Large Interfacial Rashba Interaction Generating Strong Spin–Orbit Torques in Atomically Thin Metallic Heterostructures

Abstract

The hallmark of spintronics has been the ability of spin–orbit interactions to convert a charge current into a spin current and vice versa, mainly in the bulk of heavy metal thin films. Here, we demonstrate how a light metal interface profoundly affects both the nature of spin–orbit torques and its efficiency in terms of damping-like (H_DL) and field-like (H_FL) effective fields in ultrathin Co films. We measure unexpectedly H_FL/H_DL ratios much larger than 1 by inserting a nanometer-thin Al metallic layer in Pt|Co|Al|Pt as compared to a similar stacking, including Cu as a reference. From our modeling, these results evidence the existence of large Rashba interaction at the Co|Al interface generating a giant H_FL, which is not expected from a metallic interface. The occurrence of such enhanced torques from an interfacial origin is further validated by demonstrating current-induced magnetization reversal showing a significant decrease of the critical current for switching.

In modern nanomagnetism, spin–orbit coupling (SOC) at interfaces is exploited to generate strong interfacial perpendicular anisotropy (PMA) or antisymmetric exchange interactions.¹ In spintronics, SOC is the key interaction to generate spin-current via the spin Hall effect (SHE) in heavy metals, enabling magnetization switching²⁻⁶ and driving skyrmions⁷ and domain walls. In atomically thin layers with broken inversion symmetry, the interplay of low-dimensionality and SOC may also lead to a Rashba spin-splitting⁸⁻¹⁰ modifying the electronic ground state, thus affecting the spin transport via the Rashba–Edelstein (REE)¹¹ or orbital Rashba effects (ORE).^12,13 These phenomena, namely, SHE^5,14,15 and REE (or ORE),^{5,10,11,15,16} may convert a charge current into either an out-of-equilibrium spin-current or spin accumulation μ̂ (out-of equilibrium spin-density) carrying an angular momentum. Upon current injection, those can, in turn, transfer their angular momentum to the adjacent ferromagnetic layer by precessing around the exchange field.

Both and μ̂ may exert spin–orbit torques (SOTs) onto a magnetization vector with two components: damping-like torque (DLT), τ̂_DL ∝ m̂ × (μ̂ × m̂), and field-like torque (FLT), τ̂_FL ∝ μ̂ × m̂. The nature and strength of the corresponding DL (H_DL) and FL (H_FL) effective fields strongly depend on the relaxation of the transverse spin i.e. on the spin decoherence length, which is predicted to be a few atomic lattice parameters.^17,18 Manipulating the magnetization via SOTs and disentangling the exact origin of SOTs to use them adequately are still challenging today for writing processes in magnetoelectronic devices.

In the pioneer experiments by Miron et al. in Pt|Co|AlO_x,² SOT was discussed in terms of dominating FLT arising from REE at the Co|Oxide interface, larger than SHE-DLT from Pt, suggesting the crucial role of a large interfacial electric field at the ferromagnet/oxide interface. Although, in metals, SHE is largely considered as the primary source of DLT,^3,19−21 a significant interfacial REE has been recently observed in Ir|ferromagnetic|Ta contributing to DLT.²² In the limit of atomically thin magnetic layers, additional mechanisms might also influence the strength of the SOTs: spin-filtering or charge quantum confinement,²³⁻²⁷ surface states of topological insulators (TIs)²⁸ and 2D electron gases.²⁹

Moreover, recent theory has evidenced additional orbital currents in light elements from orbital Hall effects (OHE) and/or orbital Rashba effects (ORE) superimposing to the spin currents.³⁰ These orbital currents may result in the generation of orbital torques^12,31 and orbital Rashba magnetoresistance.^13,32 This questions the actual origin of the magnetic torques in multilayers with light elements.

In this study, we investigate the properties of SOTs in atomically thin metallic structures, namely, Co layers ranging from 1.4 nm down to 0.4 nm, sandwiched between Pt and light element overlayers, i.e., Al or Cu. Using the second harmonic Hall measurement technique,^33,34 we precisely determine the amplitude of the SOT vs the ferromagnetic film thickness, the light-element overlayer, and the heavy-element. Compared to the best-reported results,³⁴ we find an increase of the DLT by ∼30% together with a drastic rise in the FLT by more than ∼190%. With the help of our spin-dependent Boltzmann calculations, we explicitly demonstrate the occurrence of enhanced SOT due to a strong REE in asymmetric Pt|Co|Al|Pt stacks, from a FLT over DLT ratio as large as 2.5 for 0.55 nm thick Co, one of the highest values ever reported in metals.

Samples were grown using magnetron sputtering at the base pressure 6 × 10^–8 mbar. In Figure 1a, we show X-ray reflectivity (XRR) measurements (blue) and fit (red) on a Ta(5)|Pt(8)|Co(0.7)|Al(1.4)|Pt(3) sample where the layer thicknesses are found to be in good agreement with nominal values (<3% error). The XRR measurements reveal 0.29 and 0.12 nm roughness at Pt|Co and Co|Al interfaces, respectively, comparable with the SiO₂|Ta interface (0.45 nm). We have also performed X-ray photoelectron spectroscopy (XPS) on Pt(8)|Co(0.7)|Al(1.4)|Pt(t_Pt) with t_Pt = 2 and 3 nm to probe the chemistry of Al underneath Pt (Figure 1b with black and red colors respectively). As the Al 2p peak (71 eV) is totally screened by the 4f Pt peaks, the 2s Al bonds are probed. The peak for the 2 nm Pt capping can be fitted with two contributions attributed to AlOx (dashed) and metallic Al (dotted) respectively whereas the 3 nm Pt capping sample only reveals a single metallic state of Al thus discarding any oxidization state. In Figure 1c and d, we show the energy dispersive X-ray spectroscopy (EDX) measurements in scanning transmission electron microscopy (STEM). The Ta, Pt Co, and Al layers can be clearly distinguished by bright and black Z-contrasts in high-angle annular dark-field (HAADF) image. In Figure 1d, we show elemental distribution of Ta (white), Pt (green), Co (blue), and Al (red). Together with XRR, the HAADF and EDX characterizations clearly show homogeneous and flat interfaces without any sign of oxidation of the Al film.

Figure 1.

(a) XRR measurements (blue) and fittings (red) on Pt(8)|Co(0.7)|Al(1.4)|Pt(3) sample. (b) Measurements of XPS on similar samples are shown by red color together with a reduced Pt capping (2 nm) with oxidized Al (in black). (c) HAADF image in STEM of the sample with corresponding EDX elemental map shown in (d).

To evaluate the two components of the SOTs, we employed the harmonic Hall measurement technique on 5 μm wide Hall bars with an AC excitation of 727 Hz (SI-I). First, we compare the results from the two series of multilayers with Al and Cu light element interfaced with Co: Pt(8)|Co(t_Co)|Al(1.4)|Pt(3) and Pt(8)|Co(t_Co)|Cu(1.4)|Pt(3). Starting from negligible torques in a fully symmetric Pt(8)|Co(0.9)|Pt(8) stack as expected (SI-V), the asymmetric “control” sample Pt(8)|Co(0.9)|Pt(3) gives H_DL = 0.80 ± 0.05 mT and H_FL 0.58 ± 0.15 mT for a current density in Pt = 10¹¹ A/m² (later used as a reference value). To obtain integrated torques over the whole ferromagnetic layer of thickness t_Co and hence to be able to make an accurate comparison, we define a normalized quantity by multiplying H_DL,FL with t_Co for a 10¹¹ A/m² current density in Pt. This corresponds to the equivalent torque values for an applied electric field owing to the Pt resistivity ρ_Pt = 25 μΩ·cm (SI-III). Our analyses mainly depend on the anisotropy field H_k, but not on the saturation magnetization at the limit of thin Co M_s = 1.1 ± 0.1 MA/m, remaining however quite independent of the Co thickness t_Co for both the Al and Cu series (SI-IV).

Several features may be highlighted with similarities and differences between the Al and Cu series. First, as shown in Figure 2a, the integrated DL component is about 65% larger in Pt|Co|Al(1.4)|Pt samples compared to Pt|Co|Cu(1.4)|Pt for almost the whole Co thickness. At t_Co = 0.9 nm, the value of DLT is about 2.5 mT × nm/(10¹¹ A·m^–2) for Al and 1.5 mT × nm/(10¹¹ A·m^–2) for Cu. We note however that the product exhibits in each case a similar maximum close to t_Co = 1.0–1.2 nm that we ascribe to the spin decoherence length at small thickness. Second, we find that the FLT exhibits an increase in reducing t_Co (Figure 2b) in both series, resulting in a dominating FLT component at small t_Co. Nevertheless, their SOT magnitude strongly differs. We observe a substantial increase of the FLT for Al(1.4), i.e., from 1.7 mT × nm/(10¹¹ A·m^–2) for t_Co = 1.4 nm to 5.2 mT × nm/(10¹¹ A·m^–2) for t_Co = 0.55 nm, whereas the maximum value of FLT reaches only 2 mT × nm/(10¹¹ A·m^–2) for Cu. Such a large FLT increase in the atomically thin Co layer has never been reported to our knowledge. This striking result manifests also by a rise of the FLT to DLT ratio for Pt|Co|Al|Pt that we will consider as a new figure of merit (see Figure 2c).

Figure 2.

(a) Damping-like (DL) field and (b) field-like (FL) field multiplied by t_Co for = 10¹¹ A/m² in Pt(8)|Co(0.55–1.4)|Al(1.4)|Pt(3) and Pt(8)|Co(0.4–1.2)|Cu(1.4)|Pt(3). (c) t_Co dependence of ζ = H_FL/H_DL. Red and blue dashed lines are fits to experimental data points using our theoretical model, and black dashed line in (c) is calculated ζ values without any Rashba interface (see SI-VII).

Such a behavior is expected either for SHE when t_Co becomes smaller than the spin-decoherence length (black curve in Figure 2c from our modeling (SI-VII) or for an increased weight of REE (red dotted line for Al and blue for Cu in Figure 2c). We find that saturates for t_Co ≳ 1.2 nm with a magnitude ζ ≈ 0.7 in the “thick” ferromagnet limit for SHE.¹⁹ This corresponds also to the case of the Cu series with moderate Rashba effects. Similar value of ζ ≃ 0.7 were also obtained on 4 nm thick Co|Ni multilayers.³⁵ Here, on reducing t_Co below 1.2 nm, ζ increases sharply for the Pt|Co|Al|Pt series (Figure 2c) and eventually reaches 2.5 for t_Co = 0.55 nm. This ratio remains smaller than unity down to t_Co = 0.7 nm for Pt|Co|Cu|Pt. Such FLT enhancement by a factor larger than three from t_Co = 1.4 nm to t_Co = 0.55 nm strongly challenges the SHE (and/or OHE) origin of SOT with Al.

In Figure 3, we present the evolution of (Figure 3a), (Figure 3b), and their ratio vs Al (red points) and Cu (blue points) thickness (Figure 3c). Both DLT and FLT exhibit a strong enhancement with t_Al in the 1–3 nm window, particularly pronounced for the FLT. We find that FLT (respectively DLT) increases from ∼0.65 mT/10¹¹ A·m^–2 (∼0.8 mT/10¹¹ A·m^–2) for t_Al = 0 nm to a saturation value of ∼7 mT/10¹¹ A·m^–2 (∼4.4 mT/10¹¹ A·m^–2) for t_Al = 3 nm. This corresponds to a boost of the FLT by more than a factor of 10 upon inserting 3 nm of Al on top of 0.9 nm Co. Conversely, the ratio ζ is also enhanced with t_Al (Figure 3c) from ζ = 0.8 for t_Al = 0 to ζ = 1.6 for t_Al ≥ 3 nm. First, we comment the behavior of DLT. Based on the results from our fits (SI-VII), we assign the rise of DLT vs t_Al to the decrease of the transmission coefficient at the top of the structure varying linearly from for t_Al = 0 nm to when t_Al > 3 nm. This results in the quenching of the opposite SHE from the top Pt. However, part of the DLT enhancement also originates from the conversion of the FLT into the DLT in the Co thickness via the spin precession mechanism. This trend is very different in the “reference” Cu series vs t_Cu as we find that and ζ ≈ 0.7 remain roughly constant vs t_Cu (blue open triangles in Figure 3a and b).

Figure 3.

(a) H_DL vs Al (red) and Cu (blue) layer thickness. The variation in H_DL is fitted by the dashed red lines (SI-VII). We used l_sf^Pt = 1.5 nm, r̃_s = 2, and the transmission coefficient varying linearly from for t_Al = 0 nm to when t_Al > 3 nm. (b) H_FL vs Al (red) and Cu (blue) layer thickness. (c) ζ = H_FL/H_DL vs Al (red) and Cu (blue) layer thickness. Thick and constant blue lines are a guide to the eye.

Two important conclusions may then be drawn for the DLT: (i) a progressive extinction of the SHE action from the top Pt on increasing the thickness of Al through the quench of the electron transmission at the Co|Al|Pt interfaces and (ii) a larger electronic transmission across Co|Cu|Pt^36,37 partially compensating the SHE torque from the bottom Pt (irrespective of t_Cu). Considering both bottom and top Pt layers, the effective spin Hall angle (SHA) (θ_SHE^eff) is

1

where θ_SHE^bulkPt is the bare SHA of bulk Pt, is the effective transmission coefficient at the top, and is the spin-loss.^36,38,39 The function :

2

describes the spin back-flow in Pt with λ_sf^Pt ≈ 1.5 nm being its spin-diffusion length (SDL) in Pt as in ref (37) and r̃_s ≈ 2 is its spin-resistance in the unit of the inverse of the Sharvin conductance (SI-VII). From our fitting procedure (Figure 3a), we could extract using θ_SHE^bulkPt ≈ 0.225 ± 0.025 in agreement with the literature for a Pt resistivity of ρ = 25 μΩ·cm.^37,40 Similar values of θ_SHE were determined from AHE.⁴⁰ We considered here and . Our fitting procedure applied to AHE (SI-IV) uses the same set of parameter values as for SOTs. The SHE compensation from the top injection then approaches 75% in our ’control’ Pt(8)|Co(0.9)|Pt(3) structure and 60% in the Pt(8)|Co(0.9)|Cu|Pt(3) series. This implies that the expected increase of the DLT is 25% (0.75/0.6) from Pt(8)|Co(0.9)|Pt(3) to Pt(8)|Co(0.9)|Cu|Pt(3) and by a factor ×2.5 to Pt(8)|Co(0.9)|Al(3)|Pt(3) (Figure 3a).

In order to highlight any additional REE (or ORE) arising from Co|Al, we reduced the bottom Pt thickness in the Pt(t_Pt)|Co(0.9)|Al(5) series to attenuate the SOTs originating from SHE. We first quantified this SHE contribution by extracting θ_SHE from H_DL according to (e is the electron charge). In Figure 4a, we observe that θ_SHE^eff increases with t_Pt according to (eq 2) before reaching its saturation value for t_Pt ≥ 5 nm. From the fitting procedure, the spin-diffusion length (SDL) and θ_SHE are, respectively, ≃1.5 nm and ≃0.08, in agreement with data of Figure 3. In Figure 4b, we show the impact of the additional REE (or ORE) occurring from Co|Al on the SOTs for t_Co = 0.9 nm. First, the FLT clearly dominates the DLT for all the Pt thicknesses. In addition, a remarkable increase of ζ is observed at the lowest t_Pt = 2–5 nm thickness range, i.e., where SHE has not yet reached its maximum efficiency. This undoubtedly supports the role of a significant Rashba interaction (i.e., REE and/or ORE) superimposed to SHE. Our data also yield a clear quantitative understanding of how the Rashba effects at metallic interfaces may strongly affect H_FL in chemically asymmetric Pt|Co|Al|Pt stacks (see Figures 2 and 3).

Figure 4.

a) Effective θ_SHE^eff vs t_Pt (green points). The solid line is the fit enabling to extract l_sf = 1.5 nm, Pt bulk θ_SHE^bulk Pt = 0.225 ± 0.025 (effective θ_SHE = 0.075 ± 0.01), and r̃_s^Pt = 2 using eq 2. (b) Plot of the ζ ratio vs t_Pt.

We then performed SOT-driven magnetization switching experiments on Pt(8)|Co(0.9)|Al(t_Al)|Pt(3) Hall cross-bars. A magnetic field H_x, either positive or negative, is applied along the current direction to break the mirror symmetry, and R_AHE is measured vs the current. Typical results of SOT-induced magnetization reversal are shown in Figure 5 for respective positive μ₀H_x = +250, 373, 495, and 608 mT (Figure 5a) and equal negative μ₀H_x = −240, −368, −495, and −600 mT (Figure 5b) fields for t_Al = 3 nm. A complete magnetization reversal is observed for J_c ≈ ±2–2.5 × 10¹¹ A·m^–2 with the polarity of the magnetization reversal cycle depending on the sign of μ₀H_x as expected. We also find that the critical current density decreases as |μ₀H_x| increases as observed in refs (35) and (41) with the typical current density reaching J_c = 3–3.5 × 10¹¹ A·m^–2. In Figure 5c, we compare magnetization reversal cycles for different t_Al = 1, 2, 3, and 4 nm, acquired under a field μ₀H_x = +250 mT much smaller than the anisotropy field H_K (SI-IV). Despite a larger H_K and larger coercive field, we find that a complete switching of magnetization (between P and AP states) may be achieved in devices with t_Al = 3 and 4 nm, whereas the ones with t_Al = 1 and 2 nm exhibit only partial reversal, thus in agreement with the enhanced SOT shown in Figure 3. We hence conclude that increasing the Al thickness in the Pt(8)|Co(0.9)|Al(t_Al)|Pt(3) series increases the SOT allowing a reduction of the critical current density for complete magnetization switching by more than 30%.

Figure 5.

Current-induced magnetization reversal in Pt(8)|Co(0.9)|Al(3)|Pt(3) for different (a) positive and (b) negative μ₀H_x. (c) R_AHE as a function of pulsed current in the Pt(8)|Co(0.9)|Al(t_Al)|Pt(3) series of samples for μ₀H_x = +250 mT. The pulse width was 100 μs.

The ensemble of the results highlighting the existence of a large interfacial Rashba effect from the Co|Al is supported by our modeling (SI-VII). In the case of thick ferromagnet, it is known that SOT from SHE is determined via the complex spin-mixing conductance.^21,42,43 For t_Co smaller than the dephasing length, the description is far more complex owing to the remaining outgoing spin-currents and additional electronic reflections. We developed numerical analyses gathering most of the ingredients discussed above based on generalized drift-precession-diffusion equations^20,44−46 able to express the profile of the vectorial spin-accumulation μ̂_F. We thus provide subsequent insights for H_DL and H_FL, the integrated value of the torque τ_SOT, by considering the precessing and dephasing processes via the s–d exchange coupling (). In particular, this implies a complex value of the propagating length in Co. The SOT acting on the Co layer by the out-of equilibrium spin μ̂_F then writes:⁴⁷

3

where is the volume of Co and μ_F is expressed in the same unit () as and is the precession time. In our treatment, the interfaces are described by their proper interfacial G_s or spin-mixing G_↑↓ (between Co and the nonmagnetic material) conductances normalized by their Sharvin values G_sh, or using corresponding transmission coefficients (spin-mixing transmission). It generally leads to possible spin-backflow processes⁴⁸ and additional spin-accumulation within the different layers. We considered:

(i) a typical precession (or Larmor) length λ_J = 2πv_Fτ_J = 4.7 nm for the transverse part of the spin accumulation and spin-current and a transverse spin-decoherence length λ_⊥ of 1.7 nm in the range of the values given in ref (45) for Co.

(ii) a large spin-mixing transmission coefficient at the Co|Pt interface^40,49 with G_↑↓ and G_sh being, respectively, the spin-mixing conductance and the Sharvin conductance.

(iii) a mean spin-mixing transmission coefficient through Cu.^36,37

(iv) a mean spin-mixing transmission coefficient varying from 0.8 to 0 when the Al thickness is increased from 0 to 3 nm and greater.

Based on our present knowledge for the Co|Pt interface,^36,49,50 the predicted SOT fields are in excellent agreement with the experimental ones for both DL and FL (see dashed lines in Figures 2 and 3). We accounted for a spin-accumulation μ_F = μ_REE at the Co|Al(Cu) interface due to REE. For Pt|Co|Cu|Pt, we consider that μ_REE is homogeneous in Co and constant for all t_Co. We quantify that REE (SHE) contributes ≈ 45% to the FLT (≈ 55%) for t_Co = 0.4 nm in the reference Cu samples. The important result is that, for the Pt|Co|Al|Pt series, a much larger spin accumulation μ_REE is required to fit the data with a certain dependence on t_Co varying within a length scale of the order of 0.75 nm. Consequently, the FLT contribution from REE (and/or ORE) reaches ≈75% for t_Co = 0.55–1.2 nm (≈ 25% from SHE), whereas it contributes only 60% for t_Co = 1.4 nm (≈ 40% from SHE).

Finally, we point out that, at this stage, and owing to the same symmetry of torques possibly generated by an ORE¹³ compared to the one by spin Rashba effect, we cannot distinguish between the two mechanisms and thus cannot discard that a large part of the FLT increase in Al-based samples may indeed originate principally from ORE. Note, however, we can discard the role of the OHE in the Al light element (nonetheless calculated to be small^30,51) from our results displayed in Figure 4 on the basis of the same arguments discussed for the spin Hall effect.

In conclusion, we have demonstrated that, in atomically thin Co, the SOT amplitudes, both for damping- and field-like symmetries, vary significantly when a light element such as Al is deposited on top of Co, exceeding the values existing in the literature. In particular, we find a large increase of the field-like component and the corresponding ratio of H_FL/H_DL at Co|Al|Pt interfaces within the single atomic Co thickness range. This demonstrates the occurrence of interfacial Rashba interactions, leading to significant conversion effects at the Co|Al interface. Beyond the fundamental interest, these results in all-metallic systems in the limit of atomically thin ferromagnets also open a new research direction for CMOS-compatible and cost-effective spinorbitronic based technology.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.nanolett.2c05091.

• (Detailed analysis of harmonic Hall measurements, measurements of resistivity and estimation of current shunt effects in the each layer of multilayers, theoretical modeling of anomalous Hall effect and spin–orbit torques PDF)

Author Present Address

^§ Department of Physics and Center for Advanced Nanoscience, University of California, San Diego La Jolla, CA, 92093, USA

The authors declare no competing financial interest.