Quantifying the large contribution from orbital Rashba–Edelstein effect to the effective damping-like torque on magnetization

The manipulation of magnetization through electrical means at room temperature, usually achieved through torques originating from pure spin current^1–4 and/or non-equilibrium spin density, and involving heavy metals or oxides,^5,6 holds huge potential for energy-efficient and high-speed spintronic device applications. These encompass spin–orbit torque based magnetic random access memory (SOT-MRAM),^7,8 logic gates,⁹ skyrmion-based racetracks,^10,11 as well as emerging neuromorphic computing applications.^12–15 However, despite more than one decade of research for current-induced torque optimization, recent observations in systems composed of light elements, i.e., weak spin–orbit interaction, have challenged the conventional understanding regarding their origin.^16–19 In fact, the spin current responsible for these torques was previously uniquely associated with the spin Hall effect (SHE) in heavy 5d transition metals (TMs)^20,21 or with the spin Rashba–Edelstein effect at interfaces with broken inversion symmetry,²² the two effects for which the relativistic spin–orbit coupling (SOC) plays a crucial role. These new findings in systems with weak SOC represent a paradigm shift by underscoring the significance of both electronic spin and orbital degrees of freedom at equal footing and even accentuate the generation of orbital currents as a potential avenue for a more efficient magnetization manipulation.^23,24

Notably, the response of orbital angular momentum (OAM) to the application of a charge current has been calculated in certain cases to exceed that of pure spin angular momentum.²⁵ Very interestingly, unlike spin angular momentum, OAM does not necessarily require SOC, thus expanding the range of materials and interface design possibilities for current-induced magnetization control.²⁶ In particular, the direct experimental observations of the OAM accumulation in a light element such as titanium,²⁷ and more recently in chromium,²⁸ via the orbital Hall effect (OHE), or by the Hanle magnetoresistance effect in manganese,²⁹ highlight its relevance. Furthermore, clear experimental demonstrations of current-induced torques at inversion-asymmetric light metal/ferromagnet interfaces have provided crucial insights into the non-equilibrium OAM phenomenon.^16,19 Two predominant mechanisms, namely OHE²³ and the orbital Rashba–Edelstein effect (OREE),¹⁶ have been proposed to explain these intriguing observations. On the one hand, OHE entails the flow of helical OAM in opposing directions, perpendicular to the charge current, thereby generating an orbital current. On the other hand, OREE accounts for the accumulation of helical OAM at inversion-asymmetric interfaces. Such orbital current and/or accumulated OAM may subsequently diffuse and propagate within an adjacent layer, being a ferromagnet or a heavy material. This feature has recently been evidenced by the longer orbital current decoherence length^29–32 compared to the corresponding spin length. However, a fundamental difference is that, contrary to spin current, the orbital current itself cannot interact directly with the magnetization through an exchange mechanism and has to involve spin–orbit interactions. In this regard, given the relatively weak SOC of ferromagnetic layers, an intermediate orbital-to-spin conversion layer has to be strategically incorporated between the ferromagnetic layer and the orbital current source, e.g., Pt^31,33 or rare-earth elements with strong SOC, such as Gd or Tb.^30,33 Therefore, the overall effectiveness of the torques acting on the magnetic layer hinges on the strength of the spin–orbit interaction (i) in the orbital layer or interface, such as air oxidized Cu in Refs. 34 and 35, (ii) in the heavy metal spacer layer, and (iii) in the ferromagnetic layer. Consequently, a systematic study on new materials is required and it becomes an important issue to be tackled from both fundamental and technological points of view.

In this study, we report on the experimental observation of the strong enhancement of the damping-like (DL) current-induced torques obtained in two types of sputtered multilayers, i.e., Pt|Co|Cu|AlOx and Co|Pt|CuOx samples with respective out-of-plane and in-plane magnetic anisotropy and compared to reference SHE Co|Pt systems. This enhancement of DL torque is explained by the strong OREE at the interface between a light element and an oxide layer. In that sense, this study differs from our recently published work,¹⁹ which focused on the huge exaltation of the field-like torque (FLT) component observed in Pt|Co|Al|Pt systems due to OREE occurring at the ferromagnet–light metal (Co|Al) interface. Furthermore, in the Co|Pt|Cu|CuOx series, we investigate the Pt thickness dependence of the subsequent orbital-to-spin conversion and demonstrate an additional impact on the DL torques. By harnessing such OREE in light transition metal (light-TM) based structures, we achieve a noteworthy twofold enhancement for the effective torques on the Co layer, as validated through harmonic Hall as well as orbital Hall magnetoresistance (OMR) measurements. Our conclusion reveals new aspects of how the orbital properties of conduction electrons may influence the magnetization dynamics, opening up new avenues to control it in future energy-efficient spintronic devices.

The different multilayers studied in this work have been grown at room temperature using dc magnetron sputtering onto thermally oxidized Si|SiO₂ (280 nm) substrates. A more detailed description of the growth conditions by sputtering deposition and device fabrication can be found elsewhere.¹⁹ The sample series having an Al or a Cu film as a top layer are naturally oxidized in air, thus forming, respectively, AlOx or Al|AlOx and CuOx or Cu|CuOx interfaces depending on the initial thickness of Al or Cu. In the following, these samples will be marked with a star symbol (∗). Note that for the samples having Pt (3 nm) as a top layer, we know from a previous study using x-ray photo-electron spectroscopy (XPS) characterization that the underlying material, i.e., Al or Cu, is fully protected from oxidization.¹⁹ For electrical and torque measurements, 5 μm wide Hall bar structures are prepared from the multilayers using optical lithography and Ar⁺ ion-milling technique.

We first investigate the current-induced torques in Ta(5)|Pt(8)|Co(1.4)|Cu(5)|Al*(2) deposited on Si|SiO₂. The number in parentheses indicates the thickness in nm. The results are then compared with the ones obtained in Ta|Pt|Co|Cu|Pt, Ta|Pt|Co|Al|Pt, and Ta|Pt|Co|Al* samples that serve as references for current-induced torque measurements (see also our recent work by Krishnia et al.).¹⁹ 

In Fig. 1(a), we show the variation in R_2ω as a function of the in-plane magnetic field in the DL geometry for various currents in the Pt(8)|Co(1.4)|Cu(5)|Al*(2) sample along with the fits using Eq. (1). The extracted H_DL vs the current density injected in the 8 nm bottom Pt (J_Pt) is shown in Fig. 1(b) (red circles). Such a local current density has been evaluated through the measurement of both longitudinal R_xx and transverse R_xy resistances within a parallel resistor scheme as described hereafter in more detail. The H_DL exhibits a linear increase with J_Pt and undergoes a sign change relative to the magnetization direction in agreement with symmetry arguments. The interesting outcome lies in the significant variation in H_DL magnitude depending on the specific top light-metal interfaces, which are Pt|Co|Cu|Pt, Pt|Co|Al|Pt, and Pt|Co|Al*. First, we find a twofold decrease in H_DL in Pt|Co|Cu|Pt (black circles) compared to the two reference samples, i.e., Pt|Co|Al|Pt (orange circles) and Pt|Co|Al* (blue circles). This reduction can be explained, to a large extent, by an opposite SHE contribution from the top 3 nm Pt given the significant electronic and spin transmission across Cu. In our previous work, such a partial compensation in the SHE between bottom and top Pt has been very precisely evaluated to be 60% for a characteristic spin-diffusion length $λsfPt$ in Pt of 1.5 nm¹⁹ and 50% for $λsfPt$ in Pt of 1.75 nm, as observed here. This result also highlights that a metallic Cu layer, free of any oxide interface, cannot directly contribute significantly to any OHE but rather serves as a current shunting pathway.¹⁹ 

A second remarkable result observed in Fig. 1(b) is the twofold increase in H_DL in Pt|Co|Cu|Al* (red circles) compared to the reference samples, i.e., Pt|Co|Al|Pt (orange circles) and Pt|Co|Al* (blue circles), which cannot be explained by only considering a contribution from SHE. In this case, it is worth mentioning that the bottom Pt|Co interface remains identical in all these samples, and thus, no significant change in the SHE action originating from the bottom Pt layer is expected. Furthermore, we note that Cu and Al are light metals with negligible spin–orbit interaction, so they are not expected to generate a sizable pure spin current through SHE. However, as discussed previously, recent experimental findings indicate the potential generation of an orbital current at a naturally oxidized Cu|CuOx interface,³¹ largely contributing to the overall net torques. Moreover, we have recently reported on SOT properties of Pt(t₁)|Co|Pt(t₂), Pt|Co|Al|Pt, and Pt|Co|Cu|Pt series in which we clearly demonstrated that Pt(8)|Co(1.4)|Al(3)|Pt(3) involving thick Co (1.4 nm) and Al (3 nm) layers can be regarded as a “reference” SHE sample in which the H_DL predominantly originates from the SHE in the bottom Pt as played by the simpler Pt|Co bilayer.¹⁹ We may then associate, at this stage, the twofold rise in H_DL in Pt|Co|Cu|Al* compared to Pt|Co|Al* and/or Pt|Co|Al|Pt with an orbital current generation at the Cu|Al* interface.

In addition to harmonic Hall measurements, we further validate the observed increase in H_DL in Pt|Co|Cu|Al* through magnetoresistance (MR) measurements. To this aim, we have measured MR in the so-called spin-Hall magnetoresistance (SMR) geometry^37–39 with the current being injected along the $x̂$ direction and $ẑ$ is the normal direction to the layers. In this case, the magnetoresistance change, ΔR_xx as a function of the angle between the magnetization and the out-of-equilibrium spin or orbital angular momentum polarization direction (generated along the $ŷ$ direction), manifests how the angular-momentum current is reflected and/or transmitted at a specific magnetic/non-magnetic interface. Any additional (“OMR”) contribution originating from the orbital current generated at the Cu|Al* interface shall result in a change in magnetoresistance according to $ΔRxxRxx=ΔRxxSMRRxxPt| Co+ΔRxxOMRROMRCo| top$ (here, “top” means Al*, Cu|Al*, Cu|Pt, or Al|Pt). We simultaneously measure both the longitudinal (R_xx) and transverse (R_xy) resistances by rotating the sample in the $(ŷ−ẑ)$ plane under the application of a fixed magnetic field of 670 mT, larger than the anisotropy field [see Fig. 1(c)].

In this geometry, the magnetization consistently remains perpendicular to the direction of the charge current flow, thereby eliminating any contribution from anisotropic magnetoresistance (AMR). Consequently, any variation in ΔR_xx solely arises from SMR and/or OMR effects as $ΔRxx=ΔRSMR+OMR(1−my2)$⁠, where ΔR^SMR+OMR is the change of the total MR due to both SMR and OMR according to the relationship $ΔRSMR+OMR=ΔRxx(m̂‖ẑorm̂⊥σ̂)−ΔRxx(m̂‖ŷorm̂‖σ̂)$⁠. Here, $m̂$ and $σ̂$ are the unit vectors of the magnetization and angular momentum (spin or orbital) polarization directions and m_y is the y component of $m̂$⁠. In Fig. 1(c), we show in red the MR ratio, ΔR_xx/R_xx vs the rotation angle for Pt|Co|Cu|Al* (red in the top panel) and for Pt|Co|Al* (blue in the bottom panel). For comparison, we also include in Fig. 1(c) the effective MR from the R_AHE data (in green) according to the relationship $ΔRxx(θ)=ΔRSMR+OMR1−Rxy(θ)RAHE2$⁠. The MR variation measured from the two different angular dependences is in excellent agreement, in particular owing to the non-collinearity between magnetization and magnetic field due to the strong anisotropy. The increase in the MR ratio by a factor of more than two between the two samples witnesses the existence of an OAM polarization originating from the Cu|Al* interface. Such orbital accumulation is then after converted either into a charge current in the Co layer or into an intermediate spin-current at the bottom Pt|Co interface by SOC (orbital-to-spin filtering effect in Pt) before being released into a charge current via the inverse spin-Hall effect (ISHE).

In this section, we focus on the study of the net DL torques acting on the Co magnetization in Co(2)|Pt(t_Pt)|Cu*(3) samples exhibiting an in-plane magnetic anisotropy. The Cu*(3) material has been chosen here because of its property to provide helical OAM at its Cu|Ox interface as shown in Refs. 16 and 40 and as displayed from our DFT calculations of the electronic band structure calculations and Rashba–Edelstein response (see Sec. IV of the supplementary material). From the experimental point-of-view, the field required to saturate the magnetization along the out-of-plane direction is about 950 mT (see Sec. III of the supplementary material). Note that for sample series, we deliberately do not include any Ta|Pt buffer layer and directly deposit the multilayers on Si|SiO₂ for avoiding spurious spin-current from any bottom SHE Pt layer, strongly competing with the orbital component. In order to determine the actual impact of orbital currents on the effective torque, we have compared the results with the ones resulting from various non-magnetic metals, including Pt|Cu*, Cu*, Pt, and Pt|Al*. The last two cases are considered as reference samples. These capping layers serve two primary purposes: first to prevent oxidation of the Co layer and second to act as a source of spin and/or orbital current.

Concerning this particular series, in which the 2 nm thin Co layer is directly grown on Si|SiO₂, it is essential to get some insights into the structural and chemical properties of the samples in order to corroborate the conclusions revealed from the torque behavior. In Fig. 2(a), we show a cross section image of the Co(2)|Pt(2)|Cu*(3) sample obtained using high-angle annular dark-field scanning transmission electron microscopy (HAADF STEM). The spatial distribution along the thickness for each element, i.e., Co (red), Pt (green), Cu (blue), and oxygen (yellow), obtained using the electron energy loss spectroscopy (EELS) technique is plotted in Fig. 2(b). These EELS data clearly show that, first, each layer is continuous, flat, and homogeneous and, second, only the top part of the Cu layer is oxidized, clearly revealing a pristine Cu of about 1.5 nm thick.

In addition, we have also performed some x-ray photo-electron spectroscopy (XPS) at various takeoff angles (TOAs) in order to gain insights into the distribution of species within the top Cu* layer in Co|Pt|Cu* and Co|Cu* stacks. This TOA corresponds to the angle between the sample surface and the collection axis of the spectrometer: TOA90 is equivalent to normal emission (maximum probing depth) and TOA30 is equivalent to a geometry with a higher degree of inclination (minimum probing depth). In case of a gradient of composition in the Cu* layer, the contribution of near-surface species to the spectrum shall be the largest for the geometry with the shallower probing depth (i.e., TOA30). The evolution of the shape of the XPS spectra at different TOAs shown in Fig. 2(c), notably close to the L₃ edge (around 932 eV), brings some evidence that a spatial variation of the oxidation state is present within the Cu*(3) top layer with a typical distribution being Cu|Cu₂O|Cu(OH)₂ along the z-direction. A much more detailed analysis of these XPS characterizations is presented in Sec. I of the supplementary material.

Complementary to the EELS and XPS results presented before, the resistance–area product (R_s) and R_AHE can also be used to check the presence of a thin metallic Cu layer through the estimation of the shunting current as described within a simple parallel resistor scheme. The evolution of the sheet resistance R_s as a function of Pt thickness t_Pt is shown is Fig. 3(a) for the two types of samples, i.e., Co(2)|Pt(t_Pt)|Cu*(3) (2 series) and Co(2)|Pt(t_Pt). The slope of $Rs−1=Gs=GPt+Grest=σPttPt+Grest$ vs t_Pt in the inset of Fig. 3(a) gives the Pt resistivity of 27 ± 2 μΩ cm. The shift of the intercept of the linear variation between the two series allows us to extract the product of the Cu*(3) material conductivity times its thickness. From this, we deduce a thickness for the pristine metallic Cu layer to be about 1 nm, considering a typical resistivity ρ_Cu = 10 μΩ cm at room temperature. As a corollary to R_s, R_AHE may also provide additional information about the current shunt mechanism in a same parallel resistance scheme. Indeed, as revealed in Fig. 3(b), the AHE amplitude severely drops as t_Pt increases over its typical mean-free path (λ^Pt), mainly due to the passive action introduced by the Pt and Cu* layers. From Ref. 41, the standard law of the AHE variation taking into account such current shunting effects reads $RAHECu*(ζ)=ζ2RAHERef$⁠, with $ζ=R(Cu*)R(Ref)$ being the ratio of the respective resistances with Cu*/and without the additional shunt.⁴¹ This ratio corresponds to the proportion of the CIP-current in the reference AHE system within the whole structure. Such a model aligns well with our experimental results. For instance, in the case for which a 1 nm Cu layer is added to a 2 nm thick Pt current shunt, R_s decreases by a factor of 2, while R_AHE = R_xy drops by a factor of 4. Similarly, for t_Pt = 4 nm, the drop in R_s from $≈78Ω/□$ to $≈50Ω/□$ (ζ = 1.56 and ζ² ≈ 2.45) with Cu* inserted leads to a drop of R_AHE by ≈2.5 from 1 to 0.4 Ω. The very good overall linearity between R_AHE and $Rs−2$ is displayed in the inset of Fig. 3(b). Importantly, it is to be emphasized that this result underlines the good growth quality of the multilayer, i.e., flatness of the layers and limited interdiffusion at interfaces, leading to a well-established spin-dependent two-channel parallel resistor modeling with/without the additional Cu* overlayer.

THz spectroscopy experiments (THz-TDS) in the so-called emission mode are an alternate method to probe the partial metallic character of Cu*. The details of the respective setup and protocol are provided in Sec. II of the supplementary material and in Refs. 41–43. The THz amplitudes obtained vs the Pt thickness are presented in Fig. 4(a), where the black and red points correspond to the absolute value of E_THz for the two opposite saturating magnetic fields orientated in the sample plane and corresponding to the +/− THz waveform polarities. The observed shape of the E_THz vs t_Pt plot results from the product of two functions, respectively, $η×A$ involving the SCC efficiency η and $A$ describing the effect of both the THz and near-infrared (NIR) optical absorptions.

The spin–charge conversion efficiency η is a growing function of t_Pt, $η(tPt)=θSHEg↑↓rstanhtPt2λsfPt1+g↑↓rs⁡cothtPtλsfPt$ passing through the origin (η = 0 for t_Pt = 0), as displayed in Fig. 4(b) (in THz arbitrary unit) and its inset giving the corresponding dependence of the effective spin-Hall angle $η=θSHEeff$ vs t_Pt. $λsfPt$ is the hot electron spin relaxation length in Pt, the typical length scale over which the ISHE occurs; $rs=ρPt×λsfPt$ is the corresponding spin resistance of Pt⁴¹ (we will further call $r̃s=g↑↓rs$ the reduced spin resistance times the spin-mixing conductance).

Accessing the Pt conductivity responsible for the optical NIR absorption allows us to determine both the thickness and the resistivity of the remaining metallic Cu layer. The estimated values are ∼1 nm and 10 μΩ cm. We have checked that the THz signal emitted from a reference sample that does not contain any Cu and/or Cu|Cu* interface [blue and black points in Fig. 4(b) for the two different field polarities] is also well recovered by the same simulation protocol. This ensures the consistency of both measurements and analyses by fixing the hot electron spin relaxation length $λsfPt=1.45±0.05$ nm and $r̃s=g↑↓rs=2$⁠.

In Fig. 5(c), we compare H_DL measured in Co|Cu*, Co|Pt|Cu*, and Co|Pt structures as a function of the current density in Pt and in Cu* for samples free of any Pt. First, we find as expected that H_DL increases linearly with the current density for all the samples, which confirms the reliability of our measurements. Second, we measure a sizable DL torque on the Co layer in a system without any heavy metal interface, i.e., Co|Cu* sample (blue solid circles). The amplitude of the damping-like effective field is found to be μ₀H_DL/J_Cu ≈0.4 mT/10¹¹ A/m² current density in the remaining 1 nm metallic Cu. The existence of such a DL torque in Co|Cu* sample hints on the orbital current generation via the orbital Rashba–Edelstein effect at the Cu|CuOx interface that, in turn, propagates into Co before being converted into a spin current via the SOC of Co. This observation agrees with results from previous studies in the NiFe|Cu*,^32,44 CoFeB|Cu*,⁴⁰ YIG|Pt|Cu*,⁴⁵ or Cu|AlOx bilayer,¹⁶ hence also emphasizing on the absence of any spin–Rashba interactions in these systems. In the same spirit, more recent results demonstrate the orbital transport and orbital conversion at the Cu|oxide (Cu|MgO) interface by OREE following ultrashort optical excitation.³⁵ A third important result in Fig. 5(c) that has to be emphasized is the observed twofold increase in the H_DL amplitude upon capping the Co|Pt (red square) bilayer with Cu* (red circle). We find that the H_DL amplitude increases from ≈1.38 mT/(10¹¹ A/m²) in the Co(2)|Pt(4) bilayer structure to ≈2.31 mT/(10¹¹ A/m²) in the Co(2)|Pt(4)|Cu*(3) trilayer for 10¹¹ A/m² current density in Pt. Thanks to THz-TDS experiments (Fig. 4), we have also checked that such results cannot originate, for example, from a change in the effective conductivity of Pt on adding Cu* on top (compared to Co|Pt| air), which would have for effect to enhance the SHE current.

In order to gain deeper insights into the origin of the strong enhancement of H_DL in Cu*-based samples, we have performed a systematic investigation of the evolution of μ₀H_DL/J_Pt as a function of t_Pt in the Co(2)|Pt(t_Pt)|Cu*(3) series and compare it to the results in the reference series Co(2)|Pt(t_Pt). As shown in Fig. 6(a), the evolution of the normalized DL torque μ₀H_DL/J_Pt for Co(2)|Pt(t_Pt) exhibits a steady increase with t_Pt that eventually starts to saturate at t_Pt = 5 nm (blue open squares). In Fig. 6(a) (black open squares), we also include the evolution of μ₀H_DL/J_Pt with t_Pt recorded for the Co(2)|Pt(t_Pt)|Al*(1) series. Note that this evolution with t_Pt followed the same trend as the one obtained from ISHE data obtained from THz-TDS presented in Fig. 4, in which the SHE efficiency vs η(t_Pt) follows the function $η(tPt)=θSHEg↑↓rstanhtPt2λsfPt1+g↑↓rscothtPtλsfPt$ as previously defined. Note that we have obtained similar evolution in η function vs t_Pt in our previous work using a thinner ferromagnetic layer with out-of-plane magnetic anisotropy.¹⁹ From this, we can conclude that the Pt|Al* interface does not play a significant role in contributing to the additional source of DL torques. By fitting the μ₀H_DL/J_Pt vs t_Pt plot (dotted line), we are able to determine the spin diffusion length of Pt, $λsfPt≈1.75±0.05$ nm, slightly larger than the previous value (1.45 nm) as found for optically excited carriers in THz-TDS and the bulk spin Hall angle of Pt, $θSHEPt=0.21±0.02$⁠. The obtained parameters (⁠$λsfPt$ and $θSHEPt$⁠) from the reference series are found in excellent agreement with our previous studies on a different sample series¹⁹ and with other studies.⁴⁶ 

While the SOT fields and related parameters in the Co(2)|Pt(t_Pt) and Co(2)|Pt(t_Pt)|Al*(1) series are in very good agreement with previous studies, we observe in Fig. 6(a) a completely distinct behavior when a Cu*(3) layer is deposited on top of Co(2)|Pt(t_Pt) bilayers. In order to demonstrate the reproducibility of the observation, we have prepared, and characterized at different time, two series with similar Co(2)|Pt(t_Pt)|Cu*(3) stacking (deposited on Si|SiO₂) that are shown in red circles and triangles in Fig. 6(a). For both of them, we observe a peak in the μ₀H_DL/J_Pt evolution corresponding to a sharp increase with a maximum around t_Pt = 4 nm, before dropping down to the same amplitude as of the reference Co|Pt values at t_Pt = 5–6 nm. It is worth mentioning that we employed a parallel resistance model to calculate the relevant current density injected in the Pt layer estimating its resistivity ≈ 27 μΩ cm [see Fig. 3(a)]. This sharp enhancement as well the increase in the torque efficiency at smaller Pt thicknesses in Co(2)|Pt(t_Pt)|Cu*(3) compared to Co(2)|Pt(t_Pt) and Co(2)|Pt(t_Pt)|Al*(1) cannot be understood by considering only spin Hall and/or spin interfacial Rashba–Edelstein effects. In consequence, this brings another unambiguous demonstration that the DL torque enhancement is due to the orbital accumulation generated at the Cu|CuOx interface and subsequently converted into a spin current by an orbital-to-spin conversion through the Pt heavy metal layer.

Our thorough investigation of torques and magnetoresistance properties in the Ta|Pt|Co|Cu|Al* and Co|Pt|Cu* series allow us to conclude that both types of oxidized interface with Cu, either Cu|Al* and Pt|Cu*, possess the property to generate sizable OAM, hereafter diffusing into Pt (Co|Pt|Cu*) or into Co (Co|Cu|Al*) to produce enhanced torques. Such OAM generation can be most probably attributed to the interfacial OREE, as shown by density functional theory calculations.¹⁶ Even if bulk Cu itself may also lead to the generation of OAM through OHE, we can exclude such a predominant contribution as the thickness of the metallic Cu remains very small in all our sample series. In our samples, it became clear that the Cu layer also serves as a transport channel for OAM from its oxidized interface toward the active Co layer within the structure, as emphasized in a previous study.¹⁶ 

It is worth noting that one of our striking results is the demonstration of a strong enhancement of spin-orbital torques in Co|Pt|Cu* systems compared to Co|Cu*. This result questions about the inner mechanism of orbital-to-spin conversion occurring in the thin intermediate Pt layer. Even if a precise theoretical description of the experimental results is beyond the scope of the present study, our first modeling points out the particular role played by the s-d spin-polarized electronic wave functions in transition metals strongly hybridized as well as related s-d diffusion processes, as proposed in the modeling of anisotropic magnetoresistance (AMR) effects.⁴⁷ 

In conclusion, we have demonstrated the significant role of the orbital Rashba–Edelstein effect to the effective current induced torques in Pt|Co|Cu|Al* and Co|Pt|Cu* (or Co|Pt|Cu|CuOx) structures, revealing previously unexplored facets of the conduction electron behavior. Through a systematic investigation of thickness dependence in the Co|Pt|Cu|CuOx series, we have extracted the key physical parameters, such as the efficiency of spin injection and related spin relaxation lengths as well as additional contributions that we assigned to the orbital component. We have then provided an experimental evidence for the presence of the orbital Rashba–Edelstein effect at the Cu|CuOx interface involving light elements, alongside SHE in Pt. Combining two added contributions allows us to achieve a twofold enhancement in the effective torques acting on the Co magnetization, highlighting the importance of including the electron’s orbital degree of freedom in the material strategy to improve drastically the net amplitude of current-induced torques. Beyond the fundamental interest, this insight opens up promising avenues for controlling magnetization in spin-based devices, potentially leading to benefits in terms of energy efficiency and eco-friendly technology applications.

The supplementary material includes a detailed analysis and additional data on the oxidation degree of Cu, an extended analysis of THz-TDS spectroscopy, measurements of anomalous and planar Hall effects, and density functional theory (DFT) simulations of orbital and spin angular momentum transport in Cu|Cu|O and Cu|Al|O structures.

We thank Michel Viret and Jean-Baptiste Moussy (SPEC, Gif-sur-Yvette, France) for fruitful discussions and Sukhdeep Dhillon (LPENS, Paris, France) for his help in THz-TDS spectroscopy measurements. This study has been supported by the French National Research Agency under the Project “ORION” ANR-20-CE30-0022-02, by a France 2030 government grant managed by the French National Research Agency PEPR SPIN ANR-22-EXSP 0007 (SPINMAT), and by the European Horizon Europe Framework Programme for Research and Innovation (2021-2027) EC Grant Agreement No. 101129641 (OBELIX). This work contains results obtained from the experiments performed at the Ernst Ruska-Centre (ER-C) for Microscopy and Spectroscopy with Electrons at the Forschungszentrum Jülich (FZJ) in Germany. The ER-C beam-time access was provided via the DFG Core Facility Project ER-C E-014.

The authors have no conflicts to disclose.

S. Krishnia: Data curation (equal); Formal analysis (equal); Methodology (equal); Writing – original draft (equal); Writing – review & editing (equal). B. Bony: Data curation (equal); Formal analysis (equal); Writing – review & editing (supporting). E. Rongione: Investigation (supporting); Writing – review & editing (supporting). L. Moreno Vicente-Arche: Formal analysis (supporting); Methodology (supporting); Writing – review & editing (supporting). T. Denneulin: Formal analysis (equal); Methodology (supporting); Writing – review & editing (supporting). A. Pezo: Formal analysis (equal); Resources (equal); Writing – review & editing (equal). Y. Lu: Formal analysis (supporting); Methodology (supporting). R. E. Dunin-Borkowski: Resources (supporting); Writing – review & editing (supporting). S. Collin: Methodology (supporting); Resources (supporting). A. Fert: Formal analysis (supporting); Supervision (supporting); Writing – review & editing (supporting). J.-M. George: Data curation (supporting); Writing – review & editing (supporting). N. Reyren: Formal analysis (equal); Supervision (supporting); Writing – review & editing (equal). V. Cros: Conceptualization (equal); Formal analysis (equal); Funding acquisition (equal); Project administration (equal); Supervision (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal). H. Jaffrès: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Methodology (equal); Project administration (equal); Supervision (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.