Introduction

The efficient control of the magnetization using currents is the key requirement to develop high-performance spintronics devices for information and communication technology. In the last decade, current-induced magnetization switching by spin-transfer torque has become a well-established technology, with nowadays major foundries and integrated device manufacturers commercializing Spin-Transfer Torque Magnetic Random Access Memories (STT-MRAM)1. Meanwhile, spin–orbit coupling emerged as an alternative method to generate spin currents and to manipulate magnetization efficiently. SOTs rely on the injection of an in-plane current in a non-magnetic material adjacent to a ferromagnet. The spin–orbit coupling creates a spin accumulation at the interface that induces a torque on the ferromagnet magnetization. In heavy metal (HM)/ferromagnetic (FM) heterostructures2,3 SOTs arise from the bulk spin Hall effect (SHE) and/or the Edelstein effect associated with an interfacial Rashba state. These spin–orbit torques (SOTs) have attracted increasing attention, owing to their ability to induce magnetization oscillations or switching4, and their potential for high speed, high endurance, and low-energy switching5.

In recent years, oxide two-dimensional electron gases (2DEGs) have emerged as a new promising SOT system6,7,8. They display an efficient spin-charge interconversion through the direct and inverse Edelstein effects, arising from their broken inversion symmetry which induces a Rashba-type spin–orbit coupling. In previous works, we showed an enhancement of the spin-to-charge conversion efficiency by two orders of magnitude in such SrTiO3-based 2DEG compared to conventional HM/FM heterostructures8, along with a nonvolatile electric control of the spin-to-charge conversion9. In this context, the nonvolatile electric control of the reciprocal charge-to-spin conversion in these 2DEGs would be of great interest for developing reconfigurable SOT-MRAM and logic gates, offering the possibility to actively manipulate the torque by electric fields, and thus to design new architectures. The direction and amplitude of the spin accumulation is the key parameter in the design of SOT applications, as it determines the direction of magnetization switching. In conventional SOT devices based on HM/FM heterostructures, however, the relative direction between the injected current and the generated spin accumulation is fixed by the material used10, inhibiting any dynamical reconfiguration. This feature results in two main limitations in present-day SOT-MRAMs. First, the fixed direction of the SOT torque requires an inversion of polarity for the applied current in order to switch between the two magnetization states, which requires additional MRAM circuitry11. Second, the fixed direction and magnitude of the SOT torque prevents the selective switching of multiple bits sharing the same write layer in conventional SOT-MRAMs, inhibiting any in-memory logic operations. Achieving the nonvolatile electric control of the SOT could thus open the way to a disruptive generation of magnetic memories and logic devices, with high-density integration and dynamical reconfigurability. Several approaches have been pursued in this direction, based on the combination of spin Hall effect heavy metal/ferromagnetic heterostructures with piezoelectric12, ferroelectric13,14, and oxide materials15,16,17 or the replacement of the heavy metal by magnetically doped topological insulators18 (TIs). However, none of the above methods provide nonvolatile control of SOT together with efficient dynamical inversion of the SOT direction in a structure compatible with magnetic tunnel junction integration.

In this work, we propose to use 2DEGs to obtain the nonvolatile gate electric-field control of SOTs. An electric modulation of the 2DEG at a SrTiO3/Ta interface is achieved, providing two remanent and switchable resistivity states of the devices, with a large contrast of 1064%. We report the observation of sizable SOTs in a SrTiO3/metal system, and we further show that the SOT strength in this system can be modulated by the gate voltage with non-volatility, an inverted hysteresis being observed in the SOT dependence with the gate-electric field. This nonvolatile control of the SOT occurs over several orders of magnitude, down to full extinction and sign inversion. We also demonstrate the dynamical control of the SOT direction by the application of voltage pulses. The modulation of the SOT is found to originate from the combination of the gate dependence of the 2DEG band structure with the electric modulation of the current injection in the 2DEG.

Results

Magnetotransport properties

Experiments were carried out on Ta(0.9 nm)\CoFeB(0.9 nm)\MgO(1.8 nm)\Ta(1 nm) stacks deposited onto 500 μm (001)-oriented SrTiO3 substrates (see “Methods” for details on the sample preparation), allowing the creation of a 2DEG at the SrTiO3/Ta interface19. The 2DEG originates from the change of oxidation state of Ti atoms at the vicinity of SrTiO3 interface, from Ti4+ to Ti3+ due to oxygen vacancies (Ti3+ acting as electron donors). The development of 2DEGs using Ta\CoFeB\MgO stacks was motivated by three key points with respect to our earlier studies based on Al/NiFe:8,9 (i) the large interfacial magnetic anisotropy of the CoFeB\MgO interface20, that ensures perpendicular magnetization to the CoFeB ferromagnetic layer21, (ii) the lower resistance of TaOx22 for higher spin transparency, and (iii) the compatibility of Ta\CoFeB\MgO heterostructures for integration in magnetic tunnel junctions with high tunnel magnetoresistance23. The stack was patterned into 200 nm–1 μm wide and 2–10 μm long Hall cross-bars, as shown in Fig. 1a. To characterize the magnetic and electrical properties, an input current of magnitude up to 600 μA was injected along the x direction (Fig. 1b), and the longitudinal Rs and transverse Hall resistances RH were measured as a function of the magnetic field \({{{H}}}_{{{{{{\rm{ext}}}}}}}\), which was applied along a direction defined by the polar and azimuthal coordinates θH and φH. Hereafter, we present results obtained from 1 μm wide Hall bars, and define the injected linear current density as \({{j}}={{I}}/{{w}}\) (where w is the width of the Hall bar).

Fig. 1: Schematic of the sample structure and its magnetotransport properties.
figure 1

a 3D schematic of the sample and of the coordinate system. b Scanning electron micrograph of a Hall cross-bar and measurement principle. c Temperature dependence of the stack sheet resistance Rs. d Out-of-plane (θH = 0°) and near in-plane (θH = 85°, φH = 0°) magnetic field dependence of the Hall resistance at 10 K, showing well- defined up and down perpendicular magnetization states. All data have been measured with a 2D current density of j = 0.1 A cm−1 (I0 = 1 µA).

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The temperature dependence of the sheet resistance of the device is shown in Fig. 1c for j = 0.1 A cm−1 (\({{{I}}}_{0}=\)1 µA). A reduction of the resistance by 380% is observed as the temperature decreases, which is characteristic of 2DEG conduction8. As shown in Fig. 1d, the anomalous Hall resistance follows a square-shaped magnetic hysteresis loop with applied out-of-plane magnetic field, indicating that the CoFeB has a perpendicular magnetization with 100% remanence. Furthermore, a reversible decrease of the Hall resistance is observed when increasing the in-plane field, indicating a coherent rotation of the CoFeB magnetization toward the hard plane direction. From the Hall resistance \({{{R}}}_{{{{{{\rm{H}}}}}}}={{{R}}}_{{{{{{\rm{AHE}}}}}}}{{\cos }}({{\theta }})+{{{R}}}_{{{{{{\rm{PHE}}}}}}}{{{\sin }}}^{2}({{\theta }})\,{{\sin }}(2{{\varphi }})\), where θ and φ are the polar and azimuthal angles of the magnetization in spherical coordinates, we determine the anomalous Hall RAHE = 25.3 Ω and planar Hall RPHE = 1.7 Ω resistances in the ungated state (see Supplementary Section S1). Note that an anomalous Hall resistance significantly larger than that of standard SiO2\Ta\CoFeB\MgO SOT devices24, 25 is achieved in our system, taking advantage of the use of ultra-thin Tantalum layer, as previously observed by Zhu et al.26.

Nonvolatile electric control of the 2DEG properties

To modulate the 2DEG properties, an electric field Eg is applied across the SrTiO3 substrate using a back-gate. Figure 2a shows the sheet resistance Rs as a function of the applied gate-electric field, at the temperature of 10 K and after initializing the ferromagnet in the up magnetization state. Hysteresis is observed in the sheet resistance, with two switchable and remanent high and low-resistivity states of the device. The Rs contrast, defined as (Rs,max−Rs,min)/Rs,min, shows a value of 1064%, with 615% remanent contrast at Eg = 0 kV cm−1 between the high and low remanent resistivity states.

Fig. 2: Nonvolatile electric-field control of the 2D gas properties.
figure 2

a Sheet resistance Rs as a function of the applied gate-electric field Eg across the sample, showing high and low-resistivity states of the device with Rs contrast of 1064%. The gate electric-field sequence is [+4, − 4, +4] kV cm−1 ([+200 V, −200V, + 200 V]), with the low-resistance state as the initial state. b Temperature dependence of the Rs contrast. c Endurance property of Rs at remanence (Eg = 0 kV cm−1) after application of positive and negative gate electric-field pulses of ±4 kV cm−1. All data have been measured at 10 K with a 2D current density of j = 0.1 A cm−1 (I0 = 1 µA), and after initialization of the ferromagnet in the up magnetization state.

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The hysteresis is inverted, i.e., it is anticlockwise, which is a typical characteristic of charge trapping effects27. It contrasts with previous results on 2DEGs at the SrTiO3\\Al interface, showing no hysteresis for 500 µm-thick SrTiO3 substrates8, and a clockwise loop compatible with field-induced ferroelectricity for thinner SrTiO3\\Al substrates9 (in which larger electric fields can be applied), as well as for ferroelectric Ca:SrTiO3\\Al system28. Here, the inverted loop is a clear indication of charge trapping29, and leads to a much larger resistance contrast. Similar inverted hysteresis were also evidenced in SrTiO3\\Metal\CoFeB\MgO 2DEG samples with different metal layers, as detailed in Supplementary Section S2. The oxidation of the metallic layer (here tantalum) creates oxygen vacancies at the surface of the TiO2-terminated SrTiO3 substrate, with a density enhanced by the annealing process at 300 °C. When applying a positive gate-electric field, the 2DEG is enriched in electrons, until reaching a saturated low 2DEG resistivity state. Some electrons gets trapped within the SrTiO3, very probably on oxygen vacancies located at the vicinity of the 2DEG29, 30. Because of these trapped electrons, the 2DEG is easily depleted when the gate-electric field is swept from positive to negative. This triggers a sharp increase of the resistivity of the 2DEG, the channel being almost completely depleted upon crossing zero field. Decreasing further the electric field toward negative values reinforce the depletion of the 2DEG, leading to a saturating high 2DEG resistivity state, and the detrapping of electrons. As the gate-electric field is reversely swept from negative to positive, the 2DEG is enriched in electrons, reaching the high conductive state again at zero field. As a result, the electron trapping and detrapping effects between the 2DEG and the SrTiO3 drives the nonvolatile behavior of the 2DEG conductivity.

As seen in Fig. 2b, the Rs contrast decreases upon increasing the temperature until full extinction of the Rs contrast at about 105 K, corresponding to the antiferrodistortive transition from cubic to the tetragonal phase of SrTiO331, in agreement with others charge trapping studies in SrTiO3-based 2DEG30. The dynamic switching between the high and low-resistivity states was studied using a sequence of pulsed gate-electric field. The endurance of the device after application of successive positive and negative 200-ms-pulses is shown in Fig. 2c. The switching between stable high- and low-resistivity states shows a constant contrast, and no sign of fatigue within the 105 cycle attempts. This confirms the technological potential of the charge trapping-related hysteretic effect observed here to control the 2DEG properties.

Spin–orbit–torques characterization

We used the harmonic Hall voltage measurements method to quantify the spin–orbit torques in our systems3,32,33, An AC current of frequency ω/2π = 60 Hz and amplitude \({{{I}}}_{0}=\)40 µA (j = 4 A cm−1) is injected along the x direction to induce small oscillations of the magnetization around its equilibrium. These oscillations generate first and second-harmonic contributions to the Hall resistance \({{{R}}}_{{{{{{\rm{H}}}}}}}({{{{{\rm{\omega }}}}}})={{{V}}}_{{{{{{\rm{H}}}}}}}({{{{{\rm{\omega }}}}}})/{{{I}}}_{0}={{{R}}}_{{{{{{\rm{H}}}}}},{{{{{\rm{\omega }}}}}}}+{{{R}}}_{{{{{{\rm{H}}}}}},2{{{{{\rm{\omega }}}}}}}\), providing a sensitive way to measure the current-induced fields. The first harmonic \({{{R}}}_{{{{{{\rm{H}}}}}},{{{{{\rm{\omega }}}}}}}\) corresponds to the Hall resistance measured in DC, while the second-harmonic term \({{{R}}}_{{{{{{\rm{H}}}}}},2{{{{{\rm{\omega }}}}}}}\) includes modulation of the Hall resistance by the SOT effective fields, \({{{R}}}_{{{{{{\rm{SOT}}}}}},2{{{{{\rm{\omega }}}}}}}\), as well as magneto thermal effect due to unintentional Joule heating, \({{{R}}}_{{{{{{\rm{T}}}}}},2{{{{{\rm{\omega }}}}}}}\). After subtracting longitudinal and perpendicular thermal effects contribution to \({{{R}}}_{{{{{{\rm{H}}}}}},2{{{{{\rm{\omega }}}}}}}\), SOT effective fields can be determined by sweeping the magnetic field along the x (y) direction. In the small angles approximation, one measures a longitudinal (transverse) SOT effective fields ΔHx (ΔHy), respectively:32

$$\Delta {{{H}}}_{{{{{{\rm{x}}}}}}\left({{{{{\rm{y}}}}}}\right)}=\left(\frac{{{{{{\rm{d}}}}}}{{{R}}}_{{{{{{\rm{SOT}}}}}},2{{{{{\rm{\omega }}}}}}}}{{{{{{\rm{d}}}}}}{{{H}}}_{{{{{{\rm{x}}}}}}\left({{{{{\rm{y}}}}}}\right)}}\right)/\left(\frac{{{{{{{\rm{d}}}}}}}^{2}{{{R}}}_{{{{{{\rm{H}}}}}},{{{{{\rm{\omega }}}}}}}}{{{{{{\rm{d}}}}}}{{{H}}}_{{{{{{\rm{x}}}}}}\left({{{{{\rm{y}}}}}}\right)}^{2}}\right)$$
(1)

By defining \({{{{{\rm{\xi }}}}}}=\,{{{R}}}_{{{{{{\rm{PHE}}}}}}}/{{{R}}}_{{{{{{\rm{AHE}}}}}}}\), the anti-damping effective field HAD and field-like effective field HFL are given by:32

$${{{H}}}_{{{{{{\rm{AD}}}}}}\left({{{{{\rm{FL}}}}}}\right)}=-2\frac{\Delta {{{H}}}_{{{{{{\rm{x}}}}}}\left({{{{{\rm{y}}}}}}\right)}+2{{{{{\rm{\xi }}}}}}\Delta {{{H}}}_{{{{{{\rm{y}}}}}}\left({{{{{\rm{x}}}}}}\right)}}{1-4{{{{{{\rm{\xi }}}}}}}^{2}}$$
(2)

Measurements were performed with a magnetic field µ0Hext applied close to the in-plane direction (θH = 85°, φH = 0, 90°) and swept between ± 1.1 T. Figure 3a, b shows the second-harmonic Hall resistances \({{{R}}}_{{{{{{\rm{SOT}}}}}},2{{{{{\rm{\omega }}}}}}}\) at φH = 0° and 90°, after subtraction of the thermal effects and experimental resistance offsets (see Supplementary Section S3), for positive and negative gate-electric fields of ±3.2 kV cm−1. Typical symmetric (antisymmetric) contributions are observed for the magnetic field perpendicular (parallel) to the current, corresponding to the field-like-torques and anti-damping like torques, respectively. Remarkably, we observe a sign change of \({{{{{{\rm{R}}}}}}}_{{{{{{\rm{SOT}}}}}},2{{{{{\rm{\omega }}}}}}}\) for high and low-resistivity states. When using Eqs. (1)–(2), we find µ0HAD = +6.2 mT (−0.72 mT) and µ0HFL = +1.35 mT (−0.39 mT) for the low (high) resistivity states measured at Eg = +3.2 kV cm−1 (−3.2 kV cm−1), respectively. Remarkably, the SOT effective fields are seen to be opposite for high and low-resistivity states, which we further discuss below through the study of the whole SOT electric-field dependence. It is worth noting that the amplitude of gate modulation of the field-like effective field is close to the measurement resolution limit. Hereafter, we focus on the anti-damping like torque, which is the important term for spin–orbit memory applications.

Fig. 3: Spin–orbit torques characterization by second-harmonic Hall measurement.
figure 3

a Second-harmonic Hall resistances \({{{R}}}_{{{{{{\rm{SOT}}}}}},2{{{{{\rm{\omega }}}}}}}\) at φH = 0°, corresponding to the anti-damping like signal, for Eg = ±3.2 kV cm−1. b Second-harmonic Hall resistances \({{{R}}}_{{{{{{\rm{SOT}}}}}},2{{{{{\rm{\omega }}}}}}}\) at φH = 90°, corresponding to the field-like signal, for Eg = ±3.2 kV cm−1. All data have been measured at 10 K with a linear AC current density of j = 4 A cm−1 (I0 = 40 µA).

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Nonvolatile electric-field control of the spin–orbit torques

We now repeat SOT measurements described in the previous section while modulating the 2DEG properties with gate-electric fields ranging between ± 2.6 kV cm−1. Figure 4a shows the measured SOT anti-damping like effective field per linear current density µ0HAD/j, as a function of the gate-electric field. The results show a remanent modulation of the SOT-AD effective field, with inversion of the HAD sign for opposite maximum gate-electric fields. The dependence shows a hysteresis that is inverted, similar to the resistance hysteresis shown in Fig. 2a.

Fig. 4: Nonvolatile electric-field control of the spin–orbit torques.
figure 4

a Gate electric-field dependence of the spin–orbit torques anti-damping-like effective field µ0HAD. The points A–D are examined in (c). b Measured portion p of the current injected in the 2DEG as a function of the gate-electric-field Eg. c Normalized second-harmonic Hall resistance at shifted electrical remanence Eg,r after successive application of negative (blue) or positive (red) gate-electric-field pulses of ±2.6 kV cm−1. Dashed and dotted lines are linear fits, yielding SOT effective fields µ0HAD/j = +0.29, −0.20, +0.32, and −0.18 mT/(A cm−1), respectively. All data have been measured at 10 K with a linear AC current density of j = 4 A cm−1 (I0 = 40 µA) and a nearly in-plane magnetic field (θH = 85°, φH = 45°).

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Let us discuss the origin of this SOT hysteresis. The main contribution to this loop is the nonvolatile modulation of the 2DEG resistivity and thus of the current injection in the 2DEG. Figure 4b shows the measured modulation of the current injection in the 2DEG. The 2DEG and the Ta layer constitute two parallel channels of conduction with two separate SOT contributions. At maximum negative electric field (A), the device is in a high resistivity state which corresponds to the resistivity of the partially oxidized CoFeB/Ta bilayer (see Supplementary Section S4), indicating that the 2DEG is largely depleted and has an ultra-low conductance. Hence, there is no current in the 2DEG at this negative extrema. Inversely, the 2DEG resistivity reaches 0.26 kΩ sq−1 for the maximum positive electric field (C). The device is then in the low-resistivity state, which means that 92% of the applied current is flowing in the 2DEG.

A negative SOT-AD effective field of −0.23 mT/(A cm−1) is observed at the negative end of the sweep (A) when there is no current flowing in the 2DEG. This suggests that the SOT is then due to a residual contribution from the Ta layer, this interpretation being in good agreement, both in sign and magnitude, with previous observations on SiO2/Ta/CoFeB/MgO24. The highest SOT efficiency is achieved at the positive end of the electric-field sweep (C), when the 2DEG is in the low-resistivity state, reaching +1.6 mT/(A cm−1). Notably, the SOT-AD effective field at this extrema is positive, of opposite sign compared to that of the Ta/CoFeB/MgO system24 (see Supplementary Section S4). This confirms that when the device is in the low-resistivity state, the SOT arises from the 2DEG via the Edelstein effect, rather than being due to a residual Spin Hall effect in the Tantalum layer.

If the nonvolatile modulation of the 2DEG resistivity was the sole origin of the SOT hysteresis, one would expect to have similar hysteresis loops for the SOT (Fig. 4a) and for the resistance (Fig. 4b). However, the SOT hysteresis of Fig. 4a does not simply reflect the charge current redistribution within the stack. The differences between the loops of Fig. 4a and b are very probably due to the dependence of the spin–orbit conversion with the position of the Fermi level, which is linked to specific points of the k space. This has been previously studied in SrTiO3\Al8 and SrTiO3\LAO6 samples, which have shown different gate dependence in SrTiO3/Metal 2DEG systems depending on metal and sample preparation19. For a given current density flowing in the 2DEG, the produced SOT is expected to vary with the applied electric field. The SOT hysteresis has thus to be understood as resulting from both the current redistribution in the stack when varying the 2DEG resistivity, and the variations of the conversion with the 2DEG Fermi level position (see Supplementary Section S5).

The dynamical control of the SOT-AD effective field is further evidenced in Fig. 4c, which displays the measured normalized second-harmonic Hall resistance at shifted electrical remanence Eg,r, after application of negative and positive 200-ms-long gate-electric-fields pulses of ±2.6 kV cm−1. A gate electric-field pulse is first applied to the device, then the first and second-harmonic Hall resistances are simultaneously measured at Eg,r. The reproducible inversion of the SOT torque sign is demonstrated, achieving µ0HAD/j = +0.30 ± 0.1 mT/(A cm−1) and −0.19 ± 0.1 mT/(A cm−1) after negative and positive voltage pulses, respectively. The control of the SOT shows a deviation of less than ±0.1 mT/(A cm−1) over successive trials. For applications, it would be interesting to have a large remanence of the SOT at zero electric field. Here, the experiment was not performed at zero electric field due to the small SOT difference induced by intrinsic electric-field dependence of the band structure in our SrTiO3/Ta system, but at Eg,r, where the points B and D of Fig. 4a are well splitted. Note, however, that the intrinsic electric-field dependence of the band structure strongly dependent on the stack materials, as observed by Vicente-Arche et al.19 for different SrTiO3/Metal system. Hence, further material engineering can be made to ensure a large contrast at zero-field remanence for applications.

Current and temperature dependence of the SOTs

The SOT characterizations were repeated for linear current densities ranging from 1 to 6 A cm−1 (I0 = 100–600 µA), for the device in the high (Eg = −2.6 kV cm−1) and low (Eg = +2.6 kV cm−1) resistivity states. Figure 5a shows that the amplitude of the SOT-AD effective field scales linearly with the linear current density, with a positive (negative) slope for the low (high) resistivity states, respectively. The linear scaling behavior confirms that Joule heating has a negligible impact on magnetic properties within the current range used for characterization3. This result further demonstrates that the SOT sign inversion is reproducible, with a difference as large as 8.7 mT at a current density of 6 A cm−1. Note that if the present study focuses on the quantitative measurement of the SOT modulation, both in sign and amplitude, it opens the way to magnetization-switching experiments. The device developed in this work presents large perpendicular magnetic anisotropy, together with a moderate SOT efficiency, preventing to perform magnetization switching at a current compatible with low-temperature operation. To obtain magnetization switching, several optimizations can be made, including increasing the thickness of CoFeB layer to reduce the perpendicular magnetic anisotropy, and optimizing the material and thickness of underlayer material (here Ta) for higher spin transparency and SOT efficiency.

Fig. 5: Dependence of the spin–orbit torques anti-damping like components on the injected current density and on the temperature.
figure 5

a Anti-damping like effective field µ0HAD as a function of the applied 2D current density for positive (blue) and negative (green) gate electric-field of ± 2.6 kV cm−1 at the temperature of 10 K. Dashed and dotted lines are linear fits, yielding SOT effective fields µ0HAD = +1.36 mT/(A cm−1) (−0.18 mT/(A cm−1)) for positive (negative) gate electric-field. b, Temperature dependence of the SOT anti-damping like effective field µ0HAD at j = 2 A cm−1 for positive (blue) and negative (green) gate electric-field of ± 2.6 kV cm−1. All data have been measured with a nearly in-plane applied magnetic field (θH = 85°, φH = 45°).

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Finally, the temperature dependence of µ0HAD/j in the high- and low-resistivity states is shown in Fig. 5b. In the high resistivity state (Eg = −2.6 kV cm−1), the result shows a constant AD-SOT torque-to-current ratio of – 0.23 mT/(A cm−1), with a less than ±0.01 mT/(A cm−1) deviation in the 10 K to 80 K temperature range. This is in good agreement with our hypothesis of a current injected only in the Ta layer, generating a SOT which is expected to be independent of the temperature24.

At the opposite gate electric-field (Eg = −2.6 kV cm−1), µ0HAD/j is found constant from 10 to 30 K range, at around +1.35 ± 0.10 mT/(A cm−1), followed by a decrease with increasing temperatures, reaching −0.23 mT/(A cm−1) at 80 K. Notably, the AD-SOT torque-to-current ratio at this temperature of 80 K is identical for Eg = ±2.6 kV cm−1, suggesting a common origin. This result is in good agreement with the measured Rs contrast displayed in Fig. 2b, in which we observed a merging of the high and low-resistivity states above 80 K. Above this temperature range, the conductivity in these 2DEGs is known to disappear19, and thus the current mostly flows in the Ta layer, which becomes the only SOT generator.

To conclude, the nonvolatile electric control of the spin–orbit torques in 2DEGs could open the way to a new generation of spin–orbit torques devices. Concerning memory applications, the additional functionality provided by the electric control can be used for building reconfigurable SOT-MRAM, in novel architectures suitable for efficient and fast operation. While efforts remains to be made to bring this technology to room temperature, the development of CoFeB/MgO heterostructures on SrTiO3 with strong CoFeB perpendicular magnetization ensures compatibility for future integration in magnetic tunnel junctions. Beyond memory applications, this nonvolatile control of SOTs offers an additional way to manipulate skyrmions, domain walls or magnons by permitting a local control of the SOT along circuits. It could also be used in SOT oscillators, to allow developing logic architectures and agile terahertz emitters.

Methods

The Ta(0.9 nm)/CoFeB(0.9 nm)/MgO(1.8 nm)/Ta(1 nm) samples have been deposited by DC magnetron sputtering on TiO2-terminated (001)-oriented SrTiO3 substrates of 500 μm thickness (from SurfaceNet). TiO2-termination was achieved through a chemical treatment, where the substrate was subsequently submerged in H2O for 10 min and an acid solution (HCl 3: HNO3 1: H2O 16) for 20 min. The Hall bar devices were patterned by electron-beam lithography into 200–1000 nm-wide crosses, and subsequent deposition and lift off of the stack. After deposition, the stack was annealed at 300 °C during 10 min to crystallize the MgO. A sample-wide back-gate of Ti(10 nm)/Au(100 nm) was then added by evaporation. The Hall voltage measurements were performed by using an AC current with an amplitude of 200–600 μA, modulated at ω/2π = 60 Hz. VH,ω and VH,2ω were recorded simultaneously using 2 lock-ins during sweeps of the external magnetic field for 6 s at each field step.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.