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# Giant antidamping orbital torque originating from the orbital Rashba-Edelstein effect in ferromagnetic heterostructures

## Abstract

Enhancing the in-plane current-induced torque efficiency in inversion-symmetry-breaking ferromagnetic heterostructures is of both fundamental and practical interests for emerging magnetic memory device applications. Here, we present an interface-originated magnetoelectric effect, the orbital Rashba–Edelstein effect, for realizing large torque efficiency in Pt/Co/SiO2/Pt films with strong perpendicular magnetic anisotropy (PMA). The key element is a pronounced Co 3d orbital splitting due to asymmetric orbital hybridization at the Pt/Co and Co/SiO2 interfaces, which not only stabilizes the PMA but also produces a large orbital torque upon the Co magnetization with current injection. The torque efficiency is found to be strongly magnetization direction- and temperature-dependent, and can reach up to 2.83 at room temperature, which is several times to one order of magnitude larger than those previously reported. This work highlights the active role of the orbital anisotropy for efficient torque generation and indicates a route for torque efficiency optimization through orbital engineering.

## Introduction

In heavy-metal (HM)/ferromagnet (FM)/oxide heterostructures, which are the core elements of modern magnetic memory technologies and logic devices, rich magnetic and electrical effects can emerge from the coupling between the spin and orbital of electrons. A typical effect is that of the perpendicular magnetic anisotropy (PMA) arising from the combination of orbital hybridization and spin–orbit coupling (SOC) at the HM/FM interface1 or the FM/oxide interface2. Another relevant effect is the SOC-mediated conversion of an in-plane electric current into a spin polarization through the spin Hall effect (SHE) of the HM bulk or the spin Rashba effect (SRE) at the symmetry-breaking interfaces3,4,5,6. At present, research on the control of magnetization with PMA using the torque from the generated spin polarizations constitute an active field known as spin-orbitronics7,8,9,10,11,12,13,14,15,16,17,18, which aims at constructing advanced magnetic devices with high integration density, high read/write speed, and low energy cost.

Despite its technological appeal, manipulating magnetization using the current-induced torque in HM/FM/oxide heterostructures has several challenging issues that still remain to be overcome. The first one is the conflict between high PMA and low critical current density (jc) for current-induced magnetization switching (CIMS) simultaneously. Strong PMA is of great importance for magnetic bit stability and write-in error rate reduction19 in miniaturized magnetic devices; however, it also requires high jc for CIMS, because jc is proportional to effective magnetocrystalline anisotropy (MCA) energy Keff when the device size is varied down to the scale that does not accommodate domain wall formation:

$$j_{\mathrm{c}} \propto K_{{\mathrm{eff}}}/\xi$$
(1)

where ξ is the current-induced torque efficiency. Equation 1 suggests that an effective solution to the conflict is using materials with large ξ. However, as the spin Hall angle (θSH), which determines the ξ magnitude within the SHE model, of typical HMs such as Pt, Au, Ta, and W rarely exceeds 0.3 3, a very high jc of order of 107–108 A cm−2 is typically needed for CIMS, which leads to device-heating and reliability concerns. The second issue is the physical origins of the in-plane current-induced torque in HM/FM/oxide heterostructures. The SHE of HM bulk and/or the SRE at interfaces are regarded as the main mechanisms of the torque origins in previous studies7,8,9. However, the existing SHE and SRE models cannot explain certain anomalous phenomena that have been observed in HM/FM/oxide heterostructures, such as the oxygen-engineered spin–orbit torque20,21,22 and the strong torque dependence on the magnetization direction23,24,25, indicating that either additional mechanisms exist, or more realistic electronic structures must be considered. Realizing low jc without compromised PMA, together with understanding the physical origins of the current-induced torque in HM/FM/oxide heterostructures, is crucial for promoting practical device applications.

Here, we report the experimental observation of a very large ξ of up to 2.83 and a low jc with magnitude of order of 106 A cm−2 in Pt/Co/SiO2/Pt heterostructures with strong PMA (3.92 × 106 erg cm−3 at 300 K). The torque is anisotropic with respect to the magnetization direction and shows strong temperature dependence. We demonstrate that asymmetric orbital hybridizations at the Pt/Co and Co/SiO2 play an important role in the observed phenomena, which are explained in the framework of a current-induced orbital polarization model.

## Results

### Crystal and interface electronic structures

The ferromagnetic heterostructures studied in this work had a Si/SiO2 (300)//Pt (5)/Co (1)/SiO2 (1)/Pt (1) structure (the numbers in brackets correspond to the respective nominal layer thicknesses in nm). The Si/SiO2 was the substrate. Figure 1a displays a high-resolution transmission electron microscopy image of the Pt/Co/SiO2/Pt films. The analysis of the lattice spacings shows that the bottom Pt layer has a polycrystalline structure mainly consisting of {111} and {200} textures. The SiO2 layer has an amorphous structure. We find that it is hard to discern the Pt/Co interface, which may be caused by the atom interdiffusion between the Co and Pt layers during the annealing treatment (see Methods), as Co and Pt are miscible26. Nevertheless, the Co and Pt layers can be distinguished by the different Z-contrasts. The elemental mappings presented in Fig. 1b provide a further confirmation of the presence of Co and Pt and more importantly, show that the Co distributes uniformly and forms a continuous film.

Figure 1c shows a high-resolution X-ray photoelectron spectroscopy spectrum of Co 2p level near the Co/SiO2 interface. Peak 1 at 777.69 eV and peak 4 at 792.99 eV correspond to metallic Co0 2p3/2 and 2p1/2 levels, respectively. Peak 2 at 781.01 eV and peak 5 at 796.38 eV are assigned, respectively, to Co2+ 2p3/2 and 2p1/2 levels. The presence of the Co2+ at the Co/SiO2 interface is due to the formation of CoO at the Co/SiO2 interface during deposition of the SiO2 layer27. Peak 3 (peak 6) lying ~6 eV above peak 2 (peak 5) is the satellite structure of peak 2 (peak 5), which is attributed to the charge transfer from O 2p orbital to Co 3d orbital accompanying the primary photoionization process28. The presence of the satellite structures is a strong evidence of existence of the Co 3d−O 2p orbital hybridization at the Co/SiO2 interface.

### Magnetic properties

Figure 2a, b show the magnetic hysteresis (MH) and anomalous Hall effect (AHE) resistance (RAHE) loops measured at temperatures of 50, 300, and 400 K with the external magnetic field Hext perpendicular to the film plane. These loops present sharp magnetization switching as the magnitude of Hext (Hext) changes and have high remanence, indicating that the films have well-established PMA, which is due to the Pt 5d−Co 3d orbital hybridization at the Pt/Co interface1 and the Co 3d−O 2p orbital hybridization at the Co/SiO2 interface2. As will be presented below, the combined effect of the Pt 5d−Co 3d−O 2p orbital hybridization can produce a large orbital splitting in the Co layer, which not only stabilizes the PMA state but also induces a giant torque on the Co magnetization with current injection into the films.

The temperature dependence of the saturation magnetization (Ms), RAHE and coercivity field (Hc) of the MH and RAHE loops are shown in Fig. 2c, d. All these quantities increase with decreasing temperature, typical phenomena of ferromagnetic heterostructures. We notice that there is a difference in Hc between the MH and RAHE loops, which we ascribed to the different sample size for MH and AHE measurements, the microfabrication process, and the measurement technique used (see Methods).

Ultrathin metallic FM layers with thickness <1.5 nm usually exhibit a granule-like morphology when grown on an oxide layer29,30, because the difference in the surface-free energy (δ) between the metal and oxide is typically large31,32. It was demonstrated that the granule-like morphology can have significant impact on the evaluation of the spin-transfer-torque switching efficiency30. However, the difference in δ between Co and Pt is very small (δCo = 2.71 J m−2 and δPt = 2.69 J m−2, ref. 31); the Co is expected to form a continuous film on the Pt even at a small thickness of 1 nm, supported by the element mapping shown in Fig. 1b. Moreover, no multistep-like switching and/or superparamagnetic behavior are found in the MH and RAHE curves, further confirming that the Co layer is morphologically continuous and magnetically homogeneous. Therefore, we believe that the granular effect has little influence on the ξ evaluation below.

### Evaluation of torque efficiency and magnetic anisotropy

When a charge current is injected along the film plan of HM/FM/oxide heterostructures, the FM magnetization can experience a torque, which is tentatively attributed to the spin polarizations generated by the bulk SHE and/or the interface SRE in previous studies7,8,9. Although the exact origin of the in-plane current-induced torque in HM/FM/oxide structures remains debatable, a number of experimental and theoretical studies12,18,23,24,25,33 have demonstrated that it can separate into two orthogonal components regardless of detailed mechanisms. One is an even function of the magnetization expressed as TAD = TADm × (σ × m) and is called the antidamping torque, because it can compensate the intrinsic Gilbert magnetic damping and induces magnetization switching. The other one is an odd function of the magnetization expressed as TFL = TFL(m × σ) and is called the field-like torque, as it can induce magnetization precession like a magnetic field does. Here, m is the magnetization unit vector, σ is the current-induced angular momentum polarization and TAD and TFL describe the magnitudes of TAD and TFL, respectively.

To quantify the two torque components, we measured RAHE as a function of Hext with Hext slightly tilting with respect to the xy-plane (i.e., almost along the hard magnetization axis, see the insets of Fig. 3a, b). This measurement scheme was introduced to ensure that the magnetization can rotate coherently without domain formation, such that a macrospin method is applicable to investigate the interplay of TAD and the torques exerted by Hext and the anisotropy field Han (see below). Figure 3a, b show the normalized RAHE (i.e., cosθ) curves obtained for a Pt/Co/SiO2/Pt device with positive (along y) and negative (along −y) currents, measured at 300 K and β = 3°. Here, θ is the angle between m and the film normal z, and β is the angle between Hext and the xy-plane. The RAHE decreases slowly with increasing Hext, which is due to the coherent rotation of the Co magnetization toward the hard magnetization axis. According to the torque symmetries, the RAHE curves measured with Hext in the yz-plane reflects mostly TAD contributions, whereas those measured with Hext in the xz-plane reflects mostly TFL terms9,23. When Hext sweeps in the yz-plane (Fig. 3a), significant curve splitting is apparent for currents of ±0.9 mA, indicating that TAD is sizeable. However, no curve splitting is visible when Hext is in the xz-plane (Fig. 3b), even for currents of ±1.5 mA, suggesting that TFL is negligible. We therefore focus only on TAD below.

$$H_ - ^{{\mathrm{ext}}}(\theta ) - H_ + ^{{\mathrm{ext}}}(\theta ) = 2(T_0^{{\mathrm{AD}}} + T_2^{{\mathrm{AD}}}\sin ^2\theta \\ + T_{\mathrm{4}}^{{\mathrm{AD}}}\sin ^4\theta )/\cos (\theta + \beta )$$
( 2)
$$H_ - ^{{\mathrm{ext}}}(\theta ) + H_ + ^{{\mathrm{ext}}}(\theta ) = 2(H_0^{{\mathrm{an}}} + H_2^{{\mathrm{an}}}\sin ^{\mathrm{2}}\theta \\ + H_4^{{\mathrm{an}}}\sin ^{\mathrm{4}}\theta )\cos \theta \sin \theta /\cos (\theta + \beta )$$
(3)

where H+ext(θ) and Hext(θ) are the Hext values that produce the same θ for positive and negative currents, respectively. Taking the difference between H+ext(θ) and Hext(θ) (Fig. 3c) and fitting the resulting data to Eq. 2, we obtain T0AD = 121.7 Oe, T2AD = 256.9 Oe, and T4AD = −325.3 Oe for a current of 0.9 mA. Evidently, TAD contains substantial high-order terms T2AD and T4AD, even larger than the zeroth-order term T0AD, which suggests that TAD presents a strong anisotropy. The result of the anisotropic TAD is in contrast to previous studies where TAD was demonstrated to be angular-independent8,9. We temporarily ascribed such a diversity to the difference in the electronic structures of films (see Supplementary Note 7). Figure 3d shows the sum of H+ext(θ) and Hext(θ) as a function of cosθ. By fitting the curve to Eq. 3, H0an, H2an, and H4an were estimated to be 10.09, −10.47, and 8.97 kOe, respectively. Using the formula Ku = K1sin2θ + K2sin4θ + K3sin6θ, where Ku is the uniaxial magnetic anisotropy energy and K1 (=H0anMs/2), K2 (=H2anMs/4), and K3 (=H4anMs/6) are the anisotropy energy constants, Keff (i.e., the Ku value at θ = 90°) was estimated to be 3.92 × 106 erg cm−3; this value is comparable to that of the perpendicularly magnetized Co/Pt multilayers26 but considerably larger than those of Ta/CoFeB/MgO8 and W/CoFeB/MgO12.

Having obtained the coefficients T n AD and H n an (n = 0, 2, and 4), we investigate the detailed angular distributions of TAD and Han based on their space symmetries and, more importantly, the possible interrelation between the two quantities. The variation of TAD and Han as a function of θ is plotted in Fig. 3e. Interestingly, TAD and Han exhibit an opposite θ dependence, i.e., when Han decreases (increases) with θ, TAD increases (decreases), pointing to a common mechanism which links up TAD and Han.

The TAD efficiency ξAD can be estimated using the formula (modified from Pai et al.34 and Khvalkovskiy et al.35)

$$\xi ^{{\mathrm{AD}}} = \left( {2e/\hbar } \right)M_{\mathrm{s}}t_{{\mathrm{Co}}}^{{\mathrm{eff}}}\left( {T^{{\mathrm{AD}}}/j_{{\mathrm{PtCo}}}} \right)$$
(4)

Here, e is the electron charge; ħ is the reduced Planck constant; tCoeff = 0.72 nm is the effective Co layer thickness (see Supplementary Note 3); and jPtCo = 1.35 × 106 A cm−2 is the current density shunting in the Pt (5)/Co (1) (nm) bilayer for a current of 0.9 mA (see Supplementary Note 4). It is evident that ξAD is anisotropic as shown in Fig. 3f: it increases from 2.0 at θ = 0° to 2.83 at θ ~ 40°, and then decreases to 0.88 as θ is further increased to 90°. These ξAD values are significantly higher than those previously reported in HM/FM/oxide structures such as (Pt, Pd, Ta, W)/(Co, CoFe, CoFeB)/(AlOx, MgO)8,9,12,23,25,34, which rarely exceeds 0.3.

Note here that the increase in device temperature due to current-induced Joule heating was negligibly small for a 0.9-mA current injection (see Supplementary Note 5), suggesting that thermoelectric effects such as anomalous Nernst and spin Seebeck effects should have little influence on the evaluated ξAD values. Previous studies36 have demonstrated that the thermoelectric effects are very small in Pt/Co systems. Additionally, the planar Hall effect was found to be two orders of magnitude smaller than the AHE in our Pt/Co/SiO2/Pt films (Supplementary Note 2) and thus should not influence upon the ξAD estimation.

### Temperature dependences of current-induced torque and magnetic anisotropy

We also measured the RAHEHext curves with β = 3° at different temperatures to study the temperature dependences of TAD and Ku, which are shown in Fig. 4a, b respectively. The lowest-order terms T0AD and K1 increase with decreasing temperature. With regard to the high-order terms, T2AD and the absolute value of T4AD decrease with decreasing temperature; the absolute value of K2 shows a not strictly monotonic increase with decreasing temperature and presents a salient at ~125 K, while K3 have a monotonic temperature dependence. Despite the inverse scaling of high-order terms of TAD and Han with temperature, the Keff and the degree of anisotropy of TAD (i.e., |T2AD + T4AD|) were found to possess similar temperature dependence (Fig. 4c); they increase with decreasing temperature, suggesting that the anisotropic TAD may have the same origin as Ku.

### CIMS measurements

To examine the CIMS, we applied a small, fixed Hext along y or −y, i.e., β = 0° or 180°, and then swept the quasistatic direct current with a ramp rate of 0.5 mA s−1. The CIMS experiment was performed at 300 K and monitored by measuring RAHE. The application of the small Hext was to break the time reversal symmetry in the xy-plane so that deterministic CIMS can be achieved37. We found that the Hext with magnitude of 25–400 Oe tilted the average magnetization by ~0.5–3.5° from z (Supplementary Note 6), but did not provide any preference for either up or down magnetization state in the absence of current injection. In Fig. 5a, where the Hext is applied along y, sweeping the quasistatic direct current results in hysteretic magnetic switching, where the magnetization states depend on the current direction. Moreover, the switching curves reverse their polarity when the Hext direction is changed (Fig. 5b), a characteristic of TAD-induced magnetization switching7,8,9. Similar to the field-driven switching (Fig. 2a, b), the current-driven loops shown here also exhibit sharp magnetization switching, which is due to the domain wall nucleation and propagation.

The RAHE of the curves with Hext = ± 25 Oe is ~0.045 Ω; this value is much smaller than that of the full-switching curve at 300 K shown in Fig. 2b, which indicates that, in this case, there is partial magnetization switching. For the curves with Hext = ± 50 Oe, complete switching is observed, with an average jc = (|jcup| + |jcdown|)/2 ≈ 5.83 × 106 A cm−2. Here, jcup and jcdown denote the jc values at which the magnetization switches from down to up and up to down, respectively. As Hext is further increased to ±400 Oe, the average jc decreases to ~2.53 × 106 A cm−2. These jc values are much smaller than those previously reported in Pt-based HM/FM/oxide heterostructures (usually in the order of 107 A cm−2, see refs. 7,9,20).

Note that the macrospin method is based on probing the static magnetization whereas the CIMS is by the dynamic domain wall formation and propagation. Discrepancy between the static and dynamic torque may be expected, because there can be an enormous number of pathways to overcome the energy barrier for domain-wall-based magnetization switching38. Therefore, the large ξAD is not the exclusive causal factor for the low jc values obtained here. To analyze the effects of the current-induced torque on dynamic magnetization quantitatively, a better approach is to investigate the temporal information of the torque by measuring the lifetime of magnetization reversal under the presence of an electric current38,39,40.

## Discussion

The SHE of HM bulk and the interfacial SRE are two possible mechanisms of in-plane current-induced torque in HM/FM/oxide heterostructures. In the SHE interpretation, spin currents generated in the HM bulk diffuse into the adjacent FM layer and exerts torques upon the FM magnetization. However, theoretical calculations33 have predicted SHE-generated TAD not to have any magnetization-direction dependence; the θSH of Pt bulk was suggested theoretically and experimentally to be less than 0.1 41,42, which is too small to be accounted for the large ξAD obtained here. Moreover, reported experimental works have demonstrated that the intrinsic SHE is almost unchangeable with temperature43,44. Therefore, the SHE interpretation is inadequate to explain the giant, anisotropic, and strongly temperature-dependent TAD and ξAD observed here.

On the other hand, theoretical calculations45 based on the SRE model including the anisotropic D’yakonov–Perel spin relaxation predicted that TAD will acquire an angular dependence when the Rashba SOC energy is considerably larger than the exchange interaction. However, this analytically tractable condition may be untenable in our work, because the Rashba effect and exchange interaction are both large in our films, as hinted by the presence of the strong PMA46. In addition, the absence of TFL in our study suggests that the extrinsic scattering-induced spin relaxation, which typically generates TFL in the context of SRE model33,45, is not responsible for the anisotropic TAD.

Our results suggest that additional effects contribute to TAD. It is well known that the anisotropy of the 3d orbital moment (OM) is the microscopic origin of MCA in 3d FM47. Learning from the close relationship between TAD and MCA and the strong temperature dependence of TAD shown above, we infer that the intrinsic 3d OM anisotropy is probably a key to understand our results. Particularly, orbital polarization ΔL in response to an electric current has recently been predicted in nonmagnetic tellurium crystals lacking bulk inversion symmetry48. Here, L is the orbital angular momentum operator. In principle, such a current-induced ΔL should also exist in our Pt/Co/SiO2/Pt films with symmetry-breaking interfaces. There, the Pt 5d–Co 3d and Co 3d–O 2p orbital hybridizations modify the charge distribution and give rise to a strong interfacial crystal electric field (ECEF) at the respective interface (Fig. 6a). Because the Co 3d orbitals are exposed to the crystal environment, the interfacial ECEF primarily splits the 3d orbitals into two states with opposite OM (L and −L), while the SOC, which is not strong in Co metal, only acts as a perturbation to the band energy governed by the orbital splitting and further splits them into states of spin (Fig. 6b). The split orbital states couple with their own momentum ћk via ECEF49, i.e., ECEF = L × ћk, forming Rashba-like chiral orbital textures in k-space shown in Fig. 6c, where the dashed circles represent the Fermi contours at equilibrium and k is the electron wave vector. When an in-plane current passes through the Co layer, the shift of the Fermi contours (solid circles in Fig. 6c) produces an asymmetric electron distribution in k-space and leads to a local nonequilibrium ΔL with polarization direction perpendicular to the current path. Contrast to the nonmagnetic tellurium crystals with bulk inversion asymmetry, the current-induced ΔL in our films is interface-originated and can further couple to and exert torques upon the Co magnetization via exchange interaction. Therefore, we dub this magnetoelectric effect as the orbital Rashba–Edelstein effect (OREE) and refer to the corresponding torque as orbital torque to underline its orbital origin.

We next discuss the important role of asymmetric orbital hybridizations of the Pt/Co and Co/SiO2 interfaces in achieving large orbital splitting and the giant ξAD we observed. As already mentioned, the spin states are dominated by the orbital splitting and, thus, in turn, can be taken as a gauge of the size (Δos) of the orbital splitting. In the Pt/Co/SiO2/Pt films, the interfacial ECEF of the Co/SiO2 interface increases in passing from Co to SiO2, and that of the Pt/Co interface increases in passing from Pt to Co50; the cumulative effect is a significant enhancement of the total interfacial ECEF that favors a large Δos, which overwhelms the demagnetization field and stabilizes the spin states at the normal direction, causing the PMA of the films (Fig. 2a, b). To make this point clearer, we investigated the magnetic properties of two controlled samples Pt (5)/Co (1)/Pt (1)/SiO2 (1)/Pt (1) (thickness in nm, Pt/Co/Pt for short) and Pt (5)/SiO2 (5)/Co (1)/SiO2 (1)/Pt (1) (thickness in nm, SiO2/Co/SiO2 for short). The AHE loops in Fig. 6d, e show that the two controlled samples have in-plane magnetic anisotropy, as expected. This is because that the interfacial ECEF of the Pt/Co (SiO2/Co) and Co/Pt (Co/SiO2) interfaces has opposite direction and tends to cancel out (insets of Fig. 6d, e), weakening the Δos and thereby leading to the in-plane magnetic anisotropy. As the Δos also dominates the amplitude of the current-induced ΔL, we believe that a pronounced Co 3d orbital splitting due to the combined effect of asymmetric orbital hybridizations at the Pt/Co and Co/SiO2 interfaces is the key element for the giant ξAD that was obtained in our work.

In magnetized systems, the band structures depend not only on the intrinsic Δos but also on the magnetization direction, due to exchange field-induced Fermi surface distortion effect. Figure 6f sketches Rashba-type band structures for m||z and m||y to illustrate how the magnetization direction-dependent orbital torque arises. Generally, the exchange field shifts the two Rashba-type subbands in opposite directions along the energy-axis, causing an exchange splitting (Δex). The total energy splitting Δtot for a given k is then determined by both Δos and Δex, i.e., Δtot = Δos + Δex. For m||z, the exchange field have no distortion effect on the subband structures. As the magnetization rotates toward y, an in-plane component of the exchange field appears, which shifts the two Rashba subbands in opposite directions along the x-axis and distorts the Fermi surfaces. It is apparent that the shift and distortion of the Fermi surfaces depend on the size of the in-plane component of the exchange field, i.e., they are dependent on the magnetization direction. As a result, the Δtot becomes angular-dependent, leading to the anisotropic ξAD that was observed.

The temperature dependence of the orbital torque can be interpreted as a phonon-mediated electron hopping effect. As the temperature is increased, the atomic vibration becomes stronger and promotes electron hopping between hybridizing Pt 5d, Co 3d, and O 2p orbitals via electron–phonon interaction. It is expected that the electron occupations in the hybridized orbitals become more symmetrical upon increasing temperature, which weakens the interface ECEF and reduces the Δos, resulting in the decrease of the orbital torque anisotropy (Fig. 4c). The different temperature dependence of T0AD, T2AD, and T4AD (Fig. 4a) may originate from the different temperature dependence of the lowest- and high-order terms in ECEF. This is supported by the dramatic temperature dependence of K1, K2, and K3 (Fig. 4b), which has been well studied within a temperature-dependent crystal field model51. To our knowledge, however, the temperature-dependent high-order terms in TAD has not been studied systematically yet. To get further insights into it, more experiments and calculations based on realistic electronic structures are needed.

In summary, we have reported a large, anisotropic, and strongly temperature-dependent current-induced antidamping orbital torque in Pt/Co/SiO2/Pt heterostructures with high PMA. The results cannot be simply understood using the existing SHE and SRE but can be qualitatively interpreted within an OREE model we proposed, where the antidamping torque is related to intrinsic Co 3d band structures and does not require transport of the current-induced nonequilibrium polarizations. The asymmetric orbital hybridizations at Pt/Co and Co/SiO2 interfaces can enhance the orbital splitting significantly and lead to a very large torque efficiency, making the orbital torque useful for potential applications in high-performance magnetic devices. Our results highlight the critical role of the orbital anisotropy in the generation of in-plane current-induced torque in HM/FM/oxide structures, and may improve the understanding of the previously observed anomalous spin–orbit torque phenomena20,21,22,23,24,25. In addition, the multiplicity of the orbital symmetries and their sensitivity to the interfacial orbital hybridization provide great opportunities to optimize the torque efficiency and switching current, for example, by orbital engineering using electric-field-driven ionic migration effects52,53,54.

## Methods

### Sample deposition and device fabrication

All films studied here were deposited on Si/SiO2 (300 nm) substrates by a magnetron sputtering system at room temperature. The Pt and Co were deposited by direct-current sputtering and the SiO2 were deposited by radio-frequency sputtering. The deposition rates of Pt, Co, and SiO2 were 0.08, 0.04, and 0.02 nm s−1, respectively. The base pressure of the sputtering system was better than 3 × 10−7 Torr and the working argon pressure was 4 mTorr. After deposition, the films were fabricated into Hall devices using ultraviolet lithography and ion beam etching. During the microfabrication process, the films were heated to 100 °C to solidify the photoresist and remove the deionized water at surface. The device channel width w is 10 μm, and the length l between two neighboring Hall probes is 80 μm. Au (50 nm)/Cu (10 nm) were used as contact electrodes, which were made by direct-current sputtering and lift-off technology. To improve the perpendicular magnetic anisotropy, all devices were annealed at 200 °C for 30 min in a vacuum furnace with a base pressure of 3 × 10−7 Torr. Two Pt films with thicknesses of 5 and 1 nm were also deposited separately and fabricated into Hall devices to determine their resistivity.

### Electrical and magnetic measurements

The devices were placed on a sample rotator that can perform 360° rotation with a 0.05° precision for electrical measurements. A Keithley 2400 sourceMeter was used for quasistatic direct current sweeping and a Keithley 2182A nanovoltmeter was used for voltage acquisition. The ramp rate of the sweeping current was 0.5 mA s−1. The room-temperature resistivity of the Pt (5 nm), Co (1 nm), and Pt (1 nm) layers was determined to be 55.6, 37.6, and 80.1 μΩ cm, respectively (see Supplementary Note 4). Samples with an area of 3 × 4 mm2, annealed at 200 °C for 30 min, were used for magnetization hysteresis loop measurements using a vibrating sample magnetometer (VSM). Note here that the sample area in electrical and magnetic measurements is different.

### X-ray photoelectron spectroscopy measurements

The base pressure of the X-ray photoelectron spectroscopy (XPS) system (Thermo Scientific Escalab 250Xi) was better than 5 × 10−8 Pa. The source of X-rays was Al Kα. The energy analyzer was operated at constant pass energy of 30 eV. The samples used for XPS measurements had an area of 10 × 10 mm2 and were annealed at 200 °C for 30 min. Before loading into the XPS system chamber, the samples were cleaned with acetone using an ultrasonic apparatus to remove surface contaminants. To eliminate the charge effect, all binding energies were calibrated by the Pt 4f7/2 level (70.9 eV).

### High-resolution transmission electron microscopy

Cross-sectional specimens for high-resolution transmission electron microscopy (HRTEM) was prepared by mechanical grinding, polishing and dimpling, followed by Ar-ion milling using a Gatan 695 precision ion polishing system. The HRTEM images and element mappings were acquired through a FEI Technai F20 equipped with an energy dispersive X-ray detector. The accelerating voltage for operation is 200 kV.

### Data availability

All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Information. Additional data related to this paper are available from the corresponding author on request.

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## Acknowledgements

This work was financially supported by the National Key Basic Research Program of China (2014CB931702), the China Postdoctoral Science Foundation (AD41712), NSFC (61725402, 21403109), the Fundamental Research Funds for the Central Universities (Nos. 30915012205 and 30916015106), Natural Science Foundation of Jiangsu Province (BK20140769), PAPD of Jiangsu Higher Education Institutions.

## Author information

Authors

### Contributions

X.C. and H.B.Z. conceived and designed the experiments. X.C. fabricated the samples and performed the electrical and magnetic measurements with the help of G.Y. and H.S. X.C., G.Y., and Y.L. analyzed the data. X.C., Y.L., C.H., M.H.L., and H.B.Z. wrote the manuscript. All authors discussed the results and commented on the manuscript. H.B.Z. supervised the project.

### Corresponding author

Correspondence to Haibo Zeng.

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### Competing interests

The authors declare no competing interests.

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Chen, X., Liu, Y., Yang, G. et al. Giant antidamping orbital torque originating from the orbital Rashba-Edelstein effect in ferromagnetic heterostructures. Nat Commun 9, 2569 (2018). https://doi.org/10.1038/s41467-018-05057-z

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• DOI: https://doi.org/10.1038/s41467-018-05057-z

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