# Giant and Anisotropic Enhancement of Spin-Charge Conversion in Graphene-Based Quantum System

Alberto Anadón, Armando Pezo, Iciar Arnay, Rubén Guerrero, Adrián Gudín, Alba Guio, Melissa Yactayo, Jaafar Ghanbaja, Julio Camarero, Aurelien Manchon, et al.

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Alberto Anadón, Armando Pezo, Iciar Arnay, Rubén Guerrero, Adrián Gudín, et al. Giant and Anisotropic Enhancement of Spin-Charge Conversion in Graphene-Based Quantum System. Advanced Materials, 2025, 37 (13), pp.2418541. 10.1002/adma.202418541. hal-05021881

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https://hal.univ-lorraine.fr/hal-05021881v1

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# Giant and Anisotropic Enhancement of Spin-Charge Conversion in Graphene-Based Quantum System

Alberto Anadón*, Armando Pezo, Iciar Arnay, Rubén Guerrero, Adrián Gudín, Alba Guio, Melissa Yactayo, Jaafar Ghanbaja, Julio Camarero, Aurelien Manchon, Sebastien Petit-Watelot, Paolo Perna*, Juan-Carlos Rojas-Sánchez*

Dr. A. Anadón, MSc. M. Yactayo, Dr. J Ghanbaja, Dr. S. Petit-Watelot, Dr. J.-C. Rojas-Sánchez
Université de Lorraine, CNRS, IJL, F-54000 Nancy, France

Email: anadonb@unizar.es

Email: juan-carlos.rojas-sanchez@univ-lorraine.fr

MSc. M. Yactayo

Facultad de Ciencias Físicas, Universidad Nacional Mayor de San Marcos, Lima 14, Peru

Dr. A. Pezo, Prof. A. Manchon

Aix-Marseille Université, CNRS, CINaM, Marseille, France

Dr. I. Arnay, Dr. R. Guerrero, Dr. A. Gudín, MSc. A. Guio, Prof. J. Camarero, Dr. P. Perna IMDEA

Nanoscience, C/ Faraday 9, Campus de Cantoblanco, 28049 Madrid, Spain

Email paolo.perna@imdea.org

Keywords: *Graphene*, *Magnetic Rashba interface*, *Spin pumping*

The ever-increasing demand for efficient data storage and processing has fueled the search for novel memory devices. By exploiting the spin-to-charge conversion phenomena, spintronics promises faster and low power solutions alternative to conventional electron-ics. In this work, we demonstrate a remarkable thirty-four-fold increase in spin-to-charge current conversion when incorporating a 2D epitaxial graphene monolayer between iron and platinum layers by exploring spin-pumping on-chip devices. Furthermore, we find that the spin conversion is also anisotropic. We attribute this enhancement and anisotropy to the asymmetric Rashba contributions driven by an unbalanced spin accumulation at the differently hybridized top and bottom graphene interfaces, as highlighted by ad-hoc first-principles theory. The improvement in spin-to-charge conversion as well as its anisotropy reveals the importance of inter-faces in hybrid 2D-thin film systems opening up new possibilities for engineering spin conversion in 2D materials, leading to potential advances in memory, logic applications or unconventional computing.

## 1 Introduction

Interconversion between spin and charge currents is a key operation for modern memories and one of the main research activities in today's spintronics.

In general, the generation and detection of spin currents mainly occur in materials exhibiting large spin-orbit coupling (SOC), such as heavy transition metals like Pt [1, 2] or Ta [3]. Lately, it has been realized that two-dimensional (2D) systems with inversion symmetry breaking, such as Rashba interfaces [4, 5, 6] and the surface of topological insulators [7, 8], display much larger spin-charge interconversion efficiencies compared to transition metals [9]. This superiority stems from the strong spin-momentum locking of the 2D states such as Rashba surface states induced by the strong interfacial potential gradient. Among the promising 2D systems for spin-charge interconversion [10], graphene (Gr) stands out as a particularly appealing platform.

As a matter of fact, although pristine Gr is a poor spin-charge converter due to its vanishingly small intrinsic SOC, its remarkable ability to acquire a sizable SOC by proximity effect and doping has been widely reported [11]. It has been demonstrated for example that the intercalation of either (non-magnetic or magnetic) transition or rare-earth metals underneath a Gr monolayer grown on single crystal substrates results in large magnetic anisotropy [12, 13, 14, 15], spin-polarization, Rashba states [16] and Dzyaloshinskii-Moriya interaction [17, 15, 18], or even in the appearance of non-trivial, exotic topological spin textures and emerging symmetry-broken phases [19]. In the context of spin-charge interconversion, the exceptional conductivity and tunable SOC of Gr open avenues for the design of efficient spin-charge interconverters or spin logic devices [20, 21, 22].

The physics of spin-charge interconversion in 2D systems is markedly different from that of metallic heterostructures. In the latter, the interconversion is governed by the inverse spin Hall effect (ISHE) [23],
attributed to spin-dependent extrinsic scattering or intrinsic anomalous velocity, that converts a spin *current* into a charge current. In the former, the interconversion is induced by the so-called inverse Edelstein effect (IEE), associated with the helical spin texture and that converts a spin *density* into a charge current [24, 5, 6, 25]. The spin-charge interconversion can be probed by spin-orbit torque (SOT) (charge-to-spin) or by spin-pumping (spin-to-charge) techniques, the latter being unaffected by shunting in other metallic layers for the quantification of the reciprocal effects, ISHE and IEE [9]. The figure of merit for the IEE efficiency has the unit of length since it is the result of the ratio between the two-dimensional charge current density generated in the 2D region ($j_c^{2D}$) and the three-dimensional injected spin current density ($j_s^{3D}$), and its effective value will be denoted by $\lambda = j_c^{2D}/j_s^{3D}$ [5, 6, 8].

In exfoliated Gr deposited on diverse substrates, many spin transport experiments devoted to reveal spin relaxation, diffusion, precession [26, 27], and induced SOC by proximity with heavy metal (HM) [11] or 2D materials [28, 29, 30, 31] have been reported.

In pristine Gr the spin relaxation time may change between the in-plane, $\tau_s^{\parallel}$, and out-of-plane, $\tau_s^{\perp}$, spin directions [27]. Such anisotropy can be enhanced by proximity with heavier materials, typically reaching $\tau_s^{\perp} \sim 30$ps $\gg \tau_s^{\parallel} \sim 3$ ps for Gr/WS$_2$ [32]. Instead, no spin relaxation anisotropy along different in-plane propagation directions has been reported. However, in all cases, ordinary Hall effect and shunting in the metallic layers [33] limit the straightforward and reliable quantification of the effects.

Regarding spin-charge interconversion, by using spin pumping measurements very different efficiencies were measured by interfacing Gr with other materials. For example, in Gr interfaced with Yttrium Iron Garnet ferrimagnetic insulator it was found an efficiency much lower than the interface with a HM, $\lambda_{YIG/Gr} \approx 0.001$ nm [34], $\lambda_{YIG/Gr} \approx 0.002$ nm) [35], whereas the interface with a transition metal ferromagnet Ni$_{81}$Fe$_{19}$ (Py)/Gr displayed $\lambda_{Py/Gr} \approx 0.003$ nm [35]. In addition, the YIG interface with a 2D material with larger SOC than Gr was found to present an efficiency of two orders of magnitude larger ($\lambda_{YIG/MoS_2} \approx 0.4$ nm) [36]. It is worth to note also that different successful attempts to enhance the interconversion efficiency have been performed by combining Gr with another 2D systems with larger SOC [37], e.g., $\lambda_{Py/Gr} \approx 0.011$ nm < $\lambda_{Py/Gr/WS_2} \approx 0.078$ nm [38], but still the values obtained are one or two orders of magnitude smaller than in single HMs (equivalent $\lambda$ for Pt $\approx 0.2$ nm [39, 9]).

Overall, these experimental results reveal the crucial role of interfacial SOC and the derived dependence of the spin-charge interconversion on the electronic structures of the interface, either due to IEE or ISHE effects.

In contrast, most of these experiments, including the ones cited above, were performed either in exfoliated flakes of Gr (and other van der Waals 2D materials) [40] or by using Cu substrate and polymethyl methacrylate (PMMA) polymer transfer process, which are known to leave residues that degrade the graphene's properties [41]. In all these approaches, ensuring atomic control on the Gr structure and its interfaces is extremely difficult, and avoiding possible contamination is challenging. This leads to devices with unrealistic results hindering the real potential of Gr. These non-optimized interfaces limit studying or exploring the different theories predicting spin filtering [42] or magnetic proximity effects [43, 44, 45, 46, 28, 47].

In this work, we resort to our ability to prepare epitaxial heterostructures in which a Gr single layer, ferromagnetic and heavy metallic ultra-thin layers are stacked. Such Gr-based heterostructures, deposited on insulating oxide substrates to enable transport experiments [48], are fabricated under ultra-high-vacuum (UHV) conditions and in-situ analyzed to guarantee structural atomic perfection and contaminant-free surfaces [15, 49, 13].

We demonstrate a massive enhancement of Gr-mediated spin-charge interconversion in epitaxial Ir/Fe/Gr/Pt system.

We find that the Fe/Gr/Pt system has a anisotropic charge current production with a gain of at least
17-fold compared to Gr-free Fe/Pt. We note also that this result contrasts sharply with the case of Co/Gr/Pt, where a reduction of the overall effective efficiency was previously observed using the spin Seebeck effect [48].

Based on ad-hoc first principle calculations, we demonstrate that such a different is due to the opposite effective interfacial SOC when comparing Co/Gr/Pt and Fe/Gr/Pt, which is equivalent to an effective spin Hall angle $\theta_{SHE}$ (or effective IEE length $\lambda$) of opposite sign at Co/Gr and Fe/Gr interfaces. Accordingly, our theoretical results reconcile the experimental results on Fe/Gr/Pt and Co/Gr/Pt. Remarkably, in Fe/Gr/Pt we find an overall IEE efficiency of 4.8 nm for the more effective direction, $\Gamma-M$, which is among the highest values reported so far in any system at room temperature (RT). Concurrently, we report a strong in-plane spin-charge current conversion anisotropy with an IEE efficient of 0.27 nm for the $\Gamma - K$ direction. We note that the efficiency of Pt reaches, in the same units, only 0.2 nm regardless of the experimental method used [39, 9].

## Inverse Edelstein effect at magnetic double Rashba interface

The physical mechanism driving our experimental finding is schematically illustrated in Figure 1. In panel a, we present a schematic of the unbalanced spin accumulation due to asymmetric Rashba contributions occurring at Fe/Gr and Pt/Gr interfaces. For instance, the two Rashba contours in the reciprocal space of a magnetic Rashba interface at the Fermi level are deformed by the application of a DC magnetic field along the *y*-direction. The outer contour has a counterclockwise spin polarization helicity opposite to that of the inner contour. When a spin current with a spin polarization along *y* is injected along the *z* direction, $J_{sy}^z$, the spin population is increased by $\delta s^y$. This could happen only around $+k_x$ due to the counterclockwise helical spin texture of the outer Fermi contour. On the contrary, the spin population is reduced by $-\delta s^y$ around $-k_x$ due to the spin helicity of the external contour. Consequently, the external contour is shifted $+\delta k_x$ towards $+k_x$. Since the inner contour has the opposite helical spin texture, it is shifted by $-\delta k_x'$ towards $-k_x$. This results in a net effect of spin accumulation $\delta s^y$ along $k_x$ direction as displayed in Fig. 1a. A variation of electron momentum $\delta k_x$ means that an electric or charge current is being generated laterally and transverse to the direction of injected $J_{sy}^z$. The generated charge current in this quantum system with double Rashba interface can be experimentally detected by measuring the DC spin pumping voltage in an open circuit at the magnetic resonance condition, as schematically shown in panels b and c for the Ir/Fe/Gr/Pt and Ir/Fe/Pt systems respectively.

<figure><img src="image_2.png" /><figcaption>Figure 1: Illustrations of spin-charge interconversion mechanism in a double Rashba interface detected by spin pumping experiments. (a) Schematic of the unbalanced spin accumulation due to asymmetric Rashba contributions at a magnetic interface in the reciprocal space. At the Fermi level and under a DC-applied magnetic field along *y*, the two Fermi contours, with opposite spin helicities (i.e., clockwise and contour-clockwise) are displaced due to a spin current injection. If a spin current, with spin polarization along *y*, is injected, the outer and the inner Fermi contours are shifted in the opposite directions along $k_x$ generating a net transverse charge current. (b,c) 3D view of the Gr-based heterostructure containing the double Rashba interface (Fe/Gr/Pt, panel b) and the Gr-free stack (panel c).</figcaption></figure>
## 2 Results

### Growth and structural characterization of Gr-based double Rashba interface

In order to realize atomically controlled epitaxial heterostructures in which a Gr monolayer is embedded in between a top HM and a bottom ferromagnetic (FM) layers, we have resorted to the procedure detailed in the Methods, which has been optimized from the case of Gr/Co [15, 49, 13]. In brief, for samples with Gr we first prepared a 10 nm-thick epitaxial Ir(111) buffer grown by DC sputtering on commercially available Al₂O₃(0001) single crystal substrates at 670 K, on which an epitaxial Gr monolayer was grown by ethylene chemical vapor deposition (CVD) at 1025 K under a partial pressure of 5.5 · 10⁻⁶ mbar during 30 min. The Fe film was then evaporated on top of Gr by molecular beam epitaxy (MBE) at RT in UHV and at low deposition rate. The temperature was gradually raised to less than 550 K in order to activate the Fe intercalation process while avoiding unwanted metal intermixing. Between 12 and 14 nm-thick homogeneous Fe layers with high structural order and well-defined interfaces were thus obtained (see Fig. S2 in Suppl Mat.). Concurrently, Ir/Fe samples without Gr were prepared depositing Fe by DC sputtering at RT on top of Ir. Finally, in all samples, a 5 nm-capping layer of Pt or Al was DC sputtered at RT.

To assess the structural quality and the chemical and electronic properties of the samples, we resorted to both *in-situ* Low Energy Electron Diffraction (LEED) and X-ray Photoemission Spectroscopy (XPS) and *ex-situ* High Resolution Scanning Transmission Electron Microscopy (HR-STEM) and X-ray Diffracti- on and Reflection (XRD, XRR) experiments. The former demonstrate the homogeneous and atomi- cally flat Fe layer (as well as Ir and Pt) with high structural order, well-defined interfaces and fully metal- lic states (Figure 5).

The *ex-situ* measurements further corroborate the achievement of sharp interfaces between the layers. These experiments demonstrate a high degree of structural order in all samples, with Ir atoms oriented along the [111] crystallographic direction with a face-centered structure (FCC) on top of Al₂O₃[0001], and [110] oriented base-centered cubic (BCC) Fe, as commonly observed for the Fe/Ir system with $t_{\text{Fe}} > 3$ ML [50, 51]. The structural characterizations is reported in Fig. 2 for Ir/Fe/Gr/Pt samples and for the others in Figs. S1, S2 and S3 in the Supporting Information.

A careful inspection of the Gr-based sample structure performed by acquiring XRD $\phi$-scans around [002]Ir crystallographic reflection (Fig. 2c), reveals a 60° periodicity rather than a typical 3-fold in-plane sym- metry. This is due to the presence of two in-plane configurations rotated by 180°, determining the fol- lowing crystallographic relations: $[0\bar{1}0]_{Al_2O_3} \||[\bar{1}0]_{Ir}$ and $[0\bar{1}0]_{Al_2O_3} \||[\bar{1}0]_{Ir}$.

Gr then grows axis on axis on Ir, i.e., $[0\bar{1}10]_{Al_2O_3} \||[\bar{1}0]_{Ir} \||[1\bar{1}20]_{Gr}$ and presents a characteristic 10 × 10 moiré pattern due to incommensurate lattice of Ir and Gr. [49, 13]. [50, 51].

In the $\phi$-scans acquired around the [101]Fe reflection shown in Fig. 2c, we can observe a 60° periodicity that is due to the coexistence of different in-plane configurations for the coupling between FCC Ir and BCC Fe structures as indicated in the insets, i.e., $[\bar{1}01]_{Ir} \||[001]_{Fe^{\text{BCC}}}$ (Nishiyama-Wasserman), $[\bar{1}01]_{Ir} \||[\bar{1}11]_{Fe^{\text{BCC}}}$ (left Kurdjumov-Sachs) and $[\bar{1}01]_{Ir} \||[\bar{1}11]_{Fe^{\text{BCC}}}$ (right Kurdjumov-Sachs) [52]. Fig. 2d shows the 2$\theta$-$\omega$ scans at [002]Ir and [101]Fe reflections. The maximum intensity is found at 2$\theta$=47.29(1)° and 2$\theta$=44.67(1)° for Ir and Fe respectively, which is consistent with a fully relaxed growth of both structures. To note that the asymmetric profile in the [002]Ir reflection scan is due to the presence of pseudomorphic Pt on top of Gr.

### Giant and anisotropic spin-charge current interconversion

To study and quantify the ISHE and IEE we employed the DC voltage spin-pumping ferromagnetic res- onance (SP-FMR) technique. SP-FMR measurements are performed in micrometric devices composed of the sample slab with a width of $W = 10\mu$m, an insulating 200 nm-thick SiO₂ layer separating the sample, and a coplanar waveguide (CPW) patterned on top [53, 54] as described in the Experimental Section. At the resonance condition, Fe magnetization precesses and an out-of-equilibrium spin accu- mulation occurs at the interfaces with the Fe layer, which can diffuse as a spin current in adjacent sys- tems [55]. The injected spin current is converted into charge current by the ISHE in the top Pt or bot- tom Ir layers, or by the IEE in Rashba states, if any, at the interfaces. It has been shown that Ir has the
<figure><img src="image_3.png" /><figcaption>Figure 2: **Structural characterization.** (a) High-angle annular dark field scanning transmission electron micrograph cross section of the Ir/Fe/Gr/Pt sample. The image demonstrates flat and well defined interfaces. (b) High resolution transmission electron micrographs and corresponding Fast Fourier Transform (FFT) in the Al₂O₃, Ir, Fe and Pt regions from bottom to top, respectively. FFT patterns probed [110] oriented growth of the Fe layer with BCC structure. Pt on top of graphene shows [111]-oriented epitaxial growth. (c) φ scans around Ir and Fe reflections show a 6-fold symmetry, indicating the coexistence of equivalent in plane twin boundary domains for Ir(111) as well as Nishiyama-Wassermann (NW) and Kurdjumov-Sachs (KS) configurations for FeBCC coupling with the IrFCC structure. (d) 2θ scans at [002]Ir(2θ = 47.29°) and [101]Fe(2θ = 44.67°) reflections indicate incommensurate growth of both layers, with bulk like lattice parameter. Asymmetric profile for Ir reflection is related with the presence of pseudomorphic Pt on top of Gr.</figcaption></figure>

same ISHE sign as Pt, with a much lower efficiency (of about 25% of that of Pt) [53]. Thus, the total charge current in the case of the Ir/Fe/Gr/Pt will be given by the contributions of the ISHE from top Pt [39, 53] and bottom Ir [53] (of opposite sign since at opposite side of the FM layer), and the contribution of the IEE [5, 8] due to the Rashba states.

The results of the spin pumping experiments are presented in Figure 3, in which we notice that the measured signal is due to the spin current to charge current interconversion phenomenon and that the ther-
mal contribution at FMR condition is negligible. The thermal signal in our geometry is in fact an even function with the applied DC magnetic field whereas the spin pumping signal is an odd function. To note that the raw data show an odd signal with almost the same amplitude in absolute value for positive and negative magnetic fields (see also Experimental Section 4.6) We have normalized the voltage amplitude ($V_{SP-FMR}$) by the total resistance of the slab R [53, 39] to get the total charge current produced ($I_c$).

We then have

$$ 
\begin{aligned}
I_C/W &= V_{SP-FMR}/RW \\
&= J_{s,Gr}\lambda + J_{s,Pt}\theta_{Pt}l_{sf}^{Pt} \tanh(t_{Pt}/2l_{sf}^{Pt}) - J_{s,Ir}\theta_{Ir}l_{sf}^{Ir} \tanh(t_{Ir}/2l_{sf}^{Ir}),
\end{aligned} 
\quad (1) $$

where $l_{sf}^{Pt,Ir}$ is the spin diffusion length, $\theta_{Pt,Ir}$ the effective spin Hall angle, and $t_{Pt,Ir}$ is the thickness of Pt or Ir, respectively. The effective spin current density injected at the Gr interface, $J_{s,Gr}$, is given by [53, 39]

$$ J_{s,Gr} = \frac{2e g_{\uparrow\downarrow} \gamma^2 (\mu_0 h_{rf})^2 \hbar \gamma \mu_0 M_{eff} + \sqrt{(\gamma \mu_0 M_{eff})^2 + 4\omega^2}}{8\pi\alpha^2 (\gamma \mu_0 M_{eff})^2 + 4\omega^2}, \quad (2) $$

where $e$ is the electron charge, $\gamma$ the gyromagnetic ratio, and $\omega = 2\pi f$ is the microwave pulsation. $g_{\uparrow\downarrow}$ stands for the real part of the effective spin mixing conductance.

## Giant enhancement of spin-charge conversion

The experimental results of spin-to-charge conversion are given in Figure 3a in which the charge current production $I_C$ is reported as a function of ($H - H_{res}$) for four different systems at a spin pumping frequency of $f = 22$ GHz. Here, the DC magnetic field $H$ is set along $\Gamma - M$ direction of sapphire substrate while the DC voltage is collected in the orthogonal direction, $\Gamma - K$. By looking at Fig. 3a, we first observe that Ir/Fe/Al sample has a negative signal (red line), -1.28 nA, which is consistent with $\theta_{Ir} > 0$ [53]. Since the contribution of Al is negligible as it has a weak SOC and serves only as a capping layer, the charge current is exclusively generated at the Ir/Fe interface. Once Gr is introduced between Fe and Al, i.e., in Ir/Fe/Gr/Al, the signal practically disappears, -0.15 nA (orange line). We attribute this to the Fe/Gr magnetic Rashba interface that almost completely balances the ISHE effect of Ir. We can thus conclude that $\lambda_{Fe/Gr}$ has the same sign as Ir and Pt, and its value is slightly lower than the overall efficiency of Ir, $\lambda_{Fe/Gr} \le \theta_{Ir}l_{sf}^{Ir} \approx 0.03$ nm [9, 53].

Replacing now Al by Pt, the produced charge current is positive in the reference sample Ir/Fe/Pt (black line), 0.17 nA. This is also consistent with the fact that Ir has the same sign of $\theta_{Pt}$ but is less efficient than Pt [53], so $\theta_{Ir}l_{sf}^{Ir} < \theta_{Pt}l_{sf}^{Pt} \approx 0.2$ nm [39, 9]. However, the charge current produced is greatly increased to a value of 5.74 nA (green line) when Gr is inserted. This is 34 times the charge production in Ir/Fe/Pt under the same spin pumping conditions.

This giant enhancement is consistent with the scenario that Fe/Gr contributes with a positive $\lambda$ as deduced by comparing the signals from Ir/Fe/Gr/Al and Ir/Fe/Al samples. Furthermore, the Pt layer deposited on top of Gr imprints a large SOC at the Gr interface which was not the case with Al protective coating. Thus, both Fe/Gr and Gr/Pt interfaces contribute with the same sign to the spin-to-charge conversion. Consequently, the Fe/Gr/Pt double interface is largely more efficient than Pt: $\lambda_{Fe/Gr/Pt} \gg \theta_{Pt}l_{sf}^{Pt} \approx 0.2$ nm.

Quantifying the individual contributions of each layer and interface can be a complicated puzzle. Before tackling the quantification, in the following we will discuss the anisotropic behavior of Fe/Gr/Pt.

## Anisotropic damping, $g_{\uparrow\downarrow}$, and conversion in Fe/Gr/Pt

Figure 3b shows that the charge production along the $H||\Gamma - M$, $\Delta V||\Gamma - K$ direction, 2.59 nA, is lower than the one along the $H||\Gamma - K$, $\Delta V||\Gamma - M$ direction, 5.74 nA. These measurements have been performed on slabs patterned every 30° (see Section 4.6 and Supporting Information). The observed in-plane anisotropy, which is confirmed for all measured frequencies in both damping, Fig. 3c, and charge
<figure><img src="image_4.png" /></figure>

Figure 3: **Results of spin-to-charge current conversion.** (a) Raw data of $V_{sp}$ normalized by the total resistance of the measured bar shown for 4 systems and when $H \parallel \Gamma - M$ and $\Delta V \parallel \Gamma - K$. The iridium contribution predominates in the Ir/Fe/Al trilayer. Then the signal is almost totally canceled in Ir/Fe/Gr/Al. The Pt signal predominates over Ir in Ir/Fe/Pt. The signal is strongly enhanced when Gr is sandwiched between Fe and Pt, Ir/Fe/Gr/Pt, with a 34-fold gain over Ir/Fe/Pt. In those cases, the spin pumping bar was etched along the $\Gamma - K$ or [1120] direction of the sapphire substrate. Charge current production $I_C$ (b), and bandwidth frequency dependence of the linewidth (c) along two non-equivalent in-plane directions of high symmetry for Ir/Fe/Gr/Pt. We can observe an anisotropy in amplitude and linewidth (b), i.e., a clear magnetic damping anisotropy (c). (d) f-dependence of the charge current produced according to $\Delta V$ directions in the different systems studied. Damping and charge current production are clearly different for the different directions only for Ir/Fe/Gr/Pt. This suggests an anisotropy of interconversion due to the Rashba states at Fe/Gr/Pt interfaces. The other systems have isotropic damping and charge current production. See also Suppl. Information.

current production, Fig. 3d, indicates that Gr imprints on Fe a 6-fold anisotropy, as also corroborated by the theoretical calculations shown in the next section. To note that the observed anisotropy does not appear instead in the Gr-free systems Ir/Fe/Pt and Ir/Fe/Al, as well as in the Al-capped Gr-based

To properly quantify the spin-charge conversion efficiency and determine $\lambda_{Fe/Gr/Pt}$ we reasonably assume that the conversion above the Fe layer happens at the Fe/Gr/Pt double Rashba interface, and that no spin current reaches the Pt layer, as it is also been confirmed by our theoretical results.

The strength of the microwave field on the sample at 22 GHz was experimentally determined to be $\mu_0h_{rf} = 0.055$ mT, (further details are reported in Supporting Information S14), and considering $g_{\uparrow\downarrow}^{\Gamma-K} \approx 3 \times 10^{18}$ m$^{-2}$, we have $J_s^{Ir/Fe/Gr/Pt} = 0.15$ MA/m$^2$. Thus, the total current produced in our Fe/Gr/Pt double interfaces is 7.02 nA, yielding to an overall IEE efficiency of $\lambda_{Fe/Gr/Pt}^{\Gamma-K} = 4.8 \pm 0.1$ nm for the most ef-
ficient direction (average of measurements between 5 and 23 GHz). In the other direction, considering that $g_{\uparrow\downarrow}^{\Gamma-M} \simeq 2 \times 10^{20} \text{ m}^{-2}$, we have an overall IEE efficiency $\lambda_{\text{Fe/Gr/Pt}}^{\Gamma-M} = 0.27 \pm 0.04$ nm, which is similar to the one of Pt, $\theta_{\text{Pt}} l_{\text{sf}}^{\text{Pt}} \approx 0.2$ nm.

The large anisotropic effective efficiency reported here, i.e., $\lambda_{\text{Fe/Gr/Pt}}^{\Gamma-K}/\lambda_{\text{Fe/Gr/Pt}}^{\Gamma-M} \approx 18$, might be due either to the Rashba coupling parameter, $\alpha_R$, or to the relaxation times $\tau$, both linked to the SOC of the system, $\lambda = \alpha_R\tau/\hbar$ [5]. Theoretical modeling might shed light if $\alpha_R$ or $\tau$ dominates the experimentally measured anisotropy.

Note that it is not possible to simply use a reference damping $\alpha_0$ to obtain $g_{\uparrow\downarrow}$ due to the anisotropy. Instead, a dependence on the Fe-thickness should be performed. However, this is beyond the scope of the present study, which it will tackled later on. In any case, the effective values of $g_{\uparrow\downarrow}$ used are conservative. For example, we see that even in the less efficient direction, the charge-current production, $I_C=2.59$ nA, is clearly larger than Ir/Fe/Pt, 0.15 nA. This RT giant efficiency is comparable with the result for the $\alpha$-Sn topological insulator, $\lambda_{\alpha-Sn} = 2$ nm [8].

Furthermore, the great advantage of our new system is that it is robust for the fabrication of micro and nanodevices. Our spin pumping measurements were performed entirely on-chip, which remains difficult to achieve in $\alpha$-Sn deposited on a fragile substrate like InSb or a little toxic like CdTe.

## First principles analysis of the spin-charge interconversion

To explain our experimental results, we have performed first principles calculations of two trilayers, Fe(4 ML)/Gr/Pt(6 ML) and Co(4 ML)/Gr/Pt(6 ML), following the procedure described in the Methods. The density of states (DOS) projected on each layer is reported in Figs. 4(a1-a4). We show the contributions of the majority (a1, a3) and minority spin populations (a2, a4) for Fe/Gr/Pt (a1, a3) and Co/Gr/Pt (a2, a4). Whereas the projected DOS for the majority spins is similar for the two systems, the DOS of the minority spins of Fe at the Fermi level (a3) is larger than that of Co (a4). Concomitantly, the minority spins of Gr have a reduced DOS in proximity with Co compared to Fe. This difference is reflected in the magnitude of the spin moment induced on the Gr monolayer, which amounts to -1 $\mu_B$ in Fe/Gr/Pt and -0.6 $\mu_B$ in Co/Gr/Pt (see Table 1 the Methods), manifesting a substantially different hybridization scheme. Most remarkably, the SOC induced on Gr by proximity to the transition metals is strikingly different in the two systems, as displayed in Fig. 4b for Fe/Gr/Pt (b1) and Co/Gr/Pt (b2). We find a clear inversion of the sign of the induced SOC: near the Fermi level, $\langle \mathbf{l} \cdot \mathbf{s} \rangle > 0$ in Fe/Gr/Pt, whereas $\langle \mathbf{l} \cdot \mathbf{s} \rangle < 0$ in Co/Gr/Pt.

To assess how this sign reversal influences the overall spin-charge interconversion process, we compute the direct Edelstein effect, i.e., the electrical generation of non-equilibrium spin density. Based on Onsager reciprocity, the IEE is directly proportional to the direct Edelstein effect [56]. In fact, such a proportionality relation between both direct and reciprocal effects takes the simple form of $\eta_{s-c}/\eta_{c-s} = \mu_B\sigma_C/\chi_s$, where $\eta_{c-s}$ and $\eta_{s-c}$ are the direct and inverse Edelstein coefficients, being $\sigma_C$ and $\chi_s$ the conductivity and spin susceptibility respectively. Such an effect i.e., the conversion from spin dynamics into an electric current, under the adiabatic regime, was recently studied theoretically [57]. The procedure to reach this conclusion is thoroughly explained in the Supplemental information. The current-driven spin density is computed within the linear response formalism considering the symmetrized decomposition of the Kubo-Bastin formula [58]. In the present situation, we applied an electric field along $\hat{x}$ and computed the components of the spin operators along $\hat{y}$. The results are reported in S15 (Supporting Information) where is depicted the layer projection of the spin accumulation calculated at Fermi level, showing at the same time the sign reversal of the direct Edelstein effect in Gr, consistent with the sign reversal of the SOC reported in Fig. 4b. In order to quantify the direct Edelstein effect we have calculated the Rashba-Edelstein tensor as a function of the chemical potential shown in Fig. 4c. We note that the presence of Gr enhances the response, particularly in the case of Fe/Gr/Pt. In contrast, the value of the tensor reaches similar values with and without Gr when Co is the ferromagnet.

The enhancement of the response in the presence of Gr reported in Fig. 4 offers an appealing scenario to explain the differences observed experimentally in the spin-to-charge conversion taking place in Fe/Gr/Pt
<figure><img src="image_5.png" /><figcaption>Figure 4: **Theoretical calculation.** (a) Sketch of the Gr layer showing the carbon atoms' positions. First-principles calculation of projected DOS for minority (a1, a2) and majority (a3, a4) spin populations. The left (a1, a3) and right panels (a2, a4) correspond to Fe/Gr/Pt and Co/Gr/Pt, respectively. Although the spin quantum number is strictly non-conserved in this case, we consider the diagonal parts of the full DOS which are two orders of magnitude larger than the off-diagonal contributions. (b) Spin-orbit coupling projected on Gr for Fe/Gr/Pt (b1) and Co/Gr/Pt (b2). The enhanced SOC of Gr, induced by the proximate transition metals, changes sign when changing Fe for Co, which indicates a change in the sign of the spin-to-charge conversion in these heterostructures. This is confirmed by calculating explicitly the Rashba-Edelstein tensor projected on the Pt layer next to the interface. (c) Electrically-driven effect calculated for heterostructures (Fe,Co)/Gr/Pt for blue and green curves, (Fe,Co)/Pt in orange and red curves. The inset shows the values for the Rashba-Edelstein tensor calculated at the Fermi level.</figcaption></figure>

compared to Co/Gr/Pt systems, both grown onto Ir. At the same time, our calculations show that the longitudinal conductivity increases when Gr is placed in-between the FM and Pt. This result suggests that as the proximity effect on Gr leads to an increase of its SOC, there is also an effect on Pt (see Supporting Information), therefore enhancing the spin-to-charge conversion in the full system. It's worthy to mention that an estimation of the Rashba parameter or even the size of spin splitting in graphene is challenging in this case. In contrast to what is found for the isolated Dirac cone modified by proximity effects either by a transition metal dichalcogenides (TMD) [44] or transition metals [59], in our case the band structure is highly intricate, precluding a fitting procedure. Clearly, the presence of Rashba-like spin-momentum locking introduces an anisotropic D'yakonov-Perel spin relaxation, which is known to affect the dynamics of the in-plane and out-of-plane spin components [60]. These mechanisms will affect the efficiency of the spin-charge conversion but since the magnetization precesses in the plane of the layers, the D'yakonov-Perel spin relaxation should not be dramatically different along the Γ–M and Γ–K directions. Nonetheless, the spin-dependent momentum scattering should be affected substantially due to proximity with graphene. Qualitatively, one would expect a shorter momentum scattering time along the Γ–K direction than along the Γ–M direction, thereby modifying the spin-charge conversion efficiency. Such an effect should enhance the difference of spin signal along these two directions. A detailed analysis would be necessary to provide a solid estimate of the influence of anisotropic momentum scattering.

Due to numerical constraints, our calculations were limited to a small supercell containing only 4 ML
of Co or Fe and 6 ML of Pt, which is much smaller than the real system that exceeds 10 nm of active materials. Therefore, our calculations do not fully account for the contribution of the ISHE from both Pt and Ir, but provide a strong indication of the major role played by the interfacial SOC induced on Gr. As discussed above, in the experiments the total spin-charge conversion arises from the additive con- tributions of the ISHE of Ir and Pt, as well as the IEE at the double Rashba interface, (Fe,Co)/Gr/Pt. Qualitatively, by using either Co or Fe as the spin injector, the interfacial IEE either counters or boosts the ISHE from Ir and Pt, resulting in the giant enhancement reported experimentally in Fe/Gr/Pt. Bes- sides, the large anisotropy in the spin-charge conversion we experimentally demonstrate in Fig. 3b can be understood by the strong anisotropy of Gr band structure. Indeed, Fig. 4b clearly shows that close to Fermi level, the spin-orbit coupled Gr states are concentrated around the *K* and *K'* points, and ab- sent along the Γ–*M* high symmetry line. As a result, the double Rashba interface is mostly active along Γ–*K*. Furthermore, our calculations of the spin texture along the high-symmetry line *M*′−Γ−*M* (see Supporting Information) display a behavior consistent with a Rashba effect on both sides, namely on the Pt and FM regions. In addition, when considering different directions of the magnetization *M*, that is, whether it is pointing along Γ−*M* or Γ−*K*, our simulations reveal an anisotropy, that is particularly large in the case where Gr is considered (see Supporting Information).

## 3 Conclusion

We have experimentally demonstrated a dramatic enhancement of the spin-charge conversion efficiency by exploiting epitaxial Gr monolayer to create a double Rashba interface, namely Fe/Gr/Pt. Specifi- cally, we found at RT an efficiency of $\lambda_{Fe/Gr/Pt}^{\Gamma-K} \approx 4.8$ nm that is two order of magnitude larger than what Pt displays. In addition, we experimentally provide evidence of a strong in-plane anisotropy of the spin-charge conversion, that is $\lambda_{Fe/Gr/Pt}^{\Gamma-K}/\lambda_{Fe/Gr/Pt}^{\Gamma-M} \approx 18$, which highlights the crucial role of the crys- talline texture of the materials composing the interfaces and of the derived electronic structures. Our spin-pumping experiments have been accompanied by ad-hoc first principle calculations which allow us to assess the IEE contribution at the double Rashba interface, and to demonstrate that the strong in- plane anisotropy of the spin-charge conversion derives from the strong anisotropy of the interfacial SOC imprinted into the Gr band structure, making the double Rashba interface mostly active along Γ−*K*. The Gr-based systems are also very robust against the micro and nano fabrication processes, which is generally challenging for 2D materials.

The high conductivity of Gr compared to other 2D materials, together with the induced high spin con- version is a promising feature for the realization of low-power applications. Furthermore, the anisotropy of the interconversion could enable tailored efficiency, opening its use for logic applications and uncon- ventional computing.

# 4 Experimental Section

## 4.1 Sample growth

The samples incorporating Gr (i.e., Gr/Pt or Gr/Al) and those without Gr (i.e., Pt or Al) were all fab- ricated in-situ on epitaxial Ir(111)/Fe(110) grown on sapphire crystals under controlled conditions, en- suring similar structural quality and clean interfaces. The methodology described in [15, 49] was fol- lowed. To begin, a 10 nm thick epitaxial Ir(111) layer was deposited on Al₂O₃(0001) single crystal sub- strates via DC-sputtering at 670 K with a partial Ar pressure of 8 · 10⁻³ mbar and a low deposition rate (0.3Å/s). Subsequently, for the Gr-based heterostructures, a monolayer of Gr was prepared by chemi- cal vapor deposition through ethylene dissociation at 1025 K under a partial pressure of 5.5 · 10⁻⁶ mbar. Then, Fe was deposited at RT using molecular beam epitaxy. The intercalation of Fe below Gr was facil- itated by a thermal annealing process at 550 K. This procedure leads to the formation of a homogeneous Fe layer with high structural order and well-defined interfaces, similarly to the case of Co intercalation[15, 49]. For samples without Gr, a 7 nm-thick Fe layer was deposited via DC sputtering at RT directly onto
the Ir(111) buffer. Finally, in all samples, a 5 nm capping layer of Pt or Al was DC sputtered at RT. We present in the extended Fig. 5 the schematic detail of the growth of our new heterostructure together with in-situ and ex-situ characterizations.

## 4.2 Device fabrication

The devices dedicated to spin pumping measurements were fabricated utilizing conventional UV lithography. The complete stack was patterned and then ion milled until reaching the substrate, controlled by an ion mass spectrometer employing a 4-wave IBE14L01-FA system. Subsequently, a second lithography step was done to grow a 200 nm insulating SiO₂ layer using RF sputtering via an Si target and Ar⁺ and O²⁻ plasma in a Kenositec KS400HR PVD. In a third step, contacts were then patterned and evaporated using an evaporator PLASSYS MEB400S. The dimensions of the active bar for spin pumping devices were 10 × 600 µm. The uniformity of device geometry, including SiO₂ thickness, coplanar waveguide dimensions and lateral dimensions of the milled samples, was maintained consistently across all the devices for a reliable comparison of SP-FMR voltages.

<figure><img src="image_6.png" /><figcaption>Figure 5: **Fe intercalation in epitaxial Graphene/Ir grown on Al₂O₃(0001).** In top panels, we show the sketch of the UHV fabrication processes. First, 10 nm thick epitaxial Ir(111) is deposited on Al₂O₃ (0001) single crystal substrate via DC-sputtering at 670 K with a partial Ar pressure of 8 × 10⁻³ mbar, using a deposition rate of 0.3 A/s. Subsequently, a monolayer of Gr is prepared by chemical vapor deposition (CVD) through ethylene dissociation at 1025 K under a partial pressure of 5.5 × 10⁻⁶ mbar. Then, Fe is deposited at RT using molecular beam epitaxy (MBE). The intercalation of Fe below Gr is promoted by a gentle thermal annealing process at 550 K. This procedure leads to the formation of a homogeneous Fe layer with high structural order, well-defined interfaces and fully metallic states. This is demonstrated by the corresponding LEED patterns and X-ray Photoemission Spectroscopy (XPS) measurements around the Ir 4f, Fe 2p and C 1s peaks, which have been acquired in-situ at each stage of the growth and are shown in the middle and bottom-most panels respectively. Samples without Gr, a the Fe layer has been deposited either by MBE or DC sputtering onto the Ir(111) buffer. Finally, in all samples, a 5 nm capping layer of Pt or Al was DC sputtered at RT.</figcaption></figure>

## 4.3 Structural characterization

The systematic structural characterization of the samples by x-ray diffraction was performed using a commercial Rigaku SmartLab SE multipurpose x-ray diffractometer, equipped with a non-monochromatic Cu Kα source (λ=1.54 Å). More details of our results are shown in section S1 of the supplementary information file.
Transmission electron microscopy (TEM) analysis was conducted using a JEM-ARM 200F Cold Field Emission Gun TEM/STEM (Scanning TEM) operating at 200 kV. The microscope is equipped with a GIF Quantum 965 ER and features a spherical aberration probe and image correctors, providing a point resolution of 0.12 nm in TEM mode and 0.078 nm in STEM mode. High-resolution TEM (HR-TEM) imaging was employed to investigate the atomic structure of the deposited layers. Furthermore, systematic energy dispersive spectroscopy (EDS) mapping analyses were systematically performed on the various samples.

## 4.4 Spin pumping measurements

We performed experiments to measure SP-FMR using a probe station equipped with an in-plane DC magnetic field (H) up to 0.6 T generated by an electromagnet. The schematic diagram of the SP-FMR devices used in these experiments is depicted in the inset of Fig. 3a. During the SP-FMR measurements, a fixed RF frequency current (f) in the GHz range is injected into the coplanar waveguide in the device, generating an RF magnetic field ($h_{RF}$) on the sample. We sweep the DC external magnetic field and, when the system reaches the resonance condition, the magnetization of Fe precesses and leads to the generation of a spin current injected from Fe into the attached systems (Ir, Pt, Gr/Al, or Gr/Pt). Microscopically, the spin current injected into the adjacent layers comes from the spin precession and scattering of electrons at the interfaces, making this technique perfect for studying the spin current injection in our epitaxial Gr-based asymmetric stack. This spin current is subsequently converted into a charge current by ISHE in Ir or Pt, or by IEE at Rashba interfaces. In a open circuit, we measured the voltage ($V_{SP}$) by modulating the RF power injected into the coplanar waveguide using a lock-in synchronized to this modulation while sweeping the external H. The power modulation employed a sine function with a depth of 100% and a modulation frequency of 433 Hz. The resulting SP voltage peak exhibits a characteristic Lorentzian curve symmetric around the resonance field ($H_{res}$) when the system reaches the resonance condition, as illustrated in Fig. 3a. This curve was analyzed for different frequencies to determine the effective magnetization ($M_{eff}$) and the Gilbert damping ($\alpha$) of the ferromagnetic layer. More specifically, the center ($H_{res}$) and width ($\Delta H$) of the Lorentzian peak in $V_{SP}$ were analyzed by fitting the voltage to a sum of a symmetric and an antisymmetric Lorentzian function [53, 54]. Notably, in the SP measurements, the antisymmetric part of the signal was negligible, and only the symmetric part was considered in the fit. To calculate $M_{eff}$, the Kittel formula for an in-plane easy axis was employed (see e.g. [54] for more details). Additionally, the damping was determined by considering the linear dependence of $\Delta H$ with frequency, where the Gilbert damping ($\alpha$) provided the slope, and the intercept, $\Delta H_0$, represented the frequency-independent inhomogeneous contribution [54]. Raw data of measurements on our different systems, as well as $M_{eff}$ and damping determinations are shown in Supplementary Information.

## 4.5 Isotropic damping and $I_C$ on Ir/Fe/Al and Ir/Fe/Pt

In our Gr-free samples, we observe isotropic damping and charge current production (raw data and more details in Supplemental information). This is consistent with the isotropic result reported for the magnetic damping and spin-charge interconversion in epitaxial [001]MgO||[001]Fe|MgO, and [001]MgO||[001]Fe|[001]MgO [61]. Although spin-charge interconversion is anisotropic for [220]Pt along two no-equivalent in-plane directions [62], it is isotropic for the [111]Pt in the thin-film growth direction as our case, Fig. 2a. Indeed, Gudin et al. [63] have shown that interconversion is isotropic along two no-equivalent in-planes directions for [111]Pt. In our Ir/Fe/Gr/Al sample, it is more complicated to detect whether there is an anisotropy due to the large linewidth and very low voltage or current signal.

## 4.6 Robustness and reproducibility

We have measured the DC spin pumping voltage in several devices within a 5x5 mm² block, and the results show a similar signal for slabs patterning along $\Gamma-M$ (0, and 60 degrees) and $\Gamma-K$ (30 and 90 degrees) configurations as shown in the extended Fig. 6. We have tested about four devices for each crys-
tallographic direction. As reported in Supporting Information, the experimental curves practically over-
lap for devices along the same crystallographic direction. Figure S17 shows the spin pumping results for
four devices oriented in two directions of the Ir/Fe/Gr/Pt system at 22 GHz. We can see in Fig. 6 that
for Ir/Fe/Al there is practically no anisotropy, both, in amplitude and linewidth, for the 4 directions of
high symmetries showed. In contrast, we confirmed that the results are totally different for Ir/Fe/Gr/Pt.
Here, the signal is similar for 0° and 60° which are equivalent directions in a hexagonal symmetry but
different for 30° and 90°. This implies that Gr/Pt imprints a strong SOC on the Fe layer (interface) that
enforces the hexagonal symmetry of Gr. This is another confirmation of the result in Fig. 3d. Thus, it
is plausible to consider that the SOC increases in Fe, in agreement with the theoretical results where it
is seen that the first Fe layer shows an increase of SOC due to the presence of Gr/Pt. In addition, com-
paring the jump to zero field, off-resonance, we will have another independent confirmation of our previ-
ous statement. This jump is observed in the Ir/Fe/Gr/Pt sample and not in the Ir/Fe/Al sample. The
anomalous Nernst effect (ANE) and the spin Seebeck effect (SSE) have the same symmetry. But such a
jump is not observed in Ir/Fe/Al. Consequently, such off-resonance jump is dominated by the spin See-
beck effect and its respective conversion of spin current into charge current and not by the ANE.

The spin pumping devices maintain their performance over time, tested up to more than two years af-
ter the initial measurements. This confirms on the one hand the robustness of the systems studied, in
particular the samples with intercalated graphene, and on the other hand the reproducibility of our mea-
surements. The signal measured even two years later shows the same amplitude and linewidth with a
dispersion of less than 2% for the very same devices. This also shows the reproducibility and reliabil-
ity of the RF field strength value, *h*<sub>rf</sub>, due to the microwave injected into the coplanar guide antenna
in our experimental setup. Each sample has its integrated antenna, as everything is on-chip, but the ge-
ometry and the materials (Ti, Au, and SiO<sub>2</sub>) used to establish such an antenna are the same for all the
devices thus allowing a "direct" comparison of the charge current production in the different systems for
the same RF conditions, *i.e*, frequency and power injected in the antenna.
<figure><img src="image_7.png" /><figcaption>Figure 6: **Symmetry of spin pumping measurements.** (a) Raw data of charge current production by spin pumping at 22 GHz measured in slabs patterned every 30 degree following the directions of high symmetry according to the monocrys-talline [0001]Al₂O₃ sapphire substrate as shown in the inset. We can see that Ir/Fe/Al does not exhibit anisotropy while Ir/Fe/Fe/Pt shows a repetition each 60 degrees in agreement with the hexagonal symmetry of Gr. Consequently, Gr/Pt imprints a SOC at the interface with Fe magnetic layer that dominates over the magnetocrystalline anisotropy of [110]Fe BCC. Comparing the jump to zero field off-resonance, we can conclude that it is dominated by the spin Seebeck effect (SSE). The anomalous Nernst effect (ANE) has the same symmetry as the SSE but such a jump is practically not present in the Ir/Fe/Al sample. This is another independent confirmation that Gr/Pt imprints a strong SOC on the Fe layer (at the interface).</figcaption></figure>

## 4.7 Theoretical procedure

**Realistic material simulations** - To compute the electronic and spin properties of the heterostructures, we consider trilayers having in total eleven layers, that is, four ferromagnetic layers coming from bcc Iron or HCP Co, one Gr monolayer, and six Pt layers. Due to the lattice mismatch between the three materials, we have used a 2 × 2 Gr and Fe/Co supercell along with a √3 × √3 Pt supercell having a total of 42 atoms in the unit cell. We determined the band structure and spin textures by employing fully relativistic density functional theory [64] within the On-site approximation to account for relativistic effects [65] introduced by fully relativistic pseudo-potentials along with the generalized gradient approximation (GGA) for the exchange-correlation functional [66]. The calculations are converged for a 400 Ry plane-wave cutoff using the real-space grid with a (13 × 13 × 1) ⃗k-points sampling of the Brillouin zone. We used the conjugate gradient algorithm to minimize the atomic forces below 0.01 eV/Å.

The transport properties were calculated by a homemade procedure after extracting the Hamiltonian matrices from the self-consistent *ab initio* ground state. By using SISL as a post-processing, the velocity and spin projection matrices were obtained to perform the out-of-equilibrium simulations.

**Kubo-Bastin formula** - The current-driven field is computed within the linear response formalism consid-
<table><caption>Table 1: Table showing the spin moment for each carbon atom in the Gr layer.</caption><thead><tr><th>Carbon atom</th><th>Fe</th><th>Co</th></tr></thead><tbody><tr><td>C<sub>1</sub></td><td>-0.016</td><td>-0.094</td></tr><tr><td>C<sub>2</sub></td><td>-0.114</td><td>-0.095</td></tr><tr><td>C<sub>3</sub></td><td>-0.009</td><td>-0.093</td></tr><tr><td>C<sub>4</sub></td><td>-0.127</td><td>-0.092</td></tr><tr><td>C<sub>5</sub></td><td>-0.018</td><td>0.023</td></tr><tr><td>C<sub>6</sub></td><td>-0.013</td><td>0.022</td></tr><tr><td>C<sub>7</sub></td><td>-0.127</td><td>0.018</td></tr><tr><td>C<sub>8</sub></td><td>-0.542</td><td>-0.294</td></tr></tbody></table>

ering the symmetrized decomposition of the Kubo-Bastin formula [58] which has the form:

$$h_{sy}^{Ext} = -\frac{e\hbar}{8\pi} \int \partial_{\epsilon} f(\epsilon) d\epsilon \text{Re} \left[ \text{Tr} \left\{ \hat{v}_{x}(G^{R-A}) \hat{s}_{y}(G^{R-A}) \right\} \right] \quad (3)$$

and

$$h_{sy}^{Int} = -\frac{e\hbar}{4\pi} \int f(\epsilon) d\epsilon \text{Re} \left[ \text{Tr} \left\{ \hat{v}_{x}(G^{R-A}) \hat{s}_{y}(\partial_{\epsilon} G^{R+A}) \right\} \right], \quad (4)$$

where $\hat{v}_x = \partial_{k_x} \mathcal{H}$ is the velocity operator in the direction of the applied electric field $\hat{x}$, $\hat{s}_y$ is the spin matrix along $\hat{y}$ and $f(\epsilon)$ is the equilibrium Fermi distribution function. The function $G^{R(A)}$ is the retarded (advanced) Green function and $G^{R-A} = G^R - G^A$. The set of equations Eq. 3 and Eq. 4 describe the extrinsic and intrinsic contributions to Spin-Orbit Torque. Analogously, the Rashba-Edelstein tensor is calculated using

$$\Lambda_{xy} = \frac{\sum_{n, \mathbf{k}} \langle \hat{s}^y \rangle_{n, \mathbf{k}} \langle \hat{v}^x \rangle_{n, \mathbf{k}} (\partial f_{n, \mathbf{k}} / \partial E_{n, \mathbf{k}})}{\sum_{n, \mathbf{k}} \langle \hat{v}^x \rangle_{n, \mathbf{k}} (\partial f_{n, \mathbf{k}} / \partial E_{n, \mathbf{k}})} \quad (5)$$

## Supporting Information

Supporting Information is available from the Wiley Online Library or from the author.

## Acknowledgements

This work was funded by the French National Research Agency (ANR) through the ‘Toptronic’ ANR JCJC project, grant ANR-19-CE24-0016 and by the project “Lorraine Université d’Excellence” reference ANR-15-IDEX-04-LUE. It was also partially supported by ANR CONTRABAS project, grant ANR-20-CE24-0023, by ANR through the France 2030 government grants EMCOM (ANR-22-PEEL-0009), PEPR SPIN ANR-22-EXSP-0007 and ANR-22-EXSP-0009. We also acknowledge the support from EU-H2020-RISE project Ultra Thin Magneto Thermal Sensoring ULTIMATE-I (Grant ID. 101007825), and ERC CoG project MAGNETALLIEN grant ID 101086807. A.P. was supported by the ANR ORION project, grant ANR-20-CE30-0022-01, A. M. by the Excellence Initiative of Aix-Marseille Université-A*Midex, a French "Investissements d'Avenir" program. Devices in the present study were patterned at Institut Jean Lamour's clean room facilities (MiNaLor). These facilities are partially funded by FEDER and the Grand Est region through the RANGE project. HRTEM characterization was performed at Institut Jean Lamour's microscope CC-3M facilities. IMDEA team acknowledges support from the Spanish AEI CNS2022-136143 (SPINCODE), PID2021-122980OB-C52 (ECLIPSE-ECOSON) and the "Severo Ochoa" Programme for Centres of Excellence in R&D (CEX2020-001039-S). We also acknowledge support from the Comunidad de Madrid through projects TEC-2024/TEC-380 "Mag4TIC" and "(MAD2D-CM)-UAM". A.A. acknowledges the project 3D-Sky (GAP-101108063), part of the Marie Skłodowska-Curie Actions from the Horizon Europe Program of the EU.
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Giant and anisotropic enhancement of spin-charge
conversion in graphene-based quantum system

Alberto Anadon¹*, Armando Pezo², Iciar Arnay³,
Rubén Guerrero³, Adrián Gudín³, Alba Guio³,
Melissa Yactayo¹,⁴, Jaafar Ghanbaja¹, Julio Camarero³,
Aurelien Manchon², Sebastien Petit-Watelot¹, Paolo Perna³*,
Juan-Carlos Rojas-Sánchez¹*

¹Université de Lorraine, CNRS, IJL, F-54000 Nancy, France.

²Aix-Marseille Université, CNRS, CINaM, Marseille, France.

³IMDEA Nanoscience, C/ Faraday 9, Campus de Cantoblanco, 28049 Madrid, Spain.

⁴Facultad de Ciencias Físicas, Universidad Nacional Mayor de San Marcos, Lima 14, Perú.

*Corresponding author(s). E-mail(s): anadonb@unizar.es; paolo.perna@imdea.org; juan-carlos.rojas-sanchez@univ-lorraine.fr;

**Supporting Information**

S.1 Additional structural characterization and
thickness determination by X-ray reflectivity

Figure S.1 shows out of plane θ/2θ scans for reference(Ir/Fe/Pt) and main (Ir/Fe/-Gr/Pt) systems as well as for control samples (Ir/Fe/Al and Ir/Fe/Gr/Al). XRD characterization proves Ir growth along the [111] and Fe along the [110] direction in all cases. Nevertheless, intercalation process in graphene samples favors a more textured growth of the Fe layer, as indicated by a significantly larger diffracted intensity. Apparition of Kiessig fringes around diffraction peaks confirms flat interfaces at the long range as locally confirmed by STEM. Figure S.2 shows HRTEM characterization in the Ir/Fe/Pt sample.
Figure S.3 show the results of the XRR characterization and the determined thicknesses of each layer as well as the roughness at different interfaces. XRR fitting show lower roughness values for samples with graphene regardless of the top layer (Pt or Al), which is related to the layer by layer growth induced by thermal intercalation process. We see that the Ir/Fe/Al sample has a markedly lower Fe layer thickness than the other samples. This, however, does not affect the analysis and conclusions. The charge current produced, $I_C$, being normalized by the total resistivity of the sample, takes into account these differences. On the other hand, we see a small dispersion of the iridium thicknesses. This also does not affect the analysis and conclusions. The thickness of Ir in all the samples is much larger than its spin diffusion length, 1.3 nm, so the charge current produced reaches a saturation plateau from Ir/Fe. Recall that Inverse Spin Hall Effect spin pumping obeys a $\tanh(t_{Ir}/2l_{sf}^{Ir})$ relationship.

<figure><img src="image_8.png" /><figcaption>**Fig. S.1 XRD characterization in Ir/Fe/X stacks.** Out of plane $\theta/2\theta$ XRD measurements for Fe samples with different top interfaces. Textured growth of $Fe_{BCC}$ on the [110]-direction is observed for the four samples. Fe films intercalated underneath graphene show a higher degree of crystallinity with significance larger diffracted intensity. Presence of Kiessig fringes around diffraction reflections confirm flat interfaces at the long range as indicated by STEM.</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>Fig. S.2 HR-TEM characterization in Ir/Fe/Pt. High resolution transmission electron micrograph and corresponding Fast Fourier Transform (FFT) in the Al₂O₃ Ir and Fe regions respectively. FFT patterns probed [110] oriented growth of the Fe layer with BCC structure, similarly to the ones observed in the Gr/Pt samples.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. S.3 XRR results on Ir/Fe/X stacks. X-ray reflectivity a) Ir/Fe/Pt and Ir/Fe/Gr/Pt and b) Ir/Fe/Al and Ir/Fe/Gr/Al along with the results of their respective analyses where we know the thickness of different layers as well as the roughness at different interfaces.</figcaption></figure>
S.2 Study of the magnetization reversal processes
and magnetic anisotropy of the films

The study of the magnetization reversal processes and magnetic anisotropy of the films
is performed by measuring the angular dependence of the in-plane vectorial-resolved
magnetooptical Kerr effect (MOKE) as depicted in Fig.

<figure><img src="image_11.png" /></figure>

Fig. S.4 Study of the magnetization reversal processes and magnetic anisotropy of the films by MOKE. The study of the magnetization reversal processes and magnetic anisotropy of the films is performed at RT by measuring the in-plane vectorial-resolved magneto-optical Kerr effect (MOKE) hysteresis loops as a function of the in-plane angular rotation αH for the whole angular range with step of 4.5°, keeping fixed the external magnetic field direction. αH = 0° refers to the [1110] in-plane crystallographic direction of the Al₂O₃ substrate, as indicated in panel c. The sketch of the MOKE setup in longitudinal geometry is shown in panel a. We used p-polarized light (with 635 nm wavelength) focused on the sample surface and analyzed the Kerr rotation. The representative hysteresis loop acquired at αH = 0° is presented in panel b, in which we normalized the magnetization M to the saturation Msat value. By extracting the value of the magnetization remanence Mrem (i.e., at zero field) from the M vs. H loops at any angle, we construct the angular behavior of the Mrem normalized to the saturation value (Msat) displaying a clear isotropic behavior. This indicates the absence of any preferential direction for the magnetization
S.3 Crystallographic orientations of spin pumping
devices

As described in the main text, the samples were grown on a single crystal sapphire
substrate according to the perpendicular orientation [0001]. In-plane symmetry for
the sapphire, Ir FCC as well as Gr, and Pt layers is then hexagonal. The relationship
we describe is according to the substrate directions which have a notch at each cor-
ner according to the Γ − K direction, which in our devices corresponds to $H\parallel[100]$.
The perpendicular direction is Γ − M and in our devices corresponds to the $H\parallel[010]$
direction. Therefore, and according to the epitaxial relations found for Ir and Gr lay-
ers, Γ-K and Γ-M directions are aligned to the [1100]$_{Gr}$ and [11\bar{2}0]$_{Gr}$ crystallographic
directions, respectively. The DC spin pumping voltage, as highlighted, is measured
in the direction perpendicular to the direction of the applied DC magnetic field. All
devices were etched at different orientations on the same chip. Figure S.5 shows a
schematic of the orientations of the substrate and spin pumping devices.

<figure><img src="image_12.png" /><figcaption>**Fig. S.5 Crystallographic orientations of spin pumping devices. (a,b)** Our commercial single crystal sapphire [0001] substrates (@ Surfacenet) were always arranged in the same way for lithography. On a 10 × 10 cm² chip, we can pattern several devices for different experiments, including spin pumping. The $H\parallel100$ orientation in our devices corresponds to $H||[-1100]||\Gamma - K$ as shown in the Figure. Since the voltage is measured orthogonal to that direction, the charge current production is measured along $\Gamma - M$. On the same chip, we have the devices along different crystallographic orientations as shown in (c) for the case $H\parallel010$. The yellow block represents the Ti/Au that forms the coplanar waveguide antenna, and the $V^+$, $V^-$ parts are the electrodes for measuring the spin pumping voltage. The sample, a 10 µm wide bar, is underneath the 200 nm $SiO_2$ which is represented by the blue color.</figcaption></figure>
## S.4 Raw spin pumping DC voltage data on Ir/Fe/Al

The function to fit the spin pumping voltage is as follows:

$$V_{\text{dc}} = V_{\text{S}} \frac{\Delta H^2}{(H - H_r)^2 + \Delta H^2} + V_{\text{A}} \frac{\Delta H(H - H_r)}{(H - H_r)^2 + \Delta H^2} + V_{\text{offset}}, \quad (\text{S.1})$$

where $H_r$ is the resonance field and $\Delta H$ is the linewidth (half width at half maximum). $V_S$ and $V_A$ stand for the amplitudes of the symmetric and antisymmetric components of $V_{\text{dc}}$, respectively. We can see that in our raw data, the signals are symmetric, i.e. $V_A \sim 0$. That guarantees that our symmetrical signal is purely due to the spin pumping effect and conversion of spin current into charge current. Independently, verified in other systems such as NiFe/Pt and NiFe/Ta.

The raw data for the different systems are shown in the following figures. Some curves for the $H \parallel 100$ direction (right panel) are noisy, due to the displacement of the GSG (Grounded-Signal-Grounded) contacts in our RF setup. This does not alter the parameters to be obtained from the resonance field ($M_{\text{eff}}$), and linewidth (damping). For a comparison of the amplitudes between the different directions and samples, we have considered strictly measurements under the same conditions.

<figure><img src="image_13.png" /><figcaption>Fig. S.6 Raw data of spin pumping voltage on Ir/Fe/Al. Spin pumping voltage in devices where the external DC magnetic field is applied along the direction 010 (left) and 100 (right) corresponding to the directions of the sapphire substrate $\Gamma - M$ and $\Gamma - K$, respectively. In (b) are also shown the Lorenztian fittings as described in the text. The frequency range is as specified on the respective panels every 1 GHz. The resistance of the spin pumping slab in each device is also indicated.</figcaption></figure>

## S.5 Raw spin pumping DC voltage data on Ir/Fe/Pt
<figure><img src="image_14.png" /><figcaption>Fig. S.7 Raw data of spin pumping voltage on Ir/Fe/Pt. Spin pumping voltage in devices where the external DC magnetic field is applied along the direction 010 (left) and 100 (right) corresponding to the directions of the sapphire substrate $\Gamma - M$ and $\Gamma - K$, respectively. The frequency range is as specified, and every 1 GHz in the left panel. The resistance of the spin pumping slab in each device is also indicated.</figcaption></figure>

## S.6 Raw spin pumping DC voltage data on Ir/Fe/Gr/Al

<figure><img src="image_15.png" /><figcaption>Fig. S.8 Raw data of spin pumping voltage on Ir/Fe/Gr/Al. Spin pumping voltage in devices where the external DC magnetic field is applied along the direction 010 (left) and 100 (right) corresponding to the directions of the sapphire substrate $\Gamma - M$ and $\Gamma - K$, respectively. In the right panel are also shown the Lorenztian fittings as described in the text. The frequency range is as specified on the respective panels every 1 GHz. The resistance of the spin pumping slab in each device is also indicated.</figcaption></figure>

## S.7 Raw spin pumping DC voltage data on Ir/Fe/Gr/Pt
<figure><img src="image_16.png" /><figcaption>**Fig. S.9 Raw data of spin pumping voltage on Ir/Fe/Gr/Pt.** Spin pumping voltage in devices where the external DC magnetic field is applied along the direction 010 (left) and 100 (right) corresponding to the directions of the sapphire substrate $\Gamma-M$ and $\Gamma-K$, respectively. The frequency range is as specified, and every 1 GHz. The resistance of the spin pumping slab in each device is also indicated.</figcaption></figure>

## S.8 Effective magnetic saturation $M_{eff}$

The effective magnetic saturation is shown in Fig. for three of the systems studied. The fit was performed using Kittel in-plane law considering a uniaxial in-plane anisotropy too. The $H_{uni}$ and $M_{eff}$ parameters were shared to be the same in each branch of the measurements, $H > 0$ and $H < 0$. If left unrestricted, the fitted values were also quite close.

<figure><img src="image_17.png" /><figcaption>**Fig. S.10 Effective magnetic saturation $M_{eff}$.** The Effective magnetic saturation $M_{eff}$ determination is shown for three different systems. The directions always correspond to the sapphire as previously described.</figcaption></figure>
S.9 Magnetic damping constant α

The magnetic damping constant determination is shown for the different systems stud-
ied in the attached figure. The directions always correspond concerning the sapphire
as previously described. There are data for H > 0 and for H < 0. We see that in
the Ir/Fe/Al system, it seems that the damping is slightly different along the two
no-equivalent directions, but the error bar does not allow us to discern this. If the
adjustment is made at low-frequency ranges, both directions have the same slope. If
the fit considers only f > 15 GHz, the slopes are also the same, but with a different
ΔH₀. The independent fit in each direction is shown for this Ir/Fe/Al system. In the
Ir/Fe/Pt sample there is no damping anisotropy, however, its value is relatively high.
In the Ir/Fe/Gr/Al sample, the width is quite large; the data are scattered. As seen in
the Vsp raw data, as the signal intensity or height is low, the noise level increases. In
the main sample, we unambiguously observe a damping anisotropy beyond the error
bar. This is also shown in the main text. Together with the damping anisotropy, its
values are lower than in the Ir/Fe/Pt and Ir/Fe/Gr/Al cases. That is, here the Gr has
served to improve the quality of the sample as a whole as well.

<figure><img src="image_18.png" /><figcaption>**Fig. S.11 Magnetic damping constant α.** The magnetic damping constant estimation is shown for the different systems studied. The directions always correspond to the sapphire as previously described. We see that in the Ir/Fe/Pt system there is no damping anisotropy, however, its value is relatively high.</figcaption></figure>
## S.10 Ir/Fe/Al isotropic spin-charge current conversion

We show here that, in addition to damping, the spin pumping voltage and charge current production are also isotropic. A complete sweep of the raw data of the voltage normalized by the resistance of each spin pumping bar patterned each 30° as a function of the applied DC magnetic field is also shown in Extended Figure A. We can observe there that, within the experimental accuracy, the spin-pumping FMR peaks are similar.

<figure><img src="image_19.png" /><figcaption>Fig. S.12 Ir/Fe/Al isotropic spin-charge current conversion. (a) Amplitude of DC spin pumping voltage as a function of frequency. (b) f-dependence production of charge current. Two different orientations are displayed where "-" stands for $H < 0$, and "+" for $H > 0$.</figcaption></figure>

## S.11 Ir/Fe/Pt isotropic spin-charge current conversion

Previously it was shown that the damping is isotropic in the two crystallographic directions studied. In this section, we show that, in addition to the damping, the spin pumping voltage, and the current (slightly modified by the resistance of each device) are similar. That is, they are also isotropic as expected. We also show the raw data of the current production at 16 GHz.
<figure><img src="image_20.png" /><figcaption>Fig. S.13 Ir/Fe/Pt spin-charge current conversion. (a) Amplitude of DC spin pumping voltage as a function of frequency. (b) f-dependence production of charge current. The different orientations are displayed. For the case $H < 0$ the negative is presented for a better comparison. Beyond the noise level, it is difficult to conclude that there is anisotropy. In the measurements on the device with $H||100$ the RF contact GSG spikes were slightly shifted, especially between 17 and 20 GHz.</figcaption></figure>

<figure><img src="image_21.png" /><figcaption>Fig. S.14 Ir/Fe/Pt isotropic spin-charge current conversion. Production of charge current for different slabs patterned every 30 degrees. The different orientations are displayed in the inset according to the substrate directions. We can observe that all the signals have the same amplitude, linewidth, and resonance field.</figcaption></figure>

## S.12 Ir/Fe/Gr/Al isotropic spin-charge current conversion

We show in this section the amplitude of the pumping spin voltage as a function of frequency. Also the charge current production vs f. We see that in the two non-equivalent crystallographic directions studied, we have the same results, or the noise level does not allow us to discern anymore. This would indicate that the charge production is isotropic in-plane in this system.
<figure><img src="image_22.png" /><figcaption>Fig. S15 Ir/Fe/Gr/Al spin-charge current conversion. (a) Amplitude of DC spin pumping voltage as a function of frequency. (b) f-dependence of charge current.</figcaption></figure>

<figure><img src="image_23.png" /><figcaption>Fig. S16 Ir/Fe/Gr/Al isotropic spin-charge current conversion. Production of charge current for different slabs patterned every 30 degrees. The different orientations are displayed in the inset according to the substrate directions. We can observe that all the signals have similar amplitude and linewidth, but slightly different resonance fields for 0° and 60°, 0.307 T, than for 30° and 90°, 0.287 T. The 60° device has a higher contribution to the zero-field jump (orange curve). This could be due to some lithography defect or that the device is closer to the edge of the substrate. However, the spin pumping signal has similar amplitude and linewidth as in the other equivalent direction.</figcaption></figure>

## S.13 Reproducibility of spin-charge current conversion along different devices

We obtained very similar results (practically, the raw data overlap) across devices. In addition to the above measurements shown for devices in the different samples, Fig. S6-S9, and for different devices in the same sample, Ir/Fe/Pt (Fig. S14) or Ir/Fe/Gr/Al (Fig. S16), for different crystallographic directions, here we show another example of the high reproducibility of our results. Fig. S17 shows the result of 4 devices measured along two crystallographic directions for Ir/Fe/Gr/Pt.
<figure><img src="image_24.png" /><figcaption>Fig. S17 (a) Raw voltage data measured on 4 devices, along two non-equivalent directions. Two were measured along the most efficient direction, $V \parallel \Gamma - K$, and the other two along the $V \parallel \Gamma - M$ direction. (b) Charge current produced (= $V_{sp}/R$), the width of our devices is 10 µm. The 2D charge current produced will be this value divided by 10 µm. (c) Results of the data fitting. We see that the central values are quite close, and the result of the fit yields: $5.90 \pm 0.01$ nA ($V \parallel \Gamma - K$), and $3.0 \pm 0.1$ nA ($V \parallel \Gamma - M$)</figcaption></figure>

## S.14 $h_{rf}$ experimental determination at a given GHz frequency

A critical parameter to enable quantification of the efficiency of spin current to charge current conversion by spin pumping is the strength of the $h_{rf}$ radio frequency field. We have developed a protocol to experimentally determine that parameter in our spin-pumping devices. For that, we need a set of additional measurements. Namely, the dependence on a DC bias current to modulate the voltage amplitude which is due to the combination of the spin pumping effect and magnetoresistance (MR) of the sample, $\frac{dV}{di_{dc}}$. In addition, the amplitude of the in-plane anisotropic MR variation, $\Delta R_{AMR}$. The expression for calculating $h_{rf}$ reads as follows:

$$h_{rf} = \sqrt{2\alpha} (2H_r + M_{eff}) \sqrt{\frac{dV}{di_{dc}} \frac{1}{\Delta R_{AMR}}} \sqrt{\frac{H_r}{H_r + M_{eff}}}, \quad (S.2)$$

This parameter depends on the experimental setup, it changes its performance with frequency due to RF impedance mismatches and losses in RF cables, contacts, and other elements. Therefore, an experimental determination of $h_{rf}$ on the sample at each frequency is necessary. We have carried out such a determination at different microwave frequencies to quantify the conversion of spin current to charge current. We have calibrated this $h_{rf}$ parameter in different samples and even with different SiO$_2$ thicknesses. The main measurements have been made before and after such calibrations and are quite reproducible (even after a couple of years). This indicates the repeatability of our experimental setup. As well as the geometry of the antennas etched on the same chip on a given thickness of SiO$_2$ separating the spin pumping bar we want to measure. In other words, the SiO$_2$ and Ti/Au thicknesses of the antennas are very similar and reproducible in the different lithographed samples. An example of such an experimental determination is shown in Fig. S18 for 16 GHz. It is obtained in this case for a //py(6)/AlOx sample with 95 nm of SiO$_2$ thickness separating the py/Al slab from the GSG antenna. It yields $h_{rf} = 0.53$ G for an equivalent 200 nm SiO$_2$ thickness.
<figure><img src="image_25.png" /><figcaption>Fig. S.18 Experimental determination of $h_{rf}$ at 16 GHz on /py(6)/AlOx spin pumping device. (a) raw data at 16 GHz of rectified DC voltage sweeps measured as a function of the DC magnetic field applied perpendicular to the spin pumping bar for different bias currents. The applied bias currents vary between 2.5 mA and -2.5 mA. The signal is due to the planar Hall effect (PHE) and anisotropic magnetoresistance (AMR) in a single permalloy. We can see that the voltage peaks at the resonance condition increase or decrease as a function of the signs of the applied bias current and DC magnetic field. There is no signal for low current values. This results from a combination of the dynamic effects on magnetization due to spin pumping and AMR. (b) Bias current dependence of the amplitudes of the measured voltages in (b) for $H > 0$, and $H < 0$. The offset or value at $i_{dc} = 0$ is the pure spin pumping voltage. The slope yields $R_{slope} = \frac{dV}{di_{dc}}$ and allows us to experimentally determine $h_{rf}$ according to equation S(2). (c) Resistance as a function of the applied DC magnetic field parallel (black circles - upper curve) and perpendicular (red circles - lower curve) to the spin pumping bar. This allows us to obtain $\Delta R_{AMR}$ as indicated.</figcaption></figure>

## S.15 Complement for theoretical calculation

For the numerical simulations we use state-of-the-art Density Field Theory (DFT) simulations based on SIESTA [1]. To calculate the transport properties, we first obtained the lowest energy configuration by minimizing the energy with respect to horizontal and vertical graphene relative displacements as depicted in Fig. S.19, where we confirm that the configuration chosen for performing the linear response simulations corresponds to the ground state. We've found that Gr acquires a magnetic moment due to its proximity with Fe (Co). Our results are in good agreement with previous simulations performed for Gr in metallic and magnetic environments [2, 3]. The full system electronic ground state is encoded in its Hamiltonian. Once the Hamiltonian
in momentum space is obtained by interfacing the DFT output with SISL [4] we were able to calculate a Fermi surface cut shown in Fig. S.20 (a) Fe/Pt and (b) Fe/Gr/Pt trilayers, by using

$$FS(E_F, \mathbf{k}) = \sum_n 2\left[ \frac{\langle \psi_n | \hat{O}_{Gr} | \psi_n \rangle}{1 + \cosh((E_F - E_{n,\mathbf{k}})/k_B T)} \right], \quad (S.3)$$

where $\hat{O}_{Gr}$ project the electronic wavefunction $|\psi_n\rangle$ on the Gr sheet. We note that the presence of Gr leads to an enhancement in the hexagonal symmetry of the system, furthermore, due to the exchanged field acting on Gr, we highlight brighter regions posing a three-fold symmetry, which is a clear signature of the anisotropy probed in the spin-to-charge conversion measurements.

<figure><img src="image_26.png" /><figcaption>Fig. S.19 Energy differences between stacking configurations displaced both vertically and horizontally.</figcaption></figure>
<figure><img src="image_27.png" /><figcaption>Fig. S.20 Fermi surface for Fe/Pt (a) and Fe/Gr/Pt (b) heterostructures. The highlighted regions in dashed circles correspond to spin polarized graphene states due to the proximity effect with Fe.</figcaption></figure>

In the same manner, by using

$$ \langle \hat{\mathbf{S}}_{Gr} \rangle_n = \langle \psi_n | \hat{\mathbf{S}}_{Gr} | \psi_n \rangle, $$

where the Spin matrices are projected again on the Gr layer, we calculated the spin texture projected on the Gr states. In Fig. S.21 (a) and (b) we show the in-plane spin texture for Fe and Co-based heterostructures respectively, while the colorbar displays the z component. Analogously, in Fig. S.22, we projected the spin texture on the Fe layer near to the interface without (a) and with Gr, our calculations, in agreement with previous results [5], demonstrate how the proximity effect on the Gr side also imprints the hexagonal symmetry on the FM side.
<figure><img src="image_28.png" /><figcaption>Fig. S.21 Spin texture projected on the graphene layer for Fe/Gr/Pt (a) and Co/Gr/Pt (b) heterostructures. The shape and sign of the z component reflect the qualitative differences between Fe and Co-based heterostructures, this corroborates the change in sign of the SOC projected in the band structure shown in Fig. 4.</figcaption></figure>

<figure><img src="image_29.png" /><figcaption>Fig. S.22 Spin texture projected on the nearest Fe layer to Gr for Fe/Pt (a) and Fe/-Gr/Pt (b) heterostructures. This result shows how the presence of Gr modifies the spin texture in Fe, imprinting its hexagonal symmetry leading to the 6-fold symmetry reported experimentally.</figcaption></figure>

To demonstrate the difference between different paths in the spin-to-charge conversion, by using the same expression written in the main text
<figure><img src="image_30.png" /><figcaption>Fig. S.23 Rashba-Edelstein tensor $\Gamma_{xy}$ calculated along $\Gamma-K$ and $\Gamma-M$ high symmetry lines projected on the neighbour Pt layer next to graphene.</figcaption></figure>

$$ \Lambda_{xy}^{\mathbf{k}} = \frac{\langle \hat{s}^y \rangle_{n, \mathbf{k}} \langle \hat{v}^x \rangle_{n, \mathbf{k}} (\partial f_{n, \mathbf{k}} / \partial E_{n, \mathbf{k}})}{\langle \hat{v}^x \rangle_{n, \mathbf{k}} (\partial f_{n, \mathbf{k}} / \partial E_{n, \mathbf{k}})}, \qquad (S.4) $$

we calculated the Rashba-Edelstein tensor [6] along both $\Gamma-K$ and $\Gamma-M$ high symmetry lines. Finally, the out-of-equilibrium spin accumulations are calculated for all the considered structures shown in the main text. We performed the calculations considering both intrinsic and extrinsic calculations following

$$ h_{s_y}^{\text{Ext}} = -\frac{e\hbar}{8\pi} \int \partial_{\epsilon} f(\epsilon) d\epsilon \text{Re} \left[ \text{Tr} \left\{ \hat{v}_x(G^{\text{R-A}}) \hat{s}_y(G^{\text{R-A}}) \right\} \right] \qquad (S.5) $$

and

$$ h_{s_y}^{\text{Int}} = -\frac{e\hbar}{4\pi} \int f(\epsilon) d\epsilon \text{Re} \left[ \text{Tr} \left\{ \hat{v}_x(G^{\text{R-A}}) \hat{s}_y(\partial_{\epsilon} G^{\text{R+A}}) \right\} \right], \qquad (S.6) $$

where $\hat{v}_x = \partial_{k_x} \mathcal{H}$ is the velocity operator along $\hat{x}$, $\hat{s}_y$ is the spin matrix $\hat{y}$ and $f(\epsilon)$ is the equilibrium Fermi distribution function. The function $G^{\text{R(A)}}$ is the retarded (advanced) Green function and $G^{\text{R-A}} = G^{\text{R}} - G^{\text{A}}$.

For the results shown in Figures S.24,S.25,S.27, the plots show the layer resolved spin accumulation calculated at the Fermi level set to 0.0 eV. This is extended for other values of the chemical potential in the extrinsic response Figs. S.24,S.25, where the variations on displayed are in agreement with the calculation shown for the Rashba-Edelstein tensor in the main text. On the other hand, the effect of having Fe or Co as the ferromagnet in the heterostructure is shown in Fig. S.26, where we show the
extrinsic contribution of the spin accumulation projected on the Gr layer. This is in
agreement with the SOC projected on the band structure depicted in the Fig. 4 in the
main text.

In order to clarify the role of Gr in our system we have calculated the longitudinal
conductivity projected on the layers. From the experimental standpoint, we expect
a dominant metallic contribution from the Ir, Fe, and Pt layers, which could screen
possible anisotropic conductivity. From our simulations, we obtain an enhancement
of the local conductivity on the graphene monolayer S.28. Such a modification also
leads to a Rashba-like texture observed on the FM side, as it is depicted in Fig. S.30,
where we have calculated the spin texture component $s_y$ along the high-symmetry line
$-M-G-M$ for Co/Gr/Pt Fig. S.30 (a) and Fe/Gr/Pt Fig. S.30 (b). Similarly, we
have obtained a Rashba-like texture on the Pt side Fig. S.29 in both cases when the
FM is Co Fig. S.29(a) or Fe Fig. S.29(b). From our results on the spin-charge conver-
sion, this takes place mostly on the Pt side, due to the strong Rashba effect at the
Gr/Pt interface. Therefore, the enhanced spin-charge interconversion is most likely
attributed to the enhanced interfacial IEE effect rather than the enhanced conduc-
tivity. To complement our observations, we extended our analysis of the anisotropy
by considering different directions for the magnetization M, as depicted in Fig. S.32
(with Gr) and Fig. S.31 (without Gr). Indeed, our results for the spin component
$s_z$ projected on the band structure provide additional information regarding the spin
dynamics in our setup. As the spin-orbit field behaves as an effective magnetic field
in momentum space, quasiparticles will experience an additional spin precession and
dephasing as they propagate within the sample. In Fe/Gr/Pt, as depicted in Fig. S.32,
we see that modulating the direction of the magnetization either along G-M (a) or
G-K (b), although hardly changing the energy spectrum, strongly impacts the spin
texture component $s_z$. Notice the large value of the spin projection obtained on the
color scale.
<figure><img src="image_31.png" /><figcaption>Fig. S.24 Layer resolved extrinsic effective field ($h_y^{Ext}$) for Fe/Gr/Pt (a) and Fe/Pt (b) heterostructure.</figcaption></figure>
<figure><img src="image_32.png" /></figure>

<figure><img src="image_33.png" /><figcaption>Fig. S.25 Layer resolved extrinsic effective field ($h_y^{Ext}$) for Co/Gr/Pt (a) and Co/Pt (b) heterostructure.</figcaption></figure>
<figure><img src="image_34.png" /><figcaption>Fig. S.26 Sign reversal for the spin accumulation in Gr when it's located either between Fe/Pt (black) or Co/Pt (red) curves respectively. The inset shows a sketch of both interfaces.</figcaption></figure>
<figure><img src="image_35.png" /><figcaption>Fig. S.27 Layer resolved intrinsic effective field ($h_y^{Int}$) for Fe(Co)/Gr/Pt orange (blue) (a) and Fe(Co)/Pt orange (blue) respectively.</figcaption></figure>
<figure><img src="image_36.png" /><figcaption>Fig. S.28 Layer resolved longitudinal conductivity for Fe/Gr/Pt (red) and Fe/Pt (green) bilayers, we note a clear enhancement of the response as Gr is placed in the middle, at the same time, the Pt layer next to graphene also displays a larger value compared to the case where Gr is absent.</figcaption></figure>
<figure><img src="image_37.png" /><figcaption>Fig. S.29 Band structure of (a) Co/Gr/Pt and (b) Fe/Gr/Pt trilayers projected on the spin component *s* and on the first layer of Pt adjacent to the graphene monolayer. The dashed box indicates the region close to the Fermi level. The dashed region reveals a different behaviour around the Fermi level in both cases, which might be related to the difference in the signals obtained experimentally.</figcaption></figure>

<figure><img src="image_38.png" /><figcaption>Fig. S.30 Band structure of (a) Co/Gr/Pt and (b) Fe/Gr/Pt trilayers projected on the spin component *s* and on the first layer of the ferromagnet [Co (a) or Fe (b)] adjacent to the graphene monolayer.</figcaption></figure>
<figure><img src="image_39.png" /><figcaption>Fig. S.31 $s_z$ component of the spin texture projected of the band structure of Fe/Pt when the magnetization is posting along G-M (a) and G-K (b). The absence of graphene in this case draws a completely different picture.</figcaption></figure>
<figure><img src="image_40.png" /><figcaption>Fig. S.32 s_z component of the spin texture projected of the band structure of Fe/Gr/Pt heterobilayer when the magnetization is posting along G-M (a) and G-K (b). We clearly note the different strength around the K point around which, as we have demonstrated, the Dirac electrons coming from graphene, are the main contributors for the overall effect.</figcaption></figure>

### S.15.1 Relation between the inverse and direct Edelstein effect

In this part, we provide a clear relation between the inverse and direct Edelstein effect. In the direct Edelstein effect, an applied electric field induces a nonequilibrium spin density, $\mathbf{S} = \chi\hat{z} \times \mathbf{E}$, then reciprocally we argue that a d.c. current is linear in the nonequilibrium spin density, $\mathbf{j}_{dc} = \eta\hat{z} \times \mathbf{S}$, where these two coefficients $\eta$ and $\chi$, which represent the spin-galvanic and inverse spin-galvanic effect, are connected via Onsager reciprocity. Below we elaborate on this argument.

The inverse Edelstein effect (generation of a charge current by a nonequilibrium spin density) and the direct Edelstein effect (generation of a spin density by a charge current) read

$$ \mathbf{j}_c = \eta_{s-c} \hat{z} \times \mathbf{S} $$

$$ \mathbf{S} = \eta_{c-s} \hat{z} \times \mathbf{j}_c $$

These two coefficients, $\eta_{s-c}$ and $\eta_{c-s}$ are both independent of the momentum scattering and only involve Fermi electrons (purely intraband transport phenomena). The direct Edelstein effect, $\eta_{c-s}$, can be readily computed using Kubo formula, considering the perturbative interaction $\hat{H}_{Int} = -e\mathbf{E} \cdot \hat{\mathbf{r}} = -e\mathbf{A} \cdot \hat{\mathbf{v}}$, where $\mathbf{E} = -\partial_t \mathbf{A}$,

$$ \mathbf{S} = -\frac{e\hbar}{4\pi} \int \partial_{\epsilon} f_{\epsilon} d\epsilon \text{Re Tr} \left\{ \sigma(G_{0}^{R} - G_{0}^{A}) \mathbf{v}(G_{0}^{R} - G_{0}^{A}) \right\} \mathbf{E} $$

$$ \mathbf{j}_c = \frac{e^2 \hbar}{4\pi} \int \partial_{\epsilon} f_{\epsilon} d\epsilon \text{Re Tr} \left\{ \mathbf{v}(G_0^R - G_0^A) \mathbf{v}(G_0^R - G_0^A) \right\} \mathbf{E} $$
The first expression is the direct Edelstein effect and the second one is the conductivity. In other words,

$$ \eta_{c-s} = - \frac{\int \partial_{\epsilon} f_{\epsilon} d\epsilon \operatorname{Re} \operatorname{Tr} \left\{ \sigma(G_{0}^{R} - G_{0}^{A}) \mathbf{v}(G_{0}^{R} - G_{0}^{A}) \right\}}{e \int \partial_{\epsilon} f_{\epsilon} d\epsilon \operatorname{Re} \operatorname{Tr} \left\{ \mathbf{v}(G_{0}^{R} - G_{0}^{A}) \mathbf{v}(G_{0}^{R} - G_{0}^{A}) \right\}} \quad (S.7) $$

The inverse Edelstein effect $\eta_{s-c}$ can be obtained by considering the response of the system to the perturbative interaction $\hat{H}_{Int} = +\mu_B \sigma \cdot \mathbf{B}$. In this case, the current and spin density induced by a time-varying magnetic field reads

$$ \mathbf{S} = -\frac{\mu_B \hbar}{4\pi} \int \partial_{\epsilon} f_{\epsilon} d\epsilon \operatorname{Re} \operatorname{Tr} \left\{ \sigma(G_0^R - G_0^A) \sigma(G_0^R - G_0^A) \right\} \partial_t \mathbf{B} \\ \hat{j}_c = -\frac{\mu_B e \hbar}{4\pi} \int \partial_{\epsilon} f_{\epsilon} d\epsilon \operatorname{Re} \operatorname{Tr} \left\{ \mathbf{v}(G_0^R - G_0^A) \sigma(G_0^R - G_0^A) \right\} \partial_t \mathbf{B}. $$

The first expression is the susceptibility of Fermi electrons and the second is the inverse Edelstein effect. In other words,

$$ \eta_{s-c} = - \frac{e \int \partial_{\epsilon} f_{\epsilon} d\epsilon \operatorname{Re} \operatorname{Tr} \left\{ \mathbf{v}(G_{0}^{R} - G_{0}^{A}) \sigma(G_{0}^{R} - G_{0}^{A}) \right\}}{e \int \partial_{\epsilon} f_{\epsilon} d\epsilon \operatorname{Re} \operatorname{Tr} \left\{ \sigma(G_{0}^{R} - G_{0}^{A}) \sigma(G_{0}^{R} - G_{0}^{A}) \right\}} \quad (S.8) $$

The conductivity and the spin susceptibility read

$$ \sigma_c = \frac{e\hbar}{4\pi} \int \partial_{\epsilon} f_{\epsilon} d\epsilon \operatorname{Re} \operatorname{Tr} \left\{ \mathbf{v}(G_0^R - G_0^A) \mathbf{v}(G_0^R - G_0^A) \right\} \\ \chi_s = \frac{\mu_B \hbar}{4\pi} \int \partial_{\epsilon} f_{\epsilon} d\epsilon \operatorname{Re} \operatorname{Tr} \left\{ \sigma(G_0^R - G_0^A) \sigma(G_0^R - G_0^A) \right\} $$

Therefore,

$$ \eta_{s-c} = \frac{\mu_B \sigma_c}{\chi_s} \eta_{c-s} $$

One can see that the direct Edelstein effect and the inverse Edelstein effect are simply proportional to each other. As a result, computing the direct Edelstein effect provides a reasonably good estimate of the spin-charge interconversion. Notice that this approach does not model the way the nonequilibrium spin density $\mathbf{S}$ is generated. In this sense, when the spin pumping takes place, the electrons affected are at the Fermi level and the conversion of the magnetization dynamics into a nonequilibrium spin density is governed by the interfacial spin transparency that is modified by the presence or absence of the graphene monolayer. This spin transparency is accounted for in the data analysis by considering the spin-charge interconversion length rather than the bare voltage, as discussed in the main text of our manuscript.
## S.16 Thermal contribution to the spin pumping voltage

In figures S.6 to S.9, a full-range curve of the spin pumping voltage is shown for the different stacks. We observed a voltage jump at low field when the magnetization reverses, which corresponds to the thermovoltages in the system, including the anomalous Nernst and the spin Seebeck contributions. In all cases except for Ir/Fe/gr/Al, this jump is smaller than the SP peak.

To further confirm that thermal effects can be neglected in our experiments, we approximate the precession angle of the magnetization as follows:

$$ \Theta_c = (h_{rf})/(\Delta H) \qquad (S.9) $$

We have calculated $h_{rf}$ for our devices as shown in the supp info S.14, and for all the cases, the precession angle is in the order of tenths of a degree in our measurements. Therefore, since the magnetization is not rotating significantly, the signal coming from the thermovoltages is much smaller than the SP peak and we can safely conclude that the voltage contribution from thermal effects is negligible. Additionally, while is true that the sample will absorb part of the microwave power in the resonance condition, there are two arguments that make us believe that the main contribution to thermospin voltages in resonance does not come from this absorption thermal contributions. First, the magnetic volume in the device is very small, and thus absorption is also small. Furthermore, the heat absorbed in the FM in resonance occurs in the whole layer similarly and thus the thermal gradient generated by this absorption is irrelevant out of plane and symmetrical in plane in our devices, making the resulting voltage negligible. Second, the absorbed power in the sample is much smaller than the total power injected in the CPW, and thus the out-of-plane thermal gradient generated in the CPW is more significant than any thermal gradient that could be generated inside the FM.

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