Field-free switching of perpendicular magnetization through spin-orbit torque in antiferromagnet/ferromagnet/oxide structures

Abstract

Spin-orbit torques arising from the spin-orbit coupling of non-magnetic heavy metals allow electrical switching of perpendicular magnetization. The switching is however not purely electrical in laterally homogeneous structures, since for deterministic switching, an additional in-plane magnetic field is required, which is detrimental for device applications. On the other hand, if antiferromagnets can generate spin-orbit torques, they may enable all-electrical deterministic switching since the desired magnetic field may be replaced by their exchange bias. Here we report sizable spin-orbit torques in IrMn/CoFeB/MgO structures. The antiferromagnetic IrMn layer also supplies an in-plane exchange-bias field, which enables all-electrical deterministic switching of perpendicular magnetization without any assistance from an external magnetic field. Together with sizable spin-orbit toques, these features make antiferromagnets a promising candidate for future spintronic devices. We also show that the signs of spin-orbit torques in various IrMn-based structures go beyond existing theories, which demand significant theoretical progress.

The principal discipline of spintronics is the robust generation, control, and detection of spin currents in various classes of materials¹. An emerging branch of spintronics pursues the use of antiferromagnets² where the magnetic moments are compensated on an atomic scale to make the total magnetization vanish and to suppress stray field³, which is a primary source of hazardous magnetic perturbations in integrated devices. Together with the high operating frequency of antiferromagnets in the terahertz ranges⁴, which allow ultrafast information processing superior to gigahertz-range operating frequency of ferromagnets, these features make antiferromagnets attractive materials for next generation spintronics. On the other hand, building a viable spintronic device based on antiferromagnets requires the ability to induce experimentally observable effects across the zero total magnetization in the material as well as the technology to control the antiferromagnetic order against the strong magnetocrystalline anisotropy in antiferromagnets. Owing to these challenges, research toward this direction has been limited for a long time to using antiferromagnets only as exchange biasing tools for ferromagnets⁵. Some progress has been achieved recently, which shows the spin-transfer torque effects in antiferromagnets^6-8 and the possibility of utilizing antiferromagnets as one of the electrodes in magnetic tunnel junctions^9,10 and antiferromagnet memories³, taking the advantage of zero stray fields to minimize the magnetic perturbations between neighboring devices.

Moreover, recent reports of interesting spin-orbit coupling effects in antiferromagnets^11-13 imply possibility to elevate antiferromagnets from passive to active device elements that generate spin current themselves to become an alternative to heavy metals in heavy metal/ferromagnet/oxide structures for spin-orbit-torque-active devices. Experiments with heavy-metal-based structures demonstrate that spin-orbit torques enable efficient current-induced switching of perpendicular magnetization^14,15 and domain wall motion with high speed^16,17. By replacing heavy metals with antiferromagnets, two important benefits are expected. The first benefit is the purely electrical deterministic switching of perpendicular magnetization without any assistance from an external magnetic field, since an antiferromagnet can supply an exchange-bias field, which can serve as an effective magnetic field. Without such a real or effective magnetic field, the switching probability is known to be around 50% due to the switching symmetry^14,15. In contrast, most previous experiments on the switching of perpendicular magnetization in heavy-metal based structures require the assistance of an in-plane external magnetic field to break the switching symmetry^14,15. The field-free switching is technologically important as the integration of external field sources into nano-devices is harmful for scaling and thus undesirable. Yu et al. recently reported that the field-free switching is possible by introducing a lateral symmetry breaking in the structure, i.e., oxidation wedge¹⁸. However, this recipe requires a lateral inhomogeneity and might be inadequate for real device applications because extremely good wafer-level homogeneity of magnetic and transport properties is essential for the mass production. On the other hand, the exchange bias would allow field-free switching in laterally homogeneous structures, which should work for very small devices as proven in read sensors for hard disc drives. The second important benefit is that it provides a platform for the fundamental understanding of spin-orbit torque physics and other spin-orbit-coupling-related phenomena in antiferromagnets. In contrast to heavy metals, antiferromagnets have antiferromagnetic order, whose role and combined effect with the spin-orbit coupling on spin transport are largely unexplored. Our study of the spin-orbit torque in antiferromagnet/ferromagnet/oxide structures presented in this work could offer a step towards this rich physics.

Spin-orbit torques originating from antiferromagnets

Here we present our results for antiferromagnet/ferromagnet/oxide structures. We fabricate underlayer/CoFeB(1 nm)/MgO(1.6 nm)/Ta(2 nm) Hall bar structures (see Fig. 1a and Methods) where the perpendicular magnetic anisotropy is established in the CoFeB layer. We examine various underlayers including Ta, Ti, or IrMn (=Ir₁Mn₃). When the underlayer includes an antiferromagnet (i.e., IrMn), the perpendicular magnetic anisotropy is achieved only in very limited ranges of the CoFeB thickness so that we fix the CoFeB thickness at 1 nm, which is within such a range. As the CoFeB(1 nm)/MgO(1.6 nm)/Ta(2 nm) trilayer is common for all samples in our work, we will refer to this upper trilayer as CoFeB/MgO.

Figure 1 ∣. Sign of spin-orbit torques and field-free switching in the Ta(5 nm)/IrMn(9 nm)/CoFeB/MgO sample.

a, Schematics of the antiferromagnet/ferromagnet bilayer and Hall bar structure. The second harmonic signal $V_{2\omega }$ for b, the Ta(5 nm)/CoFeB/MgO sample, and d, the Ta/IrMn/CoFeB/MgO sample. Insets show the first harmonic signal $V_{1\omega }$. The switching experiment under $B_x$ for c, the Ta/CoFeB/MgO sample, and e, the Ta/IrMn/CoFeB/MgO sample. The magnetization direction is monitored by measuring the anomalous Hall resistance while sweeping a pulsed current. The dotted arrows indicate the switching direction. f, magnetic moment versus in-plane external field of the Ta/IrMn/CoFeB/MgO sample, measured by vibrating sample magnetometer. $B_{EB}$ is the exchange bias field established in the field-annealing direction. g, Field-free switching of the Ta/IrMn/CoFeB/MgO sample. The Hall bar widths of the samples are 5 μm.

We examine the spin-orbit torque that arises when an in-plane current flows through the layered structures. The spin-orbit torque is commonly decomposed into two mutually orthogonal vector components, i.e., a field-like torque ${\mathbf{T}}_{\mathrm{F}}=\gamma B_{\mathrm{F}}\mathbf{m}\times \mathbf{y}$ and a damping-like torque ${\mathbf{T}}_{\mathrm{D}}=\gamma B_{\mathrm{D}}\mathbf{m}\times (\mathbf{y}\times \mathbf{m})$, where $\gamma$ is the gyromagnetic ratio, $\mathbf{m}$ is the unit vector along the magnetization, $\mathbf{y}$ is the unit vector perpendicular to both current direction $(\mathbf{x})$ and the direction in which the inversion symmetry is broken ($\mathbf{z}$, thickness direction), and $B_{\mathrm{F}}$ and $B_{\mathrm{D}}$ are the effective spin-orbit fields corresponding to field-like and damping-like torques, respectively. We perform the lock-in harmonic Hall voltage measurement^19,20 (see Methods for details), which is commonly adopted to assess the magnitudes of the two spin-orbit torque components individually. We apply an a.c. current to generate a periodic spin-orbit torque that induces the magnetization oscillation around the equilibrium direction. The resultant oscillation of the Hall resistance combined with the a.c. current generates the second harmonic signal $V_{2\omega }$ in the Hall voltage whereas the equilibrium direction is recorded in the first harmonic signal $V_{1\omega }$. We perform the measurements for two field geometries (the external field $B=B_x$ and $B=B_y$). The sign of $V_{2\omega }$ for $B=B_x(B=B_y)$ represents the sign of damping-like (field-like) spin-orbit torque when the planar Hall voltage is much smaller than the anomalous Hall voltage²⁰ (see detailed equations in Supplementary Note 1) as in our samples (Supplementary Note 2, Table S1).

The lock-in measurement confirms that the antiferromagnetic IrMn layer indeed generates spin-orbit torques. Figures 1b and 1d show $V_{2\omega }$ for the Ta(5 nm)/CoFeB/MgO sample and the Ta(5 nm)/IrMn(9 nm)/CoFeB/MgO sample, respectively. In order to introduce an in-plane exchange bias in the Ta/IrMn/CoFeB/MgO sample, we anneal the sample at 190 °C in an in-plane magnetic field of 0.8 T that is the maximum field we can apply in our field-annealing set-up. The hysteresis loop shows a clear shift to the negative field direction only when the field is applied in the $x$ direction (Fig. 1f), which demonstrates a clear in-plane exchange bias obtained in the sample though its magnitude is about 0.5 mT, which is rather small. We observe that, by inserting an IrMn layer between Ta and CoFeB layers, the sign of $V_{2\omega }$ changes for both longitudinal $(B=B_x)$ and transverse $(B=B_y)$ field geometries, demonstrating the sign reversal of both field-like and damping-like spin-orbit torques. The absolute magnitude of the effective spin-orbit field for the damping-like torque of the Ta/IrMn/CoFeB/MgO sample is comparable to that of the Ta/CoFeB/MgO sample (Supplementary Note 3). We also perform the harmonic Hall voltage measurements for the samples with different underlayers, such as Ta(5 nm)/Ti(5 nm)/CoFeB/MgO sample and the Ta(5 nm)/Ti(5 nm)/IrMn(3 nm)/CoFeB/MgO sample, where we also observe a similar sign reversal of spin-orbit torque by introduction of IrMn layer (Supplementary Note 4). These results confirm unambiguously that the IrMn layer is responsible for the sign reversal of spin-orbit torques and thus acts as a spin-orbit torque source.

Field-free spin-orbit torque switching

In order to prove that the antiferromagnets make field-free spin-orbit torque switching possible by combining spin-orbit torque and exchange bias effects, we perform the switching experiment by applying current pulses (pulse width of 10 μs). Under a positive external field $B_x$, we find that a positive current favours the switching from $-z$ to $+z$ direction for the Ta/CoFeB/MgO sample (Fig. 1c). In contrast, a negative current is required for the same switching direction in the Ta/IrMn/CoFeB/MgO sample (Fig. 1e). We also perform the switching experiment for the Ta/IrMn/CoFeB/MgO sample under no external field when the current flows in the $x$ direction, parallel to the exchange bias (Fig. 1g). The switching direction is deterministic and the same as that of Fig. 1e, consistent with the expected switching direction from the exchange bias (Fig. 1f). These results confirm that the IrMn layer supplies not only spin-orbit torque but also in-plane exchange bias, which enables the field-free spin-orbit torque switching.

The results in Fig. 1 provide a proof-of-principle for the active role of antiferromagnets in the field-free spin-orbit torque switching. The perpendicular switching under no field is however incomplete as indicated by black arrows in Fig. 1g. Considering that the standard spin-orbit torque sample geometry without an antiferromagnet layer suffers a similar problem if an external in-plane magnetic field is weak (Supplementary Note 5), we attribute this incomplete switching to the rather small exchange bias in our sample, which is possibly due to an insufficient magnetic field strength during the field-annealing process. We suspect that the sample annealing at higher magnetic field generates stronger exchange bias and solves the incomplete switching problem. Another option is to explore other antiferromagnet materials, which may generate higher exchange field than IrMn.

An alternative way to improve the in-plane effective field induced by the interfacial exchange coupling is to introduce another CoFeB(3 nm) layer with the in-plane anisotropy just below the IrMn layer, Ta(5 nm)/CoFeB(3 nm)/IrMn(3 nm)/CoFeB(1 nm)/MgO sample. We expect the antiferromagnetic moment can be coupled with the bottom in-plane CoFeB(3 nm) layer and the resultant antiferromagnetic order can in turn provide a stronger exchange-coupling-induced in-plane field for the top perpendicular CoFeB(1 nm) layer. As demonstrated in Fig. 2, we achieve complete field-free deterministic switching of perpendicular magnetization through spin-orbit torques by introducing the bottom in-plane CoFeB(3 nm) layer. We initially apply a set-field $B_{\text{set}}$ of +0.35 T in the $x$ direction to fully saturate the in-plane moment of the bottom CoFeB(3 nm) layer, which would set the direction of the antiferromagnetic moment. After removing $B_{\text{set}}$, we apply repeated current pulses of +10 mA, 0 mA, or −10 mA (i.e., 10 mA corresponds to the current density of 4.2×10¹¹ A m⁻²). We find that a negative (positive) current pulse preferentially switches the magnetization from $-z$ to $+z$ ($+z$ to $-z$) direction (Figs. 2b and 2d), which is the same switching direction as that of the Ta/IrMn/CoFeB/MgO sample (Fig. 1g). Therefore, a positive $B_{\text{set}}$ establishes a positive in-plane effective field in the CoFeB(3 nm)-inserted sample. When we initially apply a negative $B_{\text{set}}$ of −0.35 T, the exact opposite switching direction is obtained (Fig. 2e).

Figure 2 ∣. Field-free spin-orbit torque switching in the Ta(5 nm)/CoFeB(3 nm)/IrMn(3 nm)/CoFeB/MgO sample.

a, A conceptual schematics for the establishment of an in-plane effective field $B_{eff}$ induced by an external set-field $B_{set}$. b, Field-free spin-orbit torque switching in the CoFeB(3 nm)-inserted sample $(B_{set}=+0.35\mathrm{T})$. c, Anomalous Hall resistance measured with an out-of-plane magnetic field, $B_z$. The control of magnetization direction by the repeated current pulses of +10 mA, 0 mA, or −10 mA (i.e., 10 mA corresponds to the current density of 4.2×10¹¹ A m⁻²) for d, $B_{\text{set}}=+0.35\mathrm{T}$ and e, $B_{\text{set}}=-0.35\mathrm{T}$. The Hall bar width of the samples is 5 μm for b, c and 2 μm for d, e.

These results evidence that there must be a reversible in-plane effective magnetic field generated in the top CoFeB layer, defining the switching polarity. However, it is technically difficult to directly detect the in-plane effective magnetic field in the sample where the top CoFeB layer has a perpendicular magnetic anisotropy because its anisotropy field (of the order of 0.5 T) is much larger than a typical antiferromagnet-induced magnetic field (a few to tens of millitesla, mT)⁵, and the in-plane effective field reverses upon the reversal of the bottom in-plane CoFeB(3 nm) layer. In order to overcome the technical difficulty, we replace a perpendicularly magnetized top CoFeB layer with an in-plane magnetized top Co layer, which allows us to confirm that the exchange coupling between IrMn and ferromagnetic layers generates an effective in-plane magnetic field (See details in Supplementary Note 6 and 7). However this is not the only source for the in-plane effective field in the CoFeB(3 nm)-inserted sample. The second possible source is the stray field, which is however in the opposite direction to $B_{\text{set}}$ so that it cannot explain the switching direction. The third possible source is the orange-peel coupling field originating from the bottom CoFeB(3 nm) layer.

To shed light on the main source of the in-plane effective field observed in the Ta/CoFeB(3 nm)/IrMn(3 nm)/CoFeB(1 nm)/MgO sample (IrMn-inserted sample), we fabricate the Ta/CoFeB(3 nm)/Ta(3 nm)/CoFeB/MgO sample (Ta-inserted sample) as a test sample and compare the results between the two samples. Since the layer structure of the Ta-inserted sample is identical to that of the IrMn-inserted sample except for the replacement of the IrMn layer by the Ta layer, the second and third sources are expected to produce similar magnitudes of the in-plane effective field in both samples. Hence the difference in the net in-plane effective fields between the two samples allows one to estimate the relative importance of the first source versus the second and third combined.

In order to characterize the net in-plane effective field in the Ta-inserted sample, we first examine the spin-orbit torque in the Ta-inserted sample through the lock-in measurement (Fig. 3b). The signs of $V_{2\omega }$ for longitudinal $(B=B_x)$ and transverse $(B=B_y)$ field geometries are the same as those of the Ta/CoFeB/MgO sample. Therefore, we conclude that the spin-orbit torque in the Ta-inserted sample originates mainly from the inserted Ta layer. By the way, we observe an abrupt jump in the $V_{2\omega }$ for longitudinal $(B=B_x)$ field geometry. It is nothing but the anomalous Nernst signal originating from the bottom CoFeB(3 nm) layer as evidenced by the $V_{2\omega }$ signal for the only-CoFeB(3 nm) sample without any other layers (Fig. 3c), which is irrelevant to the spin-orbit torque. We exclude a possible contribution from the spin current generated by the spin-orbit coupling effects in the bottom CoFeB(3 nm) layer because the spin-orbit torque originating from the anisotropic magnetoresistance or anomalous Hall effect has very different angular dependence²¹ from what we observe (Fig. 3b) and the Ta layer is too thick to be transparent for the spin current.

Figure 3 ∣. Field-free spin-orbit torque switching in the Ta(5 nm)/CoFeB(3 nm)/Ta(3 nm)/CoFeB/MgO samples.

a, A conceptual schematics for the establishment of an in-plane effective field $B_{eff}$. We note that $B_{eff}$ in this sample is the opposite to that of Ta/CoFeB(3 nm)/IrMn/CoFeB/MgO sample (Fig. 2). b, The second harmonic signal $V_{2\omega }$ of Ta/CoFeB(3 nm)/Ta/CoFeB/MgO sample. Insets show the first harmonic signal $V_{1\omega }$. c, The second harmonic signal $V_{2\omega }$ of only-CoFeB(3 nm) sample where all other layers are excluded. Switching experiments with pulsed current for d, $B_{\mathrm{x}}=+20\text{mT}$ and e, $B_{\mathrm{x}}=0\text{mT}$. The Hall bar width of the sample is 5 μm.

This information of the spin-orbit torque signs allows one to determine the sign of the effective in-plane field through the switching measurement. Figures 3d and 3e show the switching results of the Ta-inserted sample under $B_x$ of +20 mT and 0 mT, respectively. In case of $B_x=0$, the CoFeB(3 nm) magnetization is initially set to the $+x$ direction. Under $B_x$ of +20 mT (Fig. 3d), the switching direction is the same as that of the Ta/CoFeB/MgO sample (Fig. 1c), consistent with the sign of $V_{2\omega }$ (Figs. 1b and 3b). Interestingly, the deterministic switching persists even for $B_x=0$ (Fig. 3e), which implies the existence of an effective in-plane field. However, the switching direction for $B_x=0$ is opposite to that for $B_x=+20$ mT. It means that the sign of the effective in-plane effective field in the CoFeB(3 nm)/Ta/CoFeB/MgO sample is negative (consistent with the sign of the stray field). This effective in-plane field sign is opposite to that of the CoFeB(3 nm)/IrMn/CoFeB/MgO-sample. Because these two samples have nominally the same stray and orange-peel coupling fields, this sign difference between the two samples suggests that the in-plane effective field in the CoFeB(3 nm)/IrMn/CoFeB/MgO sample is dominated by the exchange-coupling-induced field originating from the IrMn layer.

Study on the origin of antiferromagnet-induced spin-orbit torque

Finally, we discuss possible origins of spin-orbit torque in the IrMn-based structures. Existing theories for the spin-orbit-torque mechanism can be classified into two groups, i.e., the spin-orbit-coupling-dependent and the antiferromagnet-order-dependent ones. The spin-orbit-coupling-dependent mechanisms include (i) the bulk spin Hall effect^15,22 in IrMn (possibly due to Ir) and (ii) the interfacial spin-orbit coupling (Rashba) effect^14,23-28 at the IrMn/CoFeB interface. The antiferromagnet-order-dependent one also includes two mechanisms: (iii) the bulk inversion asymmetry of the antiferromagnetic order²⁹ and (iv) spin-wave spin current through antiferromagnets^30,31. A more detailed description is necessary for the mechanism (iv) because it consists of several steps. In heavy metal/antiferromagnet/ferromagnet structures, a current passing through heavy metal generates spin-orbit torque that excites antiferromagnetic moments. This excitation in turn generates a spin-wave spin current in antiferromagnet, which is absorbed by ferromagnet via the exchange-coupling between antiferromagnet and ferromagnet.

We first attempt to differentiate mechanisms based on (i) the bulk spin Hall effect and (ii) the interfacial Rashba effect. For this purpose, we adopt the experimental method in Ref. 32 and fabricate $\text{Ta}(5\text{nm})∕\text{Ti}(5\text{nm})∕\text{IrMn}(5\text{nm})∕\text{Ti}(t_{\text{Ti}})∕\text{CoFeB}∕\text{MgO}$ samples where a Ti layer is inserted between the IrMn and CoFeB layers, which would diminish an interfacial effect at the IrMn/CoFeB interface. Unlike Ref. 32, where a Cu layer is inserted to diminish an interfacial effect, we choose a Ti layer instead, because the perpendicular magnetic anisotropy is not obtained for Cu-inserted structures. We note that the inserted Ti layer itself does not generate spin-orbit torque since spin-orbit torques in the Ti/CoFeB/MgO sample (with neither Ta nor IrMn) are vanishingly small (Supplementary Note 8) probably owing to the small spin-orbit coupling of Ti. We perform the harmonic Hall voltage measurement for the samples with varying Ti thickness $t_{\text{Ti}}$ from 0 nm to 3 nm. Interestingly, we observe that the sign of spin-orbit torque changes when $t_{\text{Ti}}$ is 3 nm (Figs. 4b and 4c). A similar sign change of spin-orbit torque is observed in IrMn(5 nm)/Ti(3 nm or 5 nm)/CoFeB/MgO samples where no underlayer is deposited below the IrMn layer (Supplementary Note 9, Fig. S11). The sign change of the spin-orbit torque in the sample with 3 nm Ti layer is confirmed by the reversal of the switching polarity as shown in Figs. 4e and 4f. On the other hand, in the Ta/Ti/CoFeB/MgO samples, the sign of spin-orbit torque does not change at a thicker Ti layer (Supplementary Note 9, Fig. S12). This difference in the sign change implies that the spin-orbit torque mechanism for IrMn would be distinctly different from that of Ta. Neither the bulk spin Hall effect nor the interfacial Rashba effect can explain the sign change in IrMn-based samples with thicker Ti because spin-orbit torques should simply vanish at large $t_{\text{Ti}}$ if one of these mechanisms were the origin. The mechanism (iii) (i.e., bulk inversion asymmetry of antiferromagnetic order) by itself cannot explain the sign change, because the sign of spin-orbit torque arising from this mechanism should be fixed by the inversion asymmetry.

Figure 4 ∣. The sign of spin-orbit torque in the $\mathbf{Ta}(5\mathbf{nm})∕\mathbf{Ti}(5\mathbf{nm})∕\mathbf{IrMn}(5\mathbf{nm})∕\mathbf{Ti}({\mathit{t}}_{\mathbf{Ti}})∕\mathbf{CoFeB}∕\mathbf{MgO}$ samples.

a, Layer structure. b, The first harmonic signal $V_{1\omega }$ versus in-plane external field $B$. c, The second harmonic signal $V_{2\omega }$ for $B$ parallel to the $x$ direction (i.e., damping-like spin-orbit torque). d, The second harmonic signal $V_{2\omega }$ for $B$ parallel to the $y$ direction (i.e., field-like spin-orbit torque), e, f, Spin-orbit torque switching $(B_x=4\text{mT})$ for the samples with different Ti thickness of $t_{Ti}=1\text{nm}$ and $t_{Ti}=3\text{nm}$, respectively. The Hall bar widths of the samples are 5 μm.

We next check the mechanism (iv) (i.e., spin-wave spin current through antiferromagnet). We perform the harmonic Hall voltage measurement for the Ti(5 nm)/IrMn(5 nm)/CoFeB/MgO sample where no $5d$ element is present below the IrMn layer. We obtain clear spin-orbit-torque signals with the same sign of other IrMn-based structures (Supplementary Note 10). As the spin-orbit torque originating from Ti is negligible (Supplementary Fig. S10), and the magnitudes of $V_{1\omega }$ and $V_{2\omega }$ signals in the Ti/IrMn/CoFeB/MgO sample are similar to those in the Ta/Ti/IrMn/CoFeB/MgO sample (Supplementary Fig. S2), we conclude that the mechanism (iv) is not dominant in our sample. Furthermore, the mechanism (iv) cannot by itself explain the sign change of spin-orbit torque shown in Fig. 4 and Fig. S11. Therefore, the sign change of spin-orbit torque at a thicker Ti cannot be explained solely by one of existing theories, suggesting that two or more mechanisms may co-exist or another yet-unidentified mechanism may be important. We hope our results will motivate further theoretical and experimental efforts to uncover the dominant mechanism of spin-orbit torques in antiferromagnets, which would be beyond the current understanding of spin-orbit torque physics. We end this paper by emphasizing that we demonstrate field-free spin-orbit torque switching in three types of laterally homogeneous structures by utilizing an antiferromagnet, an in-plane magnetized ferromagnet, or both, which will broaden the scope of material choice and be beneficial for real device applications utilizing the spin-orbit torque.

Note added in proof

The authors would like to state that while we were preparing the revised manuscript, we became aware that a similar work was done by other group³³.

Methods

Sample preparation

The samples are prepared by magnetron sputtering on thermally oxidized Si substrates with base pressure of less than 4.0×10⁻⁶ Pa (3.0×10⁻⁸ Torr) at room temperature. All metallic layers are grown by d.c. sputtering with working pressure of 0.4 Pa (3 mTorr), while MgO layer is deposited by RF sputtering (150 W) from an MgO target at 1.33 Pa (10 mTorr). The composition of CoFeB is Co₃₂Fe₄₈B₂₀. The top Ta layer is used as a capping layer to protect the MgO layer. In order to promote the perpendicular magnetic anisotropy, samples are annealed at 150 °C for 40 min in vacuum condition, unless otherwise specified. The Hall-bar structures are fabricated by photo- or e-beam-lithography, followed by Ar ion-beam etching.

Measurements

The effective magnetic fields ($B_{\mathrm{F}}$ and $B_{\mathrm{D}}$) arising from spin-orbit torques are measured by using the harmonic lock-in technique with 2 μm to 5 μm wide Hall-bar samples. We apply an a.c. current oscillating at 50 Hz and simultaneously measure the first and second harmonic Hall voltages during the sweep of in-plane external magnetic fields, in longitudinal $(B_x)$ or transverse $(B_y)$ directions to the current. The switching experiments are done with 0.5 μm to 5 μm wide Hall bar structures by measuring the anomalous Hall voltage after applying a current pulse of 10 μs at each sweeping $B_x$ or by sweeping current with a fixed $B_x$. All measurements are carried out at room temperature. The single standard deviation uncertainty of the lock-in harmonic Hall voltage measurements is ±0.15 μV. Corresponding error bars are included in the figures. In most cases, the error bars are smaller than symbols in the figures. More than three samples are measured for each type of sample; data are qualitatively reproducible.

Material resistivity

The resistivity of each layer is determined by measuring the longitudinal resistance in the Hall bar structure as a function of the thicknesses of each layer. The resistivities of each layer are (267±27) ×10⁻⁸ Ω·m (CoFeB), (230±33) ×10⁻⁸ Ω·m (Ta), (258±25) ×10⁻⁸ Ω·m (Ti), and (584±43) ×10⁻⁸ Ω·m (IrMn), so that the current is not localized significantly in any one of layers.