateral variation of barrier height (ϕ) of the gate oxide, where the black and red line indicate the potential barrier height of oxide layer. c, d Field-like SOT component of depending on pre-biased gate voltage V_G corresponding to ±2.5 MV/cm for Pt (0.5 nm)/Co (2 nm)/AlO_x (₂ nm)/TiO₂ (40 nm) (c) and Pt (0.5 nm)/Co (2 nm)/AlO_x (₂ nm)/ZrO₂ (40 nm) (d) samples. The error bars are due to the uncertainty of the fitting of the $R_{xy}^{2\omega }$ versus $\phi$ curves to Eq. (1).

Fig. 5. Non-equilibrium spin density for the structures with and without the lateral oxygen gradient.

a, b Schematics of the two different Pt/Co/O structures in yz-plane (side view) (a) and xy-plane (top view) (b). In b, the left panel shows the structure without the lateral oxygen gradient ($\nabla V_{\mathrm{o}}$), and the right panel shows the structure with the lateral oxygen gradient. The direction of lateral symmetry breaking is indicated by yellow arrow. In both a and b, the directions of magnetization ($\mathbf{m}$) and electric field ($\mathbf{E}$) are denoted by red arrows. c–e Atomic layer resolved non-equilibrium spin densities $\delta s_x$ (c), $\delta s_y$ (d), and $\delta s_z$ (e) for the Pt/Co/O structure with and without lateral oxygen gradient.