Electric-field control of spin accumulation direction for spin-orbit torques

Electric field is an energy-efficient tool that can be leveraged to control spin–orbit torques (SOTs). Although the amount of current-induced spin accumulation in a heavy metal (HM)/ferromagnet (FM) heterostructure can be regulated to a certain degree using an electric field in various materials, the control of its direction has remained elusive so far. Here, we report that both the direction and amount of current-induced spin accumulation at the HM/FM interface can be dynamically controlled using an electric field in an oxide capped SOT device. The applied electric field transports oxygen ions and modulates the HM/FM interfacial chemistry resulting in an interplay between the spin Hall and the interfacial torques which in turn facilitates a non-volatile and reversible control over the direction and magnitude of SOTs. Our electric-field controlled spin-orbitronics device can be programmed to behave either like the SOT systems with a positive spin Hall angle or a negative spin Hall angle.

the change of the interfacial stoichiometry. In fact, for our samples the reversal of SOT is observed once the anisotropy of the sample turns in-plane at room temperature. As shown in Supplementary   Fig. 1b the Hk reduces by ~ 33 % on application of negative Vg when measured at 160 K. Similar to the RAHE, the Hk can also be regained back to its initial value by applying a positive Vg. It should however be noted that application of excess positive Vg makes the top Co interface devoid of oxygen and can again lead to a decrease of Hk as can be seen in the last two data points of the  Supplementary Note 2. SOT direction reversal in an 800 nm-wide device.
Supplementary Fig. 2 demonstrates the sign reversal of SOTs in an 800 nm-wide Hall channel device fabricated using electron beam lithography from a Pt (1.5 nm)/Co (0.8 nm) film.
First (Vω) and second harmonic (V2ω) signals measured for the initial state of the device are shown in top panel the figure. The sign of second harmonic signal for the device in its initial state is consistent with the normal sign of spin Hall angle for a Pt device. A negative Vg of 10 V was then applied on the device for 40 s at room temperature. Subsequent harmonic measurements reveal that the sign of second harmonic signal is opposite compared to the initial device state. This sign reversal of second harmonic signal signifies the underlying reversal in the direction of currentinduced spin accumulation or the SOT polarity. The sign of spin accumulation or the SOT direction reverses again on applying a positive Vg of 4 V for 30 s. The bottom panel of the figure shows that the sign of second harmonic signal has returned to its initial state. It should be noted that for this device the modulations can be achieved by applying Vg only for few seconds at room temperature due to a use of thin gate oxide (20-30 nm). The successful demonstration of sign reversal of SOTs in a nanoscale device indicates the scalability of the proposed concept. Supplementary Fig. 2. SOT direction reversal for an 800 nm-wide device. a,b, First (a) and second harmonic (b) measurement with Hext || Iac for an 800 nm-wide Pt (1.5 nm)/Co (0.8 nm) device with successive gate voltage application events at room temperature. The external field Hext is the applied near-in-plane and Iac is the ac current.

Supplementary Note 5. Pt thickness dependence
The sign reversal in a Pt/Co/GdOx heterostructure is due to competition between SOTs generated by the spin Hall effect and interfacial spin-orbit coupling. If the Pt thickness increases, the spin Hall effect is expected to dominate over the interfacial torques. The Pt/Co samples with varying the Pt thickness from 1.5 to 3 nm were prepared. We find that a clear sign reversal of SOT was obtained in the samples with the Pt thickness of 2 nm and below. On the other hand, the samples with the Pt thickness of 2.5 nm and higher do not show any sign reversal in the SOT direction. Supplementary Fig. 6 shows the harmonic Hall voltage measurements for representative Pt thicknesses, tPt. It can be observed that a clear sign reversal is obtained for samples with a Pt thickness of 2 nm. For the samples with a tPt of 2.5 and 3 nm, no sign reversal is obtained even when the Co is oxidized to a very high extent (indicated by reduction in RAHE to ~10 %).

Supplementary Note 6. Effect of the Co/GdOx interface
In order to rule out that the Co/GdOx interface is a source of negative torque, we remove the Pt layer from our device. In the absence of Pt layer, any torque due to the Co/GdOx interface should be visible in the harmonic measurements. Co (1 nm)/GdOx film was deposited and fabricated with a gate oxide thickness of ~ 30 nm. Since in the absence of Pt the device has inplane anisotropy, we use the in-plane second harmonic technique to evaluate presence of SOTs 1 . In this technique, a magnetic field is rotated in the plane of the device while passing an ac-current through it, and the subsequent first (Vω) and second harmonic (V2ω) voltages are measured. Supplementary Fig. 7 shows the first and second harmonic signal obtained from a Pt (4 nm)/Co (1 nm)/TaOx device with an in-plane magnetic anisotropy (device was not annealed). The presence of SOT can be assessed from V2ω which resembles a cosθ function in the presence of anti-damping torque 1 . Supplementary Fig. 7. Second harmonic measurement for an in-plane SOT system. a,b, First (a) and second (b) harmonic Hall voltage for a Pt (4 nm)/Co (1 nm) device with in-plane magnetic anisotropy. Value on the x-axis represents the angle between the applied in-plane magnetic field (2 kOe) and the current. The current density through the device is 1.76×10 10 A m 2 .
However, the harmonic measurements on the Co/GdOx device do not show any discernible second harmonic signal. Supplementary Fig. 8a,b shows the first and second harmonic signal from the Co/GdOx device. While the first harmonic signal is similar to that in Supplementary Fig. 7a, there is no visible second harmonic signal from this device. The V2ω shown in Supplementary Fig.   8b mostly consists of the noise measured by the lock-in amplifiers. The absence of any second harmonic signal in the Co/GdOx device indicates the absence of any form of current-induced torque in the device. In addition, we apply a negative Vg on the device at an elevated temperature for an hour to ensure that Co/GdOx interface is sufficiently oxidized. The resistance of the device increases from ~ 28 kΩ to ~ 31 kΩ confirming the migration of oxygen in the Co layer. However, as shown in Supplementary Fig. 8d, the subsequent harmonic measurements also do not show any presence of SOTs in the device. Therefore, we conclude that Co/GdOx or even over-oxidized Co/GdOx interface is not a source of any form of SOT. Supplementary Fig. 8. Second harmonic measurements for a Co/GdOx device. a-d, First (a,c) and second (b,d) harmonic Hall voltage for a Co (1 nm)/GdOx device with an in-plane magnetic anisotropy. The harmonic voltages are plotted as a function of angle between the applied in-plane magnetic field and the current. Before the measurements in c,d a negative Vg of 3.5 V was applied at 100 C for 1 hour. The current density through the device is 1.76×10 10 A m 2 for all the measurements.

Supplementary Note 7. Evaluation of effective spin Hall angle or the SOT efficiency (SOT)
The SOT used in the main text can also be considered as the effective spin Hall angle which is different from the intrinsic spin Hall angle of Pt. SOT is equal to the intrinsic spin Hall angle for a system in which the SOTs are derived only from the pure spin Hall effect. The use of SOT helps in comparison between different SOT systems and in our case devices in different states. SOT is evaluated from the longitudinal effective field (HL) using the equation Here tFM is the thickness of the ferromagnetic layer, J is the current density, e is the electron charge, is the reduced Plank's constant, and Ms is the saturation magnetization of the ferromagnet.
On application of negative Vg in our devices, the effective thickness of the Co layer decreases due to Co oxidation. Therefore, in order to evaluate the accurate value of SOT for the devices, the effect of oxidation and subsequent thickness reduction is considered. The effective thickness of the Co layer is evaluated from the magnitude of VAHE using the relation AHE α Co 2 Co Pt + Pt Co . (2) Here tCo and tPt are the thickness of Co and Pt layer, respectively, and ρCo and ρPt are their corresponding resistivity. Supplementary Fig. 9 shows the SOT corresponding to the HL values shown in Fig. 3d of the main text.

Supplementary Note 8. Relation between the oxygen content in Co to the device state
The amount of oxygen in the Co layer for the different device states in Fig. 3d is evaluated from the value of RAHE. The oxidation of the Co results in the formation of CoO which being nonmagnetic decreases the RAHE. 2 The ratio of RAHE for a particular device state to its maximum value (initial state without any oxygen) provides an approximate idea about the ratio of O to Co (NO/NCo) atoms in the Co layer. Supplementary Fig. 10 shows the plot of NO/NCo for the different Pt (1.5 nm)/Co (0.8 nm) device states shown in Fig. 3d of the main text. Short consecutive Vg pulses are applied to attain these device states. The color of the data point represents the measured value of HL and thus denotes the device state. On applying negative Vg when the NO/NCo ratio exceeds ~ 0.35, the state of the device reverses i.e. the interfacial torque exceeds the spin Hall torque and the SOT has a negative polarity. Subsequently, when a positive Vg is applied to the device to reduce the NO/NCo ratio below 0.35, the device returns to the normal state of the positive SOT polarity. Supplementary Fig. 10. NO/NCo ratio with different voltage application events. The ratio of NO/NCo atoms in the Co layer for a Pt (1.5 nm)/Co (0.8 nm) device for the various device states. The color of the data points represents the value of longitudinal effective field, HL. Blue and red color represents normal and reversed state of the device, respectively.

Supplementary Note 9. First principles calculations
In order to simulate the oxygen migration effect in the Co film on top of Pt, we start from a CoO/Pt bilayer. At room temperature, bulk CoO crystallizes in the rocksalt structure and is in paramagnetic phase. It has a Néel temperature of 293 K and a magnetic moment of 3.98 μB. 3,4 Therefore, in the first principles calculations, we consider a CoO indicating the formation of a strained Co film in bcc lattice structure. Bulk bcc Co (with 2.8 Å lattice constant and magnetic moment of 1.53 μB) is a metastable structure that has been experimentally observed 5 . The supercell slab shown in Fig. 4a of the main text denotes the CoO (5 ML)/Co (5 ML)/Pt (4 ML) trilayer as a representative example. From first principles calculation we find a magnetic moment of 0.25 μB for proximity induced magnetic moment on the interfacial Pt layer, 1.7 μB for Co atoms in the bcc Co film and 2.7 μB for Co atoms in the rocksalt CoO film, consistent with the previous theoretical calculations [6][7][8][9][10] . The difference between the experimental magnetic moment and the theoretical spin moment yields an estimated value of 1.3 μB for the orbital moment of CoO, which is 5 times larger than the theoretical value, 0.25 μB 11 .
Using the tight-binding (TB) Hamiltonian (̂⃗ ), obtained from the VASP-Wannier90 calculations 12 as detailed in ref. 13 It should be mentioned that for simplicity the prefactor e 2 ℏ ⁄ ( is the volume of the active region) is not included in the above expression for the conductivity, therefore the units of xx in Supplementary Equation 5 is Å 2 . In this work, we use the latter approach to calculate the ERC, defined as R which allows for a quantitative comparison with the experimental measurements. In Supplementary Fig. 11b, we display the variation of the effective spin Hall conductivity (left-hand ordinate) and the effective Rashba coefficient (right-hand ordinate) as a function of Co On the other hand, the ERC depends strongly on the Co thickness in the ultrathin film limit and exhibits a sign reversal around 4 MLs of Co. However, the sign reversal of the SOT on incorporation of oxygen is not due to the reduction of the Co thickness as shown in Fig. 4b of the main text.  In order to check the stability of the normal and reversed state of the device, we continuously monitor the second harmonic SOT signal with Hext || Iac for a Pt (2 nm)/Co (0.8 nm) device over a period of 12 hours at room temperature for both normal and reversed state. Supplementary Fig. 12a,b show the measured second harmonic signal for the normal and reversed device state. There is no noticeable degradation in the measure signal which signifies that the device is quite stable at room temperature in both the normal and the reversed state.
In a separate experiment, we also monitor the device resistance for both the normal and reversed state. If the devices are unstable, there would be migration of oxygen to or from the Co layer which would result in a decrease or increase of the device resistance. However, we do not notice any observable change in the device resistance as shown in Supplementary Fig. 12c. The resistance versus time curve could not be fit with an exponential decay function of reasonable long relaxation time (e.g. ~ 10 years). This confirms that the position of oxygen in the device and subsequently the device state is quite stable for an extended period of time. Supplementary Fig. 12. Stability of normal and reversed device. a,b, Continuous monitoring of the second harmonic signal at room temperature with Hext || Iac for a Pt (2 nm)/Co (0.8 nm) device in normal state (a) and reversed state (b). c, Resistance of the device over an extended period of time for the device in the normal and reversed state.