Protyush Sahu

Yifei Yang

Yihong Fan

Henri Jaffrès

Jun-Yang Chen

Xavier Devaux

Yannick Fagot- Revurat

Sylvie Migot

Enzo Rongione

Tongxin Chen

Pambiang Abel Dainone

Jean-Marie George

Sukhdeep Dhillon

Martin Micica

Yuan Lu
email: yuan.lu@univ-lorraine.fr

Jian-Ping Wang
email: ⁑jpwang@umn.edu

Room Temperature Spin to Charge Conversion in Amorphous Topological Insulating Gd-Alloyed BixSe1-x/CoFeB Bilayers

Keywords: Spin to charge conversion, Topological insulator, Amorphous, Spin pumping, THz time-domain spectroscopy

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Room Temperature Spin-to-Charge Conversion in

Amorphous Topological Insulating Gd-Alloyed BixSe1-x/CoFeB Bilayers Protyush Sahu, Yifei Yang, Yihong Fan, Henri Jaffrès, Jun-Yang Chen, Xavier Devaux, Yannick Fagot-Revurat, Sylvie Migot, Enzo Rongione, Tongxin Chen, et al.

To cite this version:

Introduction

Bismuth selenide (Bi2Se3) based topologic insulator (TI) materials have recently received significant attention in the field of condensed matter physics due to their exotic transport properties. Recent interests have garnered from the fact that these materials can exhibit topologically protected surface states 1,2,3,4,5 protected by time reversal symmetry, making them extremely important for various spintronic applications. 6,7,8,9 Many works have demonstrated efficient spin-to-charge interconversion in TI thin films with the aim of magnetization manipulation. [START_REF] Ndiaye | Dirac Spin-Orbit Torques and Charge Pumping at the Surface of Topological Insulators[END_REF][START_REF] Ortiz | Generic Helical Edge States due to Rashba Spin-Orbit Coupling in a Topological Insulator[END_REF][START_REF] Yu | Photoinduced Inverse Spin Hall Effect of Surface States in the Topological Insulator Bi2Se3[END_REF][START_REF] Khang | A Conductive Topological Insulator with Large Spin Hall Effect for Ultralow Power Spin-Orbit Torque Switching[END_REF][START_REF] Men'shov | Intrinsic Spin Hall Conductivity in Three-Dimensional Topological Insulator/Normal Insulator Heterostructures[END_REF] However, the film growth still remains a major bottleneck since molecular beam epitaxy (MBE) is usually required to grow highly lattice ordered films on the appropriate substrate. [START_REF] Krumrain | Growth Optimization of Topological Insulator Bi2Te3 Films[END_REF][START_REF] Liu | Growth and Characterization of MBE-Grown (Bi1-xSbx)2Se3 Topological Insulator[END_REF][START_REF] Huang | Proximity Effect Induced Transport Properties between MBE grown (Bi1-xSbx)2Se3 Topological Insulators and Magnetic Insulator CoFe2O4[END_REF] Recently, the presence of strong spin-orbit coupling (SOC) in sputtered polycrystalline BixSe1-x have been demonstrated. [START_REF] Sahu | Weak Antilocalization and Low-temperature Characterization of Sputtered Polycrystalline Bismuth Selenide[END_REF][START_REF] Dc | Room-temperature High Spin-Orbit Torque due to Quantum Confinement in Sputtered BixSe1-x Films[END_REF][START_REF] Ramaswamy | Spin Orbit Torque Driven Magnetization Switching with Sputtered Bi2Se3 Spin Current Source[END_REF][START_REF] Dc | Observation of High Spin-to-Charge Conversion by Sputtered Bismuth Selenide Thin Films at Room Temperature[END_REF][START_REF] Dc | Roomtemperature Spin-to-Charge Conversion in Sputtered Bismuth Selenide Thin Films via Spin Pumping from Yttrium Iron Garnet[END_REF] Quantum transport simulations suggest that the high SOC in sputtered BixSe1-x is due to the quantum confinement effect with an enhanced charge-to-spin conversion efficiency by reduced size and dimensionality, [START_REF] Dc | Room-temperature High Spin-Orbit Torque due to Quantum Confinement in Sputtered BixSe1-x Films[END_REF] which is different from the typical heavy metal/ferromagnetic bilayer system. These discoveries reveal novel physics in disordered TI materials and shed light on the potential for developing industrial applications. The absence of a well-defined crystal lattice in disordered TI makes them less susceptible to scattering and other perturbations, potentially leading to improved performance in the presence of impurities or imperfections compared to the crystalline TI.

In most of TIs with ordered crystallographic structures, the spin-charge conversion (SCC) is a result of the inverse Edelstein effect (IEE) by the TI surface states. [START_REF] Soumyanarayanan | Emergent Phenomena Induced by Spin-Orbit Coupling at Surfaces and Interfaces[END_REF][START_REF] Das | Discovery of Highly Spin-Polarized Conducting Surface States in the Strong Spin-Orbit Coupling Semiconductor Sb2Se3[END_REF] For highly disordered TI films, there are two possibilities for the SCC. Firstly, studies have shown that the bulk of TI with low bulk resistivity may play an important role for the SCC by conventional inverse spin Hall effect (ISHE). [START_REF] Jamali | Giant Spin Pumping and Inverse Spin Hall Effect in the Presence of Surface and Bulk Spin-Orbit Coupling of Topological Insulator Bi2Se3[END_REF][START_REF] Gao | Emergence of Tunnelling Spin-Orbit Torques at Magneticmetal/Semimetal Heterojunctions[END_REF] Secondly, theoretical analyses have also shown the possibility of the existence of conducting surface states in amorphous TI films. 27 , 28 , 29 , 30 , 31 , 32 , 33 Spin-orbit torque effects have been observed in different amorphous materials experimentally since 2019. [START_REF] Fan | Spin Pumping and Large Field-Like Torque at Room Temperature in Sputtered Amorphous WTe2-x Films[END_REF][START_REF] Fan | Observation of Unidirectional Spin Hall Magnetoresistance in Amorphous PtSn4/CoFeB Bilayers[END_REF][START_REF] Peterson | Large Field Like Torque in Amorphous Ru2Sn3 Originated from the Intrinsic Spin Hall Effect[END_REF][START_REF] Sahu | Room Temperature Mott hopping and High Charge to Spin Conversion in Amorphous Gd-alloyed BixSe1-x: A Candidate for Amorphous Topological Insulator[END_REF] Recently, Corbae et al. have evidenced the TI surface states in amorphous BixSe1-x film by angle-resolved photoemission spectroscopy (ARPES). [START_REF] Corbae | Observation of Spin-Momentum Locked Surface States in Amorphous Bi2Se3[END_REF] Costa et al. also presented an experimental study of the electronic and transport properties of amorphous bismuthene systems, [START_REF] Costa | Toward Realistic Amorphous Topological Insulators[END_REF] showing that these materials may present topological properties. Moreover, the effects of various dopants in TIs have also been extensively studied. One important advantage of doping is that by embedding atoms with magnetic moment inside the alloys, one can create magnetic topological insulators with time reversal symmetry breaking to observe the quantum anomalous Hall effect (QAHE). [START_REF] Chang | Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator[END_REF][START_REF] Harrison | Study of Ho-doped Bi2Te3 Topological Insulator Thin Films[END_REF] Incorporating such impurities in TI materials could also introduce highly disordered or even amorphous structures. Therefore, it will be of great interest to explore the role of amorphous TI surface states on the spin-to-charge conversion efficiency for developing scalable spintronic devices.

To study SCC, transport techniques, such as spin-torque ferromagnetic resonance (ST-FMR) [START_REF] Mellnik | Spin-Transfer Torque Generated by a Topological Insulator[END_REF][START_REF] Wang | Topological Surface States Originated Spin-Orbit Torques in Bi2Se3[END_REF][START_REF] Wang | Room Temperature Magnetization Switching in Topological Insulator-Ferromagnet Heterostructures by Spin-Orbit Torques[END_REF][START_REF] Lv | Electric-Field Control of Spin-Orbit Torques in WS2/Permalloy Bilayers[END_REF][START_REF] Kondou | Fermi-Level-Dependent Charge-to-Spin Current Conversion by Dirac Surface States of Topological Insulators[END_REF] and spin pumping (SP) combined with the inverse spin-Hall effect, 47 ,48 , 49 are often used to measure the conversion efficiency between the charge current and the spin current or spin accumulation in ferromagnetic/non-magnetic (FM/NM) bilayer heterostructures. On the other hand, besides transport techniques, terahertz time-domain spectroscopy (THz-TDS) has also recently emerged as a powerful tool to study the interplay between charge and spin degrees of freedom by all-optical means. [START_REF] Kampfrath | Terahertz Spin Current Pulses Controlled by Magnetic Heterostructures[END_REF][START_REF] Cheng | Studying Spin-Charge Conversion using Terahertz Pulses[END_REF][START_REF] Wang | Ultrafast Spin-to-Charge Conversion at the Surface of Topological Insulator Thin Films[END_REF][START_REF] Dang | Ultrafast Spin-Currents and Charge Conversion at 3d-5d Interfaces Probed by Time-Domain Terahertz Spectroscopy[END_REF] The observed terahertz signal originates from the transient charge current converted from a photon-generated spin current into magnetic heterostructures. Compared to ST-FMR and spin pumping, THz-TDS possesses the features of a high time resolution driven by an ultrafast out of equilibrium spin-current that complement the study of SCC via those transport methods.

In this work, we have synthesized Gd-alloyed BixSe1-x (BSG) thin films by magnetron sputtering.

Structural and chemical characterizations display a mainly amorphous feature in the disordered BSG film. We

Results and discussions

Sample preparation

The multilayer stacks of MgO(2 nm)/Bi(20%)-Se(40%)-Gd(40%)(BSG)/Co20Fe60B20(CFB)(5 nm)/MgO(2 nm)/Ta(2 nm) were grown by DC magnetron sputtering (with a base pressure 7×10 -8 torr) on thermally oxidized silicon substrates. Samples with different thicknesses of BSG (tBSG=6, 8, 12, 16 nm) were prepared, which are labeled as BSG6, BSG8, BSG12 and BSG16, respectively. After the growth, the samples were processed by UV lithography for spin pumping measurements. The full film samples were also used for THz-TDS measurements. In addition, we have prepared a bare SiO2//MgO(2 nm)/BSG(8 nm) sample for ARPES characterizations. The readers can find details in the Methods section.

Interfacial structure and chemical properties

High-resolution transmission electron microscopy (HRTEM) combined with electron energy loss spectroscopy (EELS) and energy-dispersive spectroscopy (EDS) were used for the interfacial structure and chemical characterizations on the BSG8 and BSG16 samples with Ta(5 nm) capping layer. Since no annealing has been performed on the sample, the CFB layer retains an amorphous feature. [START_REF] Tao | Atomic-Scale Understanding of High Thermal Stability of the Mo/CoFeB/MgO Spin Injector for Spin-Injection in Remanence[END_REF] The BSG layer also exhibits a highly disordered amorphous character, as evidenced by FFT diffraction pattern (inset of intensity in a zone of 10 nm width and 0.5 nm depth. From the chemical maps and profiles, several pieces of information can be drawn. The distribution of Gd and Se is not homogenous in the BSG layer. Gd has a tendency to accumulate towards the bottom while, on the contrary, Se tends to segregate to the interface with CFB. This could be due to the different enthalpy of formation with bottom MgO layer for Gd and Se elements. Similar variation of the elemental composition is also observed in GdFeCo film grown by cosputtering. [START_REF] Kim | Bulk Dzyaloshinskii-Moriya Interaction in Amorphous Ferrimagnetic Alloys[END_REF] The mean atomic concentration of this area was evaluated as Bi 20%:Se 40%:Gd 40%. The ratio between Co and Fe in the CFB layer was estimated to be 1:4 without considering the B concentration (not acquired).

Fig. 2(a) shows the HRTEM image of the sample BSG16. It is found, here, that the interface roughness becomes important. By the guide of black dashed lines shown in Fig. 2(a), it is evident that the increase of interface roughness is mainly attributed to the BSG layer. CFB, MgO and Ta layers well follow the morphology of the BSG layer. Some nanocrystals inside the BSG layer can be evidenced, as marked by the red dashed zones. Energy dispersive spectroscopy (EDS) element mapping images are shown in Fig. 2(c-e) with the corresponding STEM-HAADF image in Fig. 2(b). Many zones with brighter contrast can be observed inside the BSG layer in Fig. 2(b), which is due to an inhomogeneous chemical distribution and points out the segregation of some elements. From the chemical maps, the bright contrast zone (marked with red arrow at BSG/CFB interface) is identified to be Bi rich with less Se and Gd, which can also be correlated to the nanocrystals observed in Fig. 2(a). Therefore, during the growth of a thick BSG layer, the enhanced segregation of chemical elements forms the Bi-rich nanocrystals, which results in a rough interface for the BSG16 sample.

Spin pumping measurements

We now turn to spin pumping experiments to evaluate the spin-to-charge conversion efficiency in CFB(5 nm)/BSG(t=6,8,12,16 nm) samples. Figs. . Vsym and Vasym are the magnitude of the symmetric and antisymmetric voltage contributions, respectively. Hres is the resonant field, and ∆H is the linewidth of the EMF peak. In our case, the EMF signal is characterized by a rather large symmetric contribution which witnesses a clear SCC contribution.

In Fig. The observed EMF could be attributed to two origins. One is the SP-ISHE in the 3D system where bulk BSG contributes to the spin-to-charge conversion via ISHE. The other one is the SCC in a 2D system at BSG/CFB interface via SP-IEE, as recently evidenced in the case of Rashba interface states [START_REF] Sánchez | Spin-to-Charge Conversion using Rashba Coupling at the Interface between Non-Magnetic Materials[END_REF] and topological insulator surface states [START_REF] Rojas-Sánchez | Spin to Charge Conversion at Room Temperature by Spin Pumping into a New Type of Topological Insulator: α-Sn Films[END_REF] . Although the underlying physics of the spin-to-charge conversion is different, SP-IEE has the same key features as SP-ISHE for metallic FM layers. [START_REF] Harder | Electrical Detection of Magnetization Dynamics via Spin Rectification Effects[END_REF] It is reported that ISHE or IEE signals are mostly involved in the symmetric component of EMF signal, while other spin rectification effects may also come into play to mix within the symmetric component of EMF, [START_REF] Cerqueira | Evidence of Pure Spin-Current Generated by Spin Pumping in Interface-Localized States in Hybrid Metal-Silicon-Metal Vertical Structures[END_REF][START_REF] Iguchi | Measurement of Spin Pumping Voltage Separated from Extrinsic Microwave Effects[END_REF][START_REF] Bai | Universal Method for Separating Spin Pumping from Spin Rectification Voltage of Ferromagnetic Resonance[END_REF] such as the interplay between the stray RF currents and the oscillating magnet, related to either the anisotropic magnetoresistance (AMR) or the planar or anomalous Hall effect (PHE or AHE). However, each process is characterized by its own angular dependent signature. Due to the slight asymmetry of our GSG waveguide (see details in SI Note 2), the RF excitation field hRF could have two different contributions: one is in plane along the waveguide and the other one is perpendicular to the layers, [START_REF] Keller | Relative Weight of the Inverse Spin-Hall and Spin-Rectification Effects for Metallic Polycrystalline Py/Pt, Epitaxial Fe/Pt, and Insulating YIG/Pt Bilayers: Angular Dependent Spin Pumping Measurements[END_REF] although the contribution of the in-plane is expected to be much larger than that of the out-of-plane. [START_REF] Fan | Spin Pumping and Large Field-Like Torque at Room Temperature in Sputtered Amorphous WTe2-x Films[END_REF] As reported in Ref. [59], the contribution of the SCC in the symmetric voltage displays The main conclusion can be drawn: the signal of EMF at 𝜙 = 0 is almost attributed to the SCC contribution.

This angular dependent measurement validates that the variation of EMF vs. tBSG shown in Fig. 3(c) measured at 𝜙 = 0 is mostly related to the variation of SCC signals in BSG samples for different thicknesses.

Since the generation of EMF due to ISHE or IEE relies on both the amount of spin current injected and the efficiency of spin-to-charge conversion, it is important to evaluate the spin current density (Js) injected into BSG. We have firstly extracted the corresponding damping parameters () and saturation magnetization (Ms)

for the different samples by using a standard fitting procedure from the data acquired at different excitation RF frequencies (see SI Note 3).

𝐽 = ↑↓ ℏ ( ) ( ) ( ) ( ) ] (2)
Here 𝛾 is the gyromagnetic ratio and 𝑀 is saturation magnetization. We display the variation of Js in Fig.

3(e), showing a decreasing tendency when BSG thickness increases.

The SCC generated charge current density can be derived from Ohm's law: 𝐽 = = for the 3D system and 𝐽 = = for the 2D system, where R is the stripe resistance, A is the section area, w is the stripe width and t is the thickness of the NM layer where the charge current is generated. To understand the current distribution in BSG/CFB interface, we have measured the resistivity of BSG from one specific SiO2//MgO(2 nm)/BSG(16 nm)/MgO(5 nm) sample. It is found that the BSG resistivity (65 mΩ⸱cm at RT) is much larger than that of CFB (0.16 mΩ⸱cm at RT). Therefore, the generated charge current is mainly distributed in the CFB layer. Combing with Js derived from Eq.( 2), the spin-to-charge efficiency (SCE=Jc/Js) can be determined for 3D system (also named as spin Hall angle θSH) or for 2D system (also named as IEE length λIEE). More sophisticated calculation of θSH should also take into account the spin diffusion length in BSG, which will be discussed below (see SI Note 4). As shown in Fig. 3(f), the maximum θSH or λIEE can reach 0.02 or 0.035 nm in BSG6 sample, respectively, however they decrease rapidly on increasing the BSG thickness. Although the θSH is well lower than the reported value (0.43) for a high ordered Bi2Se3/CFB system ascribed to the bulk ISHE effect [START_REF] Jamali | Giant Spin Pumping and Inverse Spin Hall Effect in the Presence of Surface and Bulk Spin-Orbit Coupling of Topological Insulator Bi2Se3[END_REF] and λIEE is smaller than the value (0.36 nm) reported for an electron beamevaporated Bi2Se3/CFB system demonstrating an interface IEE effect, [START_REF] Singh | High Spin to Charge Conversion Efficiency in Electron Beam-Evaporated Topological Insulator Bi2Se3[END_REF] the evident SCE in our case clearly proves the spin-to-charge conversion in BSG/CFB system. In order to further confirm the SCC originating from the BSG layer, we have prepared a reference sample with the stack structure of SiO2//MgO(2 nm)/CFB(5 nm)/MgO(2 nm)/Ta(2 nm). The fitted results of the EMF voltage at 9 GHz show that the symmetric and antisymmetric components are 5.63 and 8.68 µV, respectively. Compared to BSG6 sample, the symmetric component is greatly reduced, thus validating that the SCC mostly occurs due to the BSG layer. In addition, our results can also exclude the possibility of thermal induced anomalous Nernst effect (ANE), [START_REF] Noël | Negligible Thermal Contributions to the Spin Pumping Signal in Ferromagnetic Metal-Platinum Bilayers[END_REF] which could contribute to the spin pumping signal. This is because the thermal voltage will not show any appreciable thickness dependence unlike we have observed in Fig. 3(c).

THz-TDS measurements

Since for both ISHE and IEE, DC-voltage signals from SCC appear in the same direction as 𝐽 ⃗ × 𝜎 and they are picked up by the same DC-probe configuration placed on the top of BSG/CFB heterostructure, it appears difficult to distinguish them only from spin pumping measurement although the large resistivity of BSG would not favor ISHE mechanism. For that goal, THz-TDS emission spectroscopy in the time domain has recently emerged as a powerful tool to study the interplay between charge and spin degrees of freedom in an all-optical manner. Fig. 5(a) shows the schematics of THz-TDS measurements. An ultrafast laser pulse (~100 fs) at 810 nm (200 mW) was launched on the sample surface with a saturating magnetic field applied in the sample plane (between 10 mT and 0.2 T). The generated THz pulses were collected from the front surface (i.e., reflection geometry). In all measurements, we have not observed particularly strong heating mainly due to the fact that the absorption of the laser power is limited to less than 20% for transition metal thin films. [START_REF] Dang | Ultrafast Spin-Currents and Charge Conversion at 3d-5d Interfaces Probed by Time-Domain Terahertz Spectroscopy[END_REF] Moreover, THz signals showed a strong reproducibility in time on the same series of samples. emission efficiency and a broadband emission. [START_REF] Seifert | Efficient Metallic Spintronic Emitters of Ultrabroadband Terahertz Radiation[END_REF] It has been reported that the self-emission from the ferromagnetic film could exist in the thick Co layer (30 nm) due to the mechanism of photo-induced demagnetization/remagnetization dynamics, while THz emission from SCC plays the main role in the case of thin Co films (3 nm). [START_REF] Huang | Direct Observation of Terahertz Emission from Ultrafast Spin Dynamics in Thick Ferromagnetic Films[END_REF] The clear and relatively large THz signal observed doubly proves the SCC in the BSG/CFB bilayers. [START_REF] Rongione | Ultrafast Spin-Charge Conversion at SnBi2Te4/Co Topological Insulator Interfaces Probed by Terahertz Emission Spectroscopy[END_REF] As reported in Ref. [46] in ST-FMR measurement, with an insertion of a Cu layer between the TI and the ferromagnet, the spin accumulation at the surface states can be separately evaluated owing to the suppression of the exchange coupling between the ferromagnet and the surface states of TI possibly detrimental for the latter. Here, we prepared one specific sample (BSG-Cu): SiO2//MgO(2 nm)/BSG(16 nm)/Cu(5 nm)/Co20Fe60B20(5 nm)/MgO(2 nm)/Ta(2 nm) characterized by an insertion of a 5 nm thick Cu between BSG and CFB layers. Since the hot electron spin attenuation length in Cu is longer than 33 nm, [START_REF] Garramone | Measurement of the Hot Electron Attenuation Length of Copper[END_REF] . This experiment definitively proves that the origin of THz signal is due to the SCC effect by the BSG layer.

ARPES measurements

To understand the origin of SCC effect by BSG layer, we have investigated the valence band (VB) of a SiO2//MgO(2 nm)/BSG(8 nm) sample by using ARPES characterization. All spectra were recorded at room temperature. Fig. 6 summarizes the resulting band structure with the reconstructed data after subtracting the background. Bi2Se3. [START_REF] Corbae | Observation of Spin-Momentum Locked Surface States in Amorphous Bi2Se3[END_REF] Hence, our ARPES measurements clearly evidence the persistence of topological surface states in the band gap of our BSG layers, which could be the origin of SCC effect.

Discussions

One important issue is to understand the different qualitative behavior of SCC between spin-pumping and THz-TDS experiments upon BSG thickness. To clarify the different BSG thickness dependence, we have measured the surface roughness of bare BSG layers with different thicknesses by atomic force microscopy (AFM), as plotted in Fig. 3(d) compared to the damping parameters (see more details in SI Note 7). The RMS roughness of BSG layer is shown to increase with thickness and follows the same tendency as the damping parameter . Such roughness increase can be understood by the formation of Bi crystallites, as clearly evidenced by TEM characterizations in Fig. 2(a). It results in a subsequent and dominant inhomogeneous resonance ascribed to the "orange peel" magnetic coupling [START_REF] Dash | Spin Precession and Inverted Hanle Effect in a Semiconductor near a Finite-Roughness Ferromagnetic Interface[END_REF] more than due to the spin-escape effects. As a consequence, a reduction of spin pumping efficiency as well as the spin mixing conductance is expected with the increase of BSG roughness, as also demonstrated in Pd/Al/Py system [START_REF] Kitamura | Vertical Spin Transport in Al with Pd/Al/Ni80Fe20 Trilayer Films at Room Temperature by Spin Pumping[END_REF] for an equivalent roughness. As a result, the spin current density 𝐽 ∝ ↑↓ as well as SCE decreases rapidly with increasing BSG thickness as well as . Compared to spin pumping, THz-TDS measurement does not require any resonant condition for SCC, thus it is not sensitive to the roughness and reflects very fairly the true tBSG dependency of SCE.

The small variation measured in THz-TDS suggests that the efficient SCC is already statured in BSG6 sample, which is in good agreement with the spin pumping measurement. For 3D SP-ISHE, 𝑉 vs. thickness of NM layer (𝑑 ) follows the relationship of 𝑉 = 𝐼 𝑅 = 𝜃 𝑅𝑤( ℏ )𝜆tanh ( )𝑗 , where 𝜆 is the spin diffusion length in the NM material. [START_REF] Ando | Inverse Spin-Hall Effect Induced by Spin Pumping in Metallic System[END_REF] The amplitude of 𝑉 increases with the increase of thickness of NM layer, but it saturates at about a thickness of 3𝜆. In our measurement, since 𝑉 already reaches its maximum at 6 nm, the spin diffusion length in BSG should be smaller than 2 nm. In addition, the resistivity of BSG ( 65mΩ⸱cm) is about 400 times larger than that of CFB (0.16 mΩ⸱cm), which also indicates that the SCC generated charge current can only exist at the interface of BSG/CFB but not inside BSG owing to the impedance mismatch and the spin-back flow issues [START_REF] Fert | Conditions for Efficient Spin Injection from a Ferromagnetic Metal into a Semiconductor[END_REF] when the resistivity of the NM becomes very large. Therefore, it is reasonable to consider that the observed SCC is due to the 2D IEE at BSG/CFB interface involving a Rashba or a TI state.

From our ARPES measurement, the possibility of a topologically protected surface state in our amorphous BSG films is privileged. These results are in good agreement with that measured by Corbae et al. on amorphous Bi2Se3 thin films. [START_REF] Corbae | Observation of Spin-Momentum Locked Surface States in Amorphous Bi2Se3[END_REF] They demonstrated a dispersive two-dimensional surface state that crosses the bulk gap. Spin resolved photoemission spectroscopy shows this state has an anti-symmetric spin texture resembling that of the surface state of crystalline Bi2Se3. As recently predicted by several theoretical work, [START_REF] Mitchell | Amorphous Topological Insulators Constructed from Random Point Sets[END_REF][START_REF] Agarwala | Topological Insulators in Amorphous Systems[END_REF][START_REF] Agarwala | Higher-Order Topological Insulators in Amorphous Solids[END_REF][START_REF] Mansha | Robust Edge Sates in Amorphous Gyromagnetic Photonic Lattices[END_REF][START_REF] Huang | Quantum Spin Hall Effect and Spin Bott Index in a Quasicrystal Lattice[END_REF][START_REF] Huang | Theory of Spin Bott Index for Quantum Spin Hall States in Nonperiodic Systems[END_REF][START_REF] Pöyhönen | Amorphous Topological Superconductivity in a Shiba Glass[END_REF] the topological spin-momentum locking surface states can exist in an amorphous TI surface. The reason is that in random lattices fermions hop between sites within a finite range. By tuning parameters such as the density of states, the system undergoes a quantum phase transition from a trivial to a topological phase that manifests as quantized conductance in the system boundary. [START_REF] Agarwala | Topological Insulators in Amorphous Systems[END_REF] If these surface states do exist on the surface of BSG, our sample with Cu insertion indicates that the deposition of Cu has a minor role in varying the surface states of BSG for the SCC, which is consistent with the ST-FMR measurements on (Bi1-xSbx)2Te3/Cu/NiFe trilayers. [START_REF] Kondou | Fermi-Level-Dependent Charge-to-Spin Current Conversion by Dirac Surface States of Topological Insulators[END_REF]

Conclusions

In summary, we have fabricated amorphous Gd-alloyed BixSe1-x thin films by sputtering method and

Methods

Sample preparation:

The films were grown by magnetron sputtering on a thermally oxidized silicon substrate. The stacks are:

MgO(2 nm)/BSG(t nm)/CFB(5 nm)/MgO(2 nm)/Ta(2 nm). BSG was grown by co-sputtering of Bi2Se3 and Gd targets. The Ar flow during sputtering was 40 sccm and the anode bias was 60 V. The cathode power for BiSe and Gd was 30 W and 40 W, respectively. The BSG deposition rate was 0.7 Å/s.

TEM characterization:

HRTEM and STEM were performed to characterize the interfacial structure using a probe corrected JEOL ARM 200 CF operated at 200 kV. Thin lamella was extracted by focused ion beam (FIB) milling using an FEI Helios Nanolab dual beam. EELS spectrum images were recorded in STEM mode with a Gatan Quantum Imaging filter. In order to correct energy drift and estimate the local thickness, the zero-loss and the core-loss spectra were simultaneously recorded for a dispersion of 1 eV (Dual EELS method). The core loss spectra were registered in the range 670-2700 eV in order to record FeL, CoL, GdM, MgK, SeL, TaM and BiM edges. BK and OK signals with edges respectively near 188 eV and 532 eV were not recorded. The pixel size of the spectrum image was fixed at 0.4 nm for a dwell time of 0.5 s/pixel for the core loss spectra. After energy drift correction, the spectrum images were denoised using a principal component analysis method 72 before quantitative analysis. EDS spectrum images were recorded in STEM mode with a JEOL JED2300T silicondrift detector. Spectrum images were obtained by integrating 170 frames of 256×256 pixels. The pixel size was fixed at 0.23 nm for a dwell time of 0.2 msec.

Spin pumping measurement:

We performed spin pumping experiment to measure the spin-to-charge conversion. The samples were patterned into stripes with a width and length of 620 μm and 1500 μm, respectively, using UV photolithography and ion milling. A 55 nm thick silicon dioxide layer was deposited to insulate the wave guide from the film.

The wave guides and contact pads were patterned by UV photolithography, and a Ti(10 nm)/Au(150 nm) electrode was deposited. The waveguide of the spin pumping devices has the signal linewidth of 75 μm, ground linewidth of 225 μm, and separation between the lines of 37.5 μm. The RF current generates an excitation magnetic field, which causes the precession of the magnetization of the CoFeB layer at a GHz frequency.

When the frequency of magnetic field matches with the oscillation frequency of the FM layer under a certain resonance field, the spin current generated from the CoFeB layer injects into the BSG layer due to the spin pumping effect. The injected spin current is then converted to a DC charge current, which is probed by measuring the open circuit voltage on the two terminates of the stripe using a Keithley 2182A nanovoltmeter.

THz spectroscopy measurement:

The film samples were placed on a mount with a small magnetic field (between 10 mT and 0.2 T) parallel to the spin interface. An ultrafast (~100 fs pulses) Ti:Sapphire oscillator centered at 810 nm was used to photoexcite the spin carriers directly from the front surface. Average power of up to ~200 mW was used with a repetition rate of 80 MHz. The typical laser spot size on the sample was about 200×200 µm 2 . The generated THz pulses were collected from the front surface of the spin emitter (i.e., reflection geometry) using a set of parabolic mirrors of 150 and 75 mm focal length to focus on samples. Standard electrooptic sampling was used to detect the electric field of the THz pulses, using a 500-µm-thick <110> ZnTe crystal. A chopper was placed at the focal point between the second and third parabolic mirror to modulate the THz beam at 6 kHz for lock-in detection. The TDS setup was placed in a dry-air purged chamber (typically 3-5% humidity) to reduce the influence of water absorption on the THz radiation.

ARPES and XPS measurement:

The As shown in Ref. [3], the detected THz signal intensity E in FM/NM bilayer can be expressed as:

𝐸(𝑑) ∝ 𝜃 𝜆 ( / ) ∫ ( ) (S5)
Where 𝜃 is the spin-Hall angle in the NM layer. λrel can be considered as a hot-electron velocity relaxation length (typically 1 nm 2 ). A is the absorbed fraction of the incident pump power. dN is the thickness of the NM layer. 𝑑 is the total thickness (dF+dN). n1 is the refractive index of substrate. For MgO, sapphire or Si in THz domain, n1=3.5. n2 is the refractive index of air, n2=1. Z0 = 377 Ω is the vacuum impedance. 𝜎 is the conductivity of metal layer.

For simplification, the THz signal intensity ratio γ between the BSG16 and BSG-Cu samples can be given by:

γ = ( ) ( ) (S6)
by injecting the parameters: n1=3.5, n2=1, Z0 = 377 Ω, 𝜎 =1/(20×10 -6 ) Ω -1 ⸱cm -1 , 4 𝜎 =1/(65×10 -3 ) Ω -1 ⸱cm -1 , 𝜎 =1/(0.16×10 -3 ) Ω -1 ⸱cm -1 , 𝑑 =5 nm, 𝑑 =16 nm, 𝑑 =5 nm, we are able to obtain the ratio of 2.66.

Note 6. XPS of BSG sample for ARPES measurement

The SiO2//MgO(2 nm)/BSG(8 nm) sample has been characterized by XPS in order to determine the chemical nature/ordering of the BSG layer being measured by ARPES. Since the sample was transferred through air into ARPES setup, we have carried out a soft Ar + etching on the surface to remove the oxidation.

The results are presented in

  Sahu, Yifei Yang, Yihong Fan, Henri Jaffrès, Jun-Yang Chen, et al.. Room Temperature Spin-to-Charge Conversion in Amorphous Topological Insulating Gd-Alloyed BixSe1-x/CoFeB Bilayers. ACS Applied Materials & Interfaces, 2023, 15 (32), pp.38592-38602. 10.1021/acsami.3c07695. hal-04242480

Fig. 1 (

 1 a) and (b) shows the large-scale scanning transmission electron microscopy-high angle annular dark field image (STEM-HAADF) and magnified HRTEM image of the BSG8 sample, respectively. The sample shows relatively flat and sharp interfaces in the large-scale image (Fig. 1(a)). In Fig. 1(b), different layers can be distinguished.

Fig. 1 (

 1 Fig. 1(b)) on the blue dashed square zone in Fig. 1(b). The bottom MgO barrier exhibits textured features

  3(a) and (b) show the schematics of spin pumping measurement and the surface of the device, respectively. A symmetric GSG waveguide is patterned on the top of BSG/CFB structure, which is excited by GHz current to introduce a RF magnetic field in the CFB film. At the condition of ferromagnetic resonance, due to the spin pumping effect, a net spin current (Js) is injected into the BSG layer and afterward converted into a charge current (Jc) due to the spin-to-charge conversion process. This gives rise to the generation of a DC voltage (electromotive force (EMF) voltage) across the device. The inset of Fig.3(c) shows a typical spectrum of the EMF voltage acquired at the resonance frequency (9 GHz) for the BSG6 sample. The EMF spectrum is composed of two parts,[START_REF] Nakayama | Geometry Dependence on Inverse Spin Hall Effect Induced by Spin Pumping in Ni81Fe19/Pt Films[END_REF][START_REF] Harder | Electrical Detection of Magnetization Dynamics via Spin Rectification Effects[END_REF] a symmetric Lorentzian shaped signal plus an antisymmetric signal, which can be decomposed into 𝑉(𝐻)

  3(c), we have shown the variation of Vsym and Vasym as a function of BSG thickness. It is quite clear that the Vsym decreases rapidly with the increase of BSG while Vasym displays a smaller variation for the different thicknesses.

  Fig. 3(b)). Without giving more details, we have shown in Fig. 4(a) and (b) the results of the angular fit for

Fig. 3 (

 3 d) displays the variation of α as a function of the BSG thickness. α increases from 5.3×10 -3 to 1.3×10 -2 for BSG thicknesses varying from 6 to 16 nm. All these values obtained are in the range of the one obtained from a CoFeB/Pt control sample (9.610 -3 ), but are markedly larger than that of a CoFeB/Al reference sample (1.8310 -3 ) grown on the SiO2 substrate, free of any spin-current dissipation. The latter constitutes an upper bound for the intrinsic damping 0 of a 5 nm thick CoFeB layer.Those measurements reveal a certain spin-current dissipation in the CoFeB layer scaling with the difference of the damping =-0 and which may be expressed, by part, via the spin-mixing conductance 𝐺 ↑↓ =  where 𝑔 , 𝜇 , Meff, and tCoFeB are, respectively, Landé factor, Bohr magneton, effective magnetization and CoFeB layer thickness. The spin current injected from the CoFeB layer into BSG can be then determined by the following formula47 :

Fig. 5 Fig. 5 (

 55 Fig. 5(c) displays the ensemble of THz-TDS signals from the series of samples with different BSG

  the spin current injected from CFB layer should be almost conserved at BSG/Cu interface after crossing the 5nm thick Cu layer. We could expect the same amplitude of THz signal (except for the additional THz absorption in Cu) compared to the sample without Cu insertion if the BSG layer truly plays a critical role in the SCC conversion. As shown in Fig. 5(d), the Cu insertion sample shows a reduced signal by a factor about 3 compared to the BSG16 sample which is mainly explained by the additional THz absorption in Cu. After renormalization of THz signal with a factor of 2.66 obtained by considering the resistivity of the thin Cu layer (~20 µΩ⸱cm 68 ) (see details in SI Note 5), we indeed obtain almost the same amplitude of signal as the BSG16 sample (Fig. 5(d))

Fig. 6 (

 6 a) displays the ARPES intensity map as function of binding energy and wave vector focusing on the region close to the Fermi level. The corresponding X-ray photoelectron spectroscopy (XPS) study of Bi 4f, Gd 3d, Se 3d and O 1s core levels are presented in the SI Note 6. The valence band intensity is shown to fall down drastically approaching the topological gap of BSG, i.e. for binding energies smaller than -0.5 eV. Moreover, two parallel strongly dispersive states emerge from the VB until to the Fermi level (with black dashed line as a guide to the eye). Figs.6(b) and (c) show the momentum dispersion curves (MDCs) taken at and -0.1 eV and -0.3 eV, respectively. The MDCs unambiguously exhibit the existence of two strongly dispersive states in the gap symmetrically centered at k//=  0.28 Å -1 (=7°). As reported very recently[START_REF] Corbae | Observation of Spin-Momentum Locked Surface States in Amorphous Bi2Se3[END_REF] , topologic surface states can exist in amorphous Bi2Se3 film since a well-defined nearest neighbor distance should correspond to a good reciprocal length scale i.e. a good momentum quantum number k. The experimental value of k extracted here (less than 0.3 Å -1 ) is very close to the one observed in amorphous

FiguresFigure 1 :

 1 Figures

Figure 2 :

 2 Figure 2: Structural and chemical characterization of BSG16 sample by TEM. (a) HRTEM image in magnified scale on the BSG16 sample. The black dashed lines guide the eyes to show the interface roughness due to the BSG layer. The red cycles show the zone where nanocrystals can be found. (b) STEM HAADF image and corresponding EDS elemental maps for (c) Bi, (d) Se and (e) Gd. The red arrows indicate that the white contrast zone in (b) is due to the inhomogeneous element distribution with a Bi-rich character.

Figure 3 :

 3 Figure 3: Spin-to-charge conversion studied by spin pumping measurements. (a) Schematic of spin pumping measurement. (b) Schematic of the spin pumping device. Inset: schematic configuration of angle dependence measurement. (c) Decomposed symmetric and antisymmetric components of EMF voltage as a function of BSG thickness. Inset: Typical spectra of the EMF voltage acquired at the resonance frequency (9 GHz) for the BSG6 sample. The peak can be fitted by Lorentzian function to decompose the symmetric and antisymmetric components. (d) Damping parameter and BSG root mean square (RMS) roughness as a function of BSG thickness. (e) Spin current density (Js) generated by spin pumping as a function of BSG thickness. (f) Spin-tocharge conversion efficiency (SCE) as a function of BSG thickness presented either as spin Hall angle (θSH) for 3D system or as IEE length (λIEE) for 2D system.

Figure 4 :

 4 Figure 4: Extracted Vsym as a function of the angle ϕ0 between the waveguide and the DC magnetic field for BSG/CFB bilayers with (a) 8 nm thick BSG and (b) 16 nm thick BSG. The data was fitted by the model considering SCC and AMR contributions with in-plane and out-of-plane excitation RF magnetic field.

Figure 5 :

 5 Figure 5: Spin-to-charge conversion studied by THz-TDS measurements. (a) Schematic of TDS experimental setup. (b) Typical emitted electric field as a function of time for the BSG8 sample at RT with two opposite applied magnetic fields (±1k Oe). (c) THz-TDS signals from the series of samples with different BSG thicknesses in comparison with a reference sample of sapphire//W(2 nm)/CoFeB(1.8 nm)/Pt(2 nm)/MgO(2 nm). The signals have been temporally shifted for clarity. (d) Peak-to-peak amplitude of THz signal for samples with different BSG thicknesses in comparison with the control sample with an insertion of 5 nm thick Cu between BSG and CFB. The signal of Cu insertion sample has also been renormalized by taking account of THz absorption by the Cu layer.

Figure 6 : 1 𝑓

 61 Figure 6: Angle-resolved photoemission spectroscopy measurement on SiO2//MgO(2 nm)/BSG(8 nm) sample. (a) ARPES intensity map I(EB, k//). Corresponding Momentum Dispersion Curve (constant energy cut) located in the topological gap of amorphous BSG at (b) -0.1 eV and (c) -0.3 eV.

Fig. S3 :Note 4 .Note 5 .

 S345 Fig. S3: (a) EMF spectra with different frequency of RF field for the BSG6 sample as a function of DC magnetic field. (b) Typical FMR peak at 9 GHz for the BSG6 sample. The peak can be fitted by Lorentzian function to decompose the symmetric and antisymmetric components. (c) Extraction of saturation magnetization by the fit of resonant frequency as a function of resonant DC magnetic field. (d) Extraction of damping parameter by the fit of the width of EMF spectra as a function of resonant frequency.

Fig. S4 .

 S4 On one hand, the evolution of O 1s core levels as function of cleaning (5 mins at 0.75 keV/cycle of Ar + etching) presented in Fig.S4(a) allows to identify the bulk (peak 1) and surface (peak 2) contributions. The bulk O signal could come from the bottom MgO layer due the limit mean free path of photoelectron. After two cycles of etching, the surface O component are much reduced. Fig.S4(b) presented the Bi 4f spectra after two cycles of etching as function of emission angle  of the outgoing photoelectron.Two components with oxidized (high binding energy) and non-oxidized (low binding energy) states are evidenced. Increasing  leads to a decrease of the oxidized component showing that the surface is nearly free from oxidation. However, deeper in the bulk, probably the BSG in contact with MgO is oxidized. On the other hand, Gd 3d (Fig.S4(c)) and Se 3d (Fig.S4(d)) show almost no oxidation signature confirming the high quality of the BSG samples. As a consequence, ARPES measurements being carried out at low energy (21.22 eV) are more sensitive to the surface of BSG layers than the BSG/MgO/SiO2 interface.

Fig. S4 :

 S4 Fig. S4: (a) XPS spectra of O 1s before and after two cycles of Ar + etching cleaning. (b) XPS spectra of Bi 4f as function of emission angle  of the outgoing photoelectron. Inset: schematics of detection angle with respect to the sample plane. (c) XPS spectra of Gd 3d. (d) XPS spectra of Se 3d.

  studied the spin-to-charge conversion in BSG/CFB bilayers. Structural characterizations show a mainly amorphous feature for the 8 nm thick BSG film, while Bi rich crystallites appear inside the 16 nm thick BSG film. Spin pumping and THz-TDS measurements have been employed to study SCC in BSG(tBSG)/CoFeB(5 nm) bilayers with different BSG thicknesses (tBSG=6-16 nm). Both methods have proved the efficient SCC at BSG/CFB interface. The maximum SCE is measured as large as 0.035 nm for λIEE in BSG6 sample. The spin pumping measurements show a fast decay of SCE when tBSG increases due to the increase of BSG surface roughness. However, TDS measurements reveal a small tBSG dependence of SCE, validating a pure interface state related SCC. Furthermore, our APRES data is consistent with a dispersive two-dimensional surface state that crosses the bulk gap to Fermi level, privileging the origin of SCC due to the amorphous TI state. Our studies give a deep insight into the SCC in spin pumping and TDS measurements and provide a new experimental direction to the search for topological systems in amorphous solids to develop scalable topological devices.

Table S1 :

 S1 Spin Hall angle (SHA), resistivity, characterization technique and morphology of sputtered topological insulators.

	Material	SHA	Resistivity	Characterization	Morphology	Reference
			(mΩ cm)	Technique
	BixSe1-x	18.6	12.8	planar Hall	polycrystalline	5
	Bi2Se3	2.76	3.9	planar Hall	amorphous	6
	Bi0.85Sb0.15	2.4	1.0	harmonic Hall	polycrystalline	7
	Bi0.85Sb0.15	10.7	0.7	harmonic Hall	highly textured	8
	Bi2Se3	0.11	-	spin pumping	textured	9
	BSG	0.02	65	spin pumping	amorphous	this work

Acknowledgements

We acknowledge the discussion with Prof. Albert Fert. This work was supported in part by C-SPIN, one of six centers of STARnet, and is partly supported by ASCENT, one of six centers of JUMP, a Semiconductor Research Corporation program that is sponsored by MARCO and DARPA. Portions of this work were conducted in the Minnesota Nano Center, which is supported by the National Science Foundation through the National Nano Coordinated Infrastructure Network (NNCI) under Award Number ECCS-1542202. Y.Lu acknowledges the support from the French National Research Agency (ANR) FEOrgSpin (No. ANR-18-CE24-0017-01) and SOTspinLED (No. ANR-22-CE24-0006-01) projects.

TOC figure

Supporting Information

Room Temperature Spin to Charge Conversion in Amorphous Topological Insulating Gd-Alloyed BixSe1-x/CoFeB Bilayers Protyush Sahu 1# , Yifei Yang 1# , Yihong Fan 1 , Henri Jaffrès 4 , Jun-Yang Chen 2 , Xavier Devaux 4 , Yannick Fagot-Revurat 4 , Sylvie Migot 4 , Enzo Rongione 3 , Tongxin Chen 4 , Pambiang Abel Dainone 4 , Jean-Marie George 3 , Sukhdeep Dhillon 5 , Martin Micica 5 , Yuan Lu 4 *, and Jian-Ping Wang # authors having equal contributions corresponding authors: *yuan.lu@univ-lorraine.fr; ⁑ jpwang@umn.edu

Note 1. Magnetic characterization of BSG film

We have performed magnetic characterizations by superconducting quantum interference device (SQUID) for the bare 16 nm BSG sample at different temperature, as shown in Fig. S1. The curves show only linear variation behavior due to the paramagnetic character of Si/SiO2 substrate. The signal from BSG layer can be extracted after subtracting the linear background. However, we found that the signal from BSG is very small, which indicates that the BSG layer is almost non-magnetic although the Gd atom is magnetic.

Note 2. Origin of out-of-plane excitation RF magnetic field

For the spin pumping measurement, we use a GSG waveguide to generate the RF magnetic field, as shown in Fig. S2(a). The waveguide contains one source line (S) and one ground line with two terminals (G1 and G2). Using Ampere's law, the in-plane RF magnetic field generated by the waveguide is estimated to be 0.43 Oe, when an excitation frequency of 9 GHz and an amplitude of 2 V are used. As discussed in the main text, the output voltage of spin pumping has a component associated with the perpendicular RF magnetic field. Here we found that this field can possibly originate from the asymmetric geometry of the spin pumping device.

If the device is perfectly symmetric, as shown in Fig. S2(b), the perpendicular fields induced by source and ground lines will cancel each other out. However, if the device has some asymmetry, which could result from the patterning process, a perpendicular field will arise. Fig. S2(c) shows an asymmetric source line, with a width of d missing at one side. Since there is more sample area on the left side of the source line, the perpendicular field will be larger than that on the right side. Assuming d is 10% of the total width of the source line, the estimated perpendicular magnetic field on the sample is 0.037 Oe, which is about one order of magnitude smaller than the in-plane field.

Note 3. Extraction of damping parameters

To extract the parameters of damping and effective magnetization, we have measured FMR resonant spectra at different resonant frequency from 9 GHz to 17 GHz. As shown in Fig. S3(a) for BSG6 sample, with the increase of frequency, the DC magnetic field to obtain FMR also increases. At the meantime, the amplitude of peak decreases and the width of peak increases with increasing the frequency. As shown in Fig. S3(b) for 9 GHz excitation, the resonant spectrum can be fitted by a combination of symmetric and anti-symmetric Lorentzian fit following: 1