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## Creator

[Taisuke Horaguchi](https://orcid.org/0009-0000-7435-6075), [Cong He](https://orcid.org/0000-0002-7548-9344), [Zhenchao Wen](https://orcid.org/0000-0001-7496-1339), [Hayato Nakayama](https://orcid.org/0009-0006-0510-2454), [Tadakatsu Ohkubo](https://orcid.org/0000-0003-3548-1951), [Seiji Mitani](https://orcid.org/0000-0002-1348-0774), [Hiroaki Sukegawa](https://orcid.org/0000-0002-4034-7848), [Junji Fujimoto](https://orcid.org/0000-0002-5669-1299), [Kazuto Yamanoi](https://orcid.org/0000-0001-5356-0712), [Mamoru Matsuo](https://orcid.org/0000-0003-1303-7614), [Yukio Nozaki](https://orcid.org/0000-0002-7262-0124)

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Copyright © 2025 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution License 4.0 (CC BY).[Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/)

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[Nanometer-thick Si/Al gradient materials for spin torque generation](https://mdr.nims.go.jp/datasets/367a40df-36f1-4580-8bea-2c58e207d619)

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Nanometer-thick Si/Al gradient materials for spin torque generationHoraguchi et al., Sci. Adv. 11, eadr9481 (2025)     9 May 2025S c i e n c e  A d v a n c e s  |  R e s e ar  c h  A r t i c l e1 of 7M AT E R I A L S  S C I E N C ENanometer-thick Si/Al gradient materials for spin torque generationTaisuke Horaguchi1†, Cong He2‡, Zhenchao Wen2, Hayato Nakayama1, Tadakatsu Ohkubo2,  Seiji Mitani2,3, Hiroaki Sukegawa2, Junji Fujimoto4§, Kazuto Yamanoi1,  Mamoru Matsuo4,5,6,7, Yukio Nozaki1,8*Green materials for efficient charge-to-spin conversion are desired for common spintronic applications. Recent studies have documented the efficient generation of spin torque using spin-orbit interactions (SOIs); however, SOI use relies on the employment of rare metals such as platinum. Here, we demonstrate that a nanometer-thick gra-dient from silicon to aluminum, which consists of readily available elements from earth resources, can produce a spin torque as large as that of platinum despite the weak SOI of these compositions. The spin torque efficiency can be improved by decreasing the thickness of the gradient, while a sharp interface was not found to increase the spin torque. Moreover, the electric conductivity of the gradient material can be up to twice as large as that of platinum, which provides a way to reduce Joule heating losses in spintronic devices.INTRODUCTIONNonequilibrium spin polarization in conduction electrons enables the magnetization direction to be manipulated via spin torque using spin-orbit interactions (SOIs) in spintronic devices such as magnetic random-access memory (1, 2) and spin torque nanooscillators (3–5). Phenomena such as the spin Hall effect (SHE) (6–10) and the Rashba-Edelstein effect (REE) (11–14) are commonly used to generate spin-polarized flow, i.e., spin currents (SCs), in strong SOI materials. Such nonequilibrium spin polarization generally requires specific materi-als with a strong SOI, usually consisting of heavy 5d metal elements such as tantalum (Ta), tungsten (W), and platinum (Pt). The figure of merit (FOM) for SC generation capability is generally determined as the product of the spin Hall angle and the electric conductivity of the material. Namely, higher-conductivity materials exhibit superior SC generation, while stronger-SOI elements generally exhibit smaller conductivities (15–19). The material choice dilemma for SC genera-tion creates a bottleneck in spintronic device production. Poor con-ductivity in SC circuits can lead to other serious problems such as wiring delays and Joule losses in integrated circuits. Moreover, semi-conductor device performance is often degraded by contamination with strong-SOI elements. Therefore, a SOI-free technology is im-portant for enabling SC circuit integration in electric devices. The problem of rare-metal element scarcity also poses a serious challenge to sustainable development.A promising technology for producing flow of spin angular mo-mentum without using SOI is spin separation produced by a mag-netic field gradient. Stern and Gerlach (20, 21) demonstrated spin separation in 1922 using a field gradient (z axis in Fig. 1A). Although their approach relies on a magnetic field gradient, it established an important precedent for exploring how spatially varying field can af-fect spins, even without strong SOI. Subsequently, Matsuo et al. (22) introduced the concept of spin-vorticity coupling (SVC), where the macroscopic vorticity ω and spins s interact via the Hamiltonian  ∝ − s ⋅ ω. Namely, ω acts as an effective magnetic field. Notably, while the original Stern-Gerlach experiment dealt with a single par-ticle, the spin-vorticity concept extends this idea to nonequilibrium many-body systems. In this picture, a nonuniform vorticity (∇ω ≠ 0) leads to a nonequilibrium spin state, giving rise to a spin current. Experiments on metallic liquid (23), thin copper (Cu) films (24–26), and quark-gluon plasma (27,  28) have demonstrated that effective magnetic fields can arise from this gyromagnetic effect. A related phenomenon in surface- and edge-oxidized Cu films (29, 30) further supports the idea that a nonuniform electric current can generate an effective magnetic field via SVC. Because a conductivity gradient in-duces vorticity in the electric current (ω = ∇ × jc), this magnitude should depend on how abruptly the electron conductivity transitions within an oxide (Fig. 1B). Our focus thus centers on leveraging such gradients to produce spin currents independently of heavy-element SOI, expanding the range of materials available for spintronic appli-cations. However, the thickness of the oxidation gradient is difficult to control atomically. This poses a problem not only for practical ap-plications of spintronic devices but also for confirming the existence of emergent magnetic fields because of electric current vorticity.In this study, we successfully fabricated a nanometer-thick artifi-cial gradient from silicon (Si) to aluminum (Al), which constitutes the second- and third-most abundant components in Earth’s crust (Fig. 1C), and we demonstrate its ability to generate a spin torque comparable to Pt. The magnitude of the spin torque increases when the compositional gradient steepens; however, an atomically sharp interface does not substantially increase the spin torque. Moreover, as reported in the study of a surface-oxidized Cu film (29), we observed 1Department of Physics, Keio University, Yokohama 223-8522, Japan. 2Research Center for Magnetic and Spintronic Materials, National Institute for Materials Sci-ence, 1-2-1 Sengen, Tsukuba 305-0047, Ibaraki, Japan. 3Graduate School of Science and Technology, University of Tsukuba, Tsukuba 305-8577, Japan. 4Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, No. 3, Nanyitiao, Zhongguancun, Haidian District, Beijing, China. 5CAS Center for Excellence in Topo-logical Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China. 6RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan. 7Advanced Science Research Center, Japan Atomic Energy Agency, Tokai 319-1195, Japan. 8Center for Spintronics Research Network, Keio University, Yokohama 223-8522, Japan.*Corresponding author. Email: nozaki@​phys.​keio.​ac.​jp†Present address: Department of Applied Physics, Fukuoka University, Fukuoka 814-0180, Japan.‡Present address: College of Materials Science and Engineering, Hunan University, Changsha 410082, China.§Present address: Department of Electrical Engineering, Electronics, and Applied Physics, Saitama University, Saitama 338-8570, Japan.Copyright © 2025 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution License 4.0 (CC BY). Downloaded from https://www.science.org at National Institute for Materials Science on May 11, 2025mailto:nozaki@​phys.​keio.​ac.​jphttp://crossmark.crossref.org/dialog/?doi=10.1126%2Fsciadv.adr9481&domain=pdf&date_stamp=2025-05-09Horaguchi et al., Sci. Adv. 11, eadr9481 (2025)     9 May 2025S c i e n c e  A d v a n c e s  |  R e s e ar  c h  A r t i c l e2 of 7a large nonreciprocity that suggests the SC generation via an emer-gent magnetic field because of electric current vorticity.RESULTSFabrication and structural analysis of Si/Al gradient materialsWe fabricated Si(10)/Al(ti/2)/Si(ti/2)/Al(10)/Ni95Cu5(10)/SiO2(20) (unit: nm) multilayer strips on a thermally oxidized Si substrate by means of a conventional liftoff method using magnetron sputtering and photolithography. Here, ti is the thickness of the interfacial Al/Si insertion, which varied from 0.25 to 2.0 nm at intervals of 0.25 nm. Al is a very conductive metal with an open 2p shell. Although Si is adja-cent to Al in the periodic table, it is a semiconductor with much lower electrical conductivity than Al. Sputter deposition processes generally lead to atomic or metallographic disturbances at an interface because of the large kinetic energy of the sputtered particles. An insertion of a few nanometers of Al/Si therefore increases the mixed region at the interface between 10-nm-thick Si and Al layers. Microstructural anal-ysis using high-angle annular dark-field scanning transmission elec-tron microscopy (HAADF-STEM) revealed an increase in the thickness of the compositional gradient from Si to Al with increasing ti. Figure 2 (A and B) displays cross-sectional HAADF-STEM images near the Si/Al interface with ti = 2.0 and 1.0 nm, respectively. In com-parison, a cross section of a Si/Al interface without Al/Si insertion (i.e., ti = 0 nm) is also shown in Fig. 2C, in which a sharp interface was clearly observed. The Al/Si insertion obscures the Si/Al boundary. Moreover, aggregation of Al and/or Si was observed at the Si/Al inter-face for ti = 2.0 nm. The formation of such aggregation features is at-tributed to nonsolid solution atomic mixing between Si and Al. Energy-dispersive spectroscopy (EDS) line profiles of each element (Si and Al) were obtained by averaging the signals in the dashed box area shown in Fig. 2 (D to F), which explicitly confirm the formation of a Si/Al gradient with a transition thickness that systematically varies with ti. The transparent bold lines in Fig. 2 (G to I) show the best fit to the following equationwhere C1 and C2 are the composition at each end of an EDS scan, zint is the center position of the interface, and L is the thickness of the compositional gradient from Si to Al. The fit of Eq. 1 indicates L values of 1.3 and 2.4 nm for ti = 1.0 and 2.0 nm, respectively. As shown in Fig. 2, some compositional fluctuations occur along the interfaces, especially for the sample with ti = 2.0 nm; thus, the value of L depends on both the size and position of the EDS signal-averaging window. The value of L determined in Fig. 2 should be regarded as an average thickness of the compositional gradient. It is known that Al and Si form a typical nonsolid solution combination at equilibrium. Few intermetallic compound or intermediate phases of these elements exist, although certain nonequilibrium states can form during the sputter deposition process at room temperature. Figure 2 (J and K) shows nanobeam electron diffraction patterns for 10-nm-thick Si and Al layers, respectively. A broad halo pattern from the amorphous structure of the Si layer is present, whereas dif-fraction spots corresponding to the polycrystalline nature of the Al layer appear in the high-resolution HAADF-STEM image in Fig. 2L.Electric current–induced spin torqueWhen an electric current is applied to the bilayer strip consisting of a nonmagnet (NM) and a ferromagnet (FM), part of the SC gener-ated in the NM is transmitted toward the FM followed by a spin torque applied on the magnetization of the FM. This torque is gener-ally referred to as a damping-like (DL) torque, τDL, whereas a sepa-rate spin torque known as the field-like (FL) torque, τFL, arises from the SC scattered at the NM/FM interface. The effect of these torques on a magnetization m produced by an SC with a polarization σs is described by the following equationComposition =C1 + C22±C2 − C12tanh( z−zintL)(1)Fig. 1. Green and rare metal–free composition gradient material for spin current generation. (A) Schematic illustration of the Stern-Gerlach experiment. Quantiza-tion of spin angular momentum σs was observed when a beam of silver atoms was split in two as it passed through a gradient of a static magnetic field B. (B) Schematic image of a fabricated Si/Al gradient material. The Cartesian coordinate system used throughout this article is also shown in (B). A nanometer-thick compositional gradient from Si to Al exists along the z axis with much more conductivity in the Al layer than the Si layer. When an electric current jc is applied along the x axis, an electric current vorticity ω = ∇ × jc appears, whose vector points along the y axis. The electron spin σs in the gradient material is polarized along the y axis by an emergent magnetic field because of the vortical electric current. As a consequence, the gradient of ω leads to a density gradient in the nonequivalent electron spin, which produces a spin current along the z axis. (C) Plot of relative elemental abundance in Earth’s crust. Si and Al represent the most abundant semiconductor and metal materials, respectively, while typical large-spin-current source materials such as Ta, W, and Pt are very rare.Downloaded from https://www.science.org at National Institute for Materials Science on May 11, 2025Horaguchi et al., Sci. Adv. 11, eadr9481 (2025)     9 May 2025S c i e n c e  A d v a n c e s  |  R e s e ar  c h  A r t i c l e3 of 7where ξDL and ξFL are the efficiencies of the DL and FL torques with respect to an electric current density jc, while e, μ0, and ℏ are the el-ementary charge, permeability of a vacuum, and the reduced Planck’s constant, respectively. Ms and dFM are the saturation mag-netization and FM thickness, respectively. Both these orthogonal torques play an important role in magnetization switching, which has been widely investigated in applications for nonvolatile magne-toresistive memory and magnetic logic devices.To evaluate the strength of the DL torque produced by applying an electric current to the sample, we conducted direct current (dc) Gilbert damping modulation of spin torque ferromagnetic reso-nance (ST-FMR) spectrum (15, 16, 18, 31–34). The theory of this technique is described in Supplementary Text S1. In the ST-FMR experiment, an alternating current was applied to the strip using a microwave with an amplitude of 20 dBm and a frequency of 20 GHz. The dc voltage Vdc because of the ST-FMR excitation was measured while sweeping the external field from 0 to 2.0 T. The measured spectrum in the absence of a dc is shown in Fig. 3A for ti = 0.5 nm, which can be reproduced by a combination of symmetric and anti-symmetric Lorentzian functions, as shown in Fig. 3B. When a dc Idc is applied simultaneously, a DL torque produced by the dc modu-lates the Gilbert damping of ferromagnetic resonance (15, 32). As shown in eq. S6, the linewidth of the ST-FMR spectrum, Δ, was changed as a function of Idc. Last, we can evaluate ξDL from the slope of the linear relation between Δ and Idc. It should be noted that an-other spin torque, i.e., the FL torque, does not contribute to the change in the linewidth at all.Figure 3C depicts the value of linewidth Δ of the ST-FMR spectra as a function of Idc in the range from −8 to 8 mA for the sample with ti = 0.5 nm. The linewidths were varied in proportion to Idc. From the curve fitting of Fig. 3C with eq. S6, we obtained ξDL = 0.66 ± 0.07, whose magnitude is comparable to the value measured for a Pt(10)/Ni95Cu5(10) bilayer film (ξDL  =  0.21 ± 0.01). Figure 3D shows ξDL as a function of ti. It is noted that the ξDL for the Pt/Ni95Cu5 bilayer is larger than the typical value of the spin Hall angle for Pt. Similar overestimation of ξDL has been commonly reported for W/CoFeB, Pt/CoFeB, and Pt/NiFe bilayers when the Gilbert damping modulation because of the dc current application is evalu-ated (35, 36). Here, we mainly discuss the influence of the composi-tional gradient interface between Si and Al on the relative change of ξDL. Compared to the sample without an Al/Si insertion layer (ti = 0 nm), samples with ti between 0.25 and 0.75 nm show a substantial en-hancement in ξDL. The sample with ti = 0.5 nm achieves a peak ξDL, approximately six times higher than that of the sample without the τ=τDL+τFL=ξDLjcℏ2e1μ0MsdFMm×(m×σs)+ξFLjcℏ2e1μ0MsdFMm×σs(2)Fig. 2. Microstructural and compositional characterization of gradients across the Si/Al interface. (A to C) HAADF-STEM images of samples with (A) ti = 2.0 nm, (B) 1.0 nm, and (C) 0.0 nm. (D to F) Enlarged views of the sample near the area analyzed by EDS. EDS profiles were generated from within the orange dashed boxes. (G to I) Averaged profiles of the atomic concentration of Si and Al for each sample along the arrows in each box. (J and K) Nanobeam diffraction patterns for Si and Al layers, re-spectively. (L) High-resolution HAADF-STEM image of the Al layer. Dashed lines indicate the grain boundaries.Downloaded from https://www.science.org at National Institute for Materials Science on May 11, 2025Horaguchi et al., Sci. Adv. 11, eadr9481 (2025)     9 May 2025S c i e n c e  A d v a n c e s  |  R e s e ar  c h  A r t i c l e4 of 7insertion layer. After this peak at ti = 0.5 nm, ξDL decreases steadily. For ti values exceeding 1.0 nm, we observed a modest increase in ξDL, potentially because of the segregation of Si or Al at the interface, as shown in Fig. 2D of the HAADF-STEM image. This segregation suggests a possible qualitative change in interfacial structure, al-though the precise mechanism remains under investigation. We also evaluated the FL torque (see Supplementary Text S2). Although pre-cision is limited, its trend is similar to that of the DL torque, with a notable peak at a 0.5-nm insertion layer. While further investigation into the origin of the FL torque is ongoing, our primary contribu-tion lies in demonstrating that the independently determined DL torque efficiency in the Si/Al gradient material is comparable to or surpasses that of the SHE in Pt, irrespective of the FL torque effi-ciency. This result represents a notable advancement in spin torque materials development and indicates a promising route for materials with enhanced spin torque properties.Origin of spin torque accompanied by Si/Al gradient materialsBelow, we discuss the origin of spin torque in the Si/Al/Ni95Cu5 trilayer film. Similarly to a torque generated via SHE and/or REE with an electric current along the x axis, the variations of Vs and Va with respect to the direction of the external magnetic field can be explained by assuming that the electron spin is polarized along the y axis (see Supplementary Text S3) (37–39). In the Si/Al/Ni95Cu5 trilayer film, most of the electric current flows not within the Si or Ni95Cu5 layer but in the Al layer because the electric conductivity of Al is much larger. However, the spin torque produced by the electric current flow in the Al layer via SHE can be ignored because the spin Hall angle for bulk Al is only 0.02 (8, 40), which is 33 times smaller than the value of ξDL in our sample with ti = 0.5 nm.One plausible explanation for the increase in ξDL is spin current generation via SVC (23, 24, 41). Because of conductivity differences between Si and Al, a nonuniform current forms in the nanometer-scale gradient layer. Supplementary Text S4 shows that the increase in ξDL correlates with SVC theory–based models. However, our simple model diverges as ti →  0 nm and thus does not directly apply at atomic scales. In addition, surface and interface scattering within the Al layer may produce nonuniform current, resulting in a gradient in current density and opposite vorticity signs between the top and bot-tom surfaces. This mechanism aligns with SVC and is consistent with prior studies on SVC in fluid systems (23). Atomic-scale interfacial disturbance caused by sputter deposition with a small ti increases electron scattering, altering the vorticity gradient distribution. The interplay between increased interfacial scattering and a reduced compositional gradient with increasing ti may produce a peak in spin torque efficiency at an optimum ti. The dependence of ξDL on ti could, in part, reflect this mechanism. To demonstrate SC generation via SVC, it is crucial to clarify how current distribution varies with ti.Furthermore, the nonmonotonic variation in ξDL for small ti val-ues may stem from the irregular interfacial mixing on Al and Si at atomic scales. Okano et al. (29) observed nonmonotonic spin cur-rent generation efficiency in oxidized Cu, attributed to variations in oxidation stages. Similar interfacial mixing behavior may apply here. Consequently, while SVC provides reasonable explanation mecha-nisms, further investigation is required to understand spin current generation mechanisms fully, including nonmonotonic variations.We must also consider the impact of inversion symmetry break-ing (ISB) at the Si/Al interface, as the REE and orbital-REE (42–47), both induced by ISB, can enhance spin torque. Increasing the inser-tion layer thickness expands the volume of the Si/Al compositional gradient interface but also blurs the interface, reducing the magni-tude of ISB. To discuss the ti dependence of spin torque efficiency, it is essential to account for these interactions. However, determining the ti dependence of ISB strength is challenging, as investigating the electronic structure of compositional gradient interfaces via first-principles calculations is not straightforward.Highly nonreciprocal SC generation in Si/Al gradient materialsIn the Si/Al gradient materials, we observe pronounced nonrecipro-cal conversion between electric current and SC, which has been re-ported in other gradient materials consisting of CuOx (29) and Ti/W (48). This nonreciprocity may represent a general characteristic of spin current generation in gradient structures and could offer valu-able insights into the underlying mechanisms of spin current gen-eration in these systems.To evaluate the conversion efficiency from SC to electric current, as shown in Supplementary Text S5, we measured the inverse SHE resulting from the SC (49, 50), which was produced by applying an alternating magnetic field (51–54). Figure 4A shows the conversion efficiency θjs→jc of the SC to an electric current as a function of ξDL, which is proportional to the conversion efficiency θjc→js from the charge current to the SC. In general, an SC source with a two-dimensional geometry, such as an interfacial SOI, suppresses θjs→jc rather than θjc→js by a factor of 5 or more (55, 56). If the SC source does produce such a geometrical effect in the Si/Al gradient mate-rial, the nonreciprocity is expected to be less than 5 because of its Fig. 3. ST-FMR experiment for evaluating electric current–induced spin torque. (A) ST-FMR spectrum measured for a Si/Al/Ni95Cu5 trilayer film with ti = 0.5 nm at a microwave frequency of 20 GHz. The dashed curve represents the best-fit result for a combination of symmetric and antisymmetric Lorentzian functions. (B) Symmetric (purple) and antisymmetric (blue) Lorentzian components included in (A). (C) FMR linewidth Δ as a function of dc current Idc for a sample with ti = 0.5 nm. The red and blue closed circles represent the results measured for a positive (φ = π∕4) bias magnetic field and a negative (φ = 5π∕4) bias magnetic field. Dashed lines indicate the results of linear fit. The vertical error bars indicate the standard deviation of 10 times measurements. (D) Damping-like torque efficiency ξDL as a function of ti. The vertical bars indicate the standard deviation of 20 times measurement. The closed circles indicate the ξDL values for samples with ti ranging from 0 to 2.0 nm. The dashed line shows the ξDL value measured for the Pt(10)/Ni95Cu5(10) bilayer.Downloaded from https://www.science.org at National Institute for Materials Science on May 11, 2025Horaguchi et al., Sci. Adv. 11, eadr9481 (2025)     9 May 2025S c i e n c e  A d v a n c e s  |  R e s e ar  c h  A r t i c l e5 of 7fuzzy interface. However, as shown in Fig. 4A, the sample with ti = 0.5 nm exhibits a ξDL ∕θjs→jc value larger than 5. On the other hand, ξDL ∕θjs→jc for ti = 0 nm is unity, at which the highest two-dimensional geometry is expected.One possible explanation for this pronounced nonreciprocity is SC generation from macroscopic vorticity in the electric current at the compositional gradient, mediated by SVC. The Berry curvature acts as an effective magnetic field, producing a spin-dependent force that is always perpendicular to the electron’s momentum because of isotropic scattering from SOI. This effect allows for reciprocal conver-sion between charge and spin currents regardless of the presence of an external electric field. In contrast to the Berry curvature, where the emergent magnetic field originating from the electron structure per-sists even when the electric field is zero, the emergent magnetic field in the SVC mechanism, which depends on current vorticity, vanishes when the electric field and current perpendicular to the conductance gradient are absent. The SVC mechanism relies on a vorticity gradient to generate spin-dependent forces directed along this gradient. When an in-plane charge current is applied, a vorticity gradient forms in the z-direction as illustrated in Fig. 1, creating spin-dependent forces along the z axis and thus enabling charge-to-spin conversion, as ob-served in the ST-FMR experiments. However, when a spin current is injected along the z axis, no in-plane charge current (or associated vorticity gradient) exists to produce spin-dependent forces, thereby preventing spin-to-charge conversion, as seen in the spin pumping experiments. The nonreciprocity observed in our study is, therefore, profoundly influenced by the presence of the vorticity gradient, which contributes to spin-dependent scattering, as well as the relative orien-tation between this gradient and the incident current.FOM for spin torque switching capability of Si/Al gradient materialsTo reduce the supply voltage required for spin torque switching, it is crucial to enhance the product of ξDL and the electrical conductivity σe of the NM layer. A higher σe also helps mitigate resistive-capacitive delays that can obstruct high-speed operation of integrated circuits. Figure 4B shows a double-logarithmic plot of ξDLσe versus σe for our Si/Al gradient samples. On the basis of these considerations, we de-fine a FOM for SC-generating materials asWe also include data for a Pt/Ni95Cu5 bilayer in Fig. 4B (see the closed square). The dependence of σe on the insertion-layer thick-ness ti is detailed in Supplementary Text S7. The dashed contours in Fig. 4B correspond to FOM = ξDLσ2e. By reducing ti from 2.0 to 0.5 nm in Si/Al gradient films, we can boost σe with increasing ξDLσe. This is unusual because strong-SOI materials (e.g., Pt, W, and Ta) typically show low σe. For ti = 0.5 nm, ξDLσ2e reaches 11.2 × 1012 (S/m)2, five times higher than the value for Pt.Furthermore, to assess power consumption in spin-orbit torque magnetic random-access memory, we use the formula from (57, 58)where s is the fraction of current shunted through the FM layer, de-rived from the resistivity ratio. Our measurements indicate that the write power for the sample with ti = 0.5 nm is less than 1∕10 that of Pt, demonstrating the exceptional energy efficiency of our Si/Al gradi-ent material. Consequently, they can serve as “green materials” for low-power applications.While our FOM emphasizes performance metrics, we also con-sider the relative abundance Pn of the constituent elements as an additional indicator of sustainability. According to the data in Fig. 1A, PSi/Al = PSi × PAl = 2.24 × 10−2, roughly seven orders of magnitude larger than that of Pt (5  ×  10−9). This highlights the potential of the Si/Al gradient for resource-friendly spintronic de-velopment. Crucially, the underlying mechanism driving spin current generation in these films does not rely on heavy-element spin-orbit coupling, broadening the design space for advanced, sustainable spin devices.DISCUSSIONIn this study, we explored an efficient charge-to-spin conversion mechanism in Si/Al compositional gradient materials, focusing on their potential for spintronic devices. By controlling the gradient width, we achieved a pronounced increase in spin torque efficiency (ξDL), highlighting how gradient optimization can facilitate spin current generation.A notable aspect of Si/Al gradient materials is their use of silicon and aluminum—two widely available, environmentally friendly ele-ments. While this benefit might be less critical for certain device FOM=(ξDLσe)×σe=[Spin torque efficiency]×[Circuit performance] (3)Pwrite ∝(1+ sξDL)2σ−1e (4)Fig. 4. Nonreciprocal conversion between charge and spin current and FOM for Si/Al gradient material. (A) Conversion efficiency from SC to charge current θjs→jc as a function of ξDL. The circles show data for samples with various ti’s, whereas the square represents values for a Pt(10)/Ni95Cu5(10) bilayer film. The vertical bars indicate the standard deviation calculated from the least-squares deviation of the fitting parameters used to calculate θjs→jc. (B) Double-logarithmic plot of electric conductivity σe and ξDLσe for samples with ti ranging from 0 to 2.0 nm. The numbers next to the plots represent the ti values in unit of nm. The data for a Pt(10)/Ni95Cu5(10) bilayer film are also plotted for comparison (square). Dashed lines are contours of ξDLσ2e.Downloaded from https://www.science.org at National Institute for Materials Science on May 11, 2025Horaguchi et al., Sci. Adv. 11, eadr9481 (2025)     9 May 2025S c i e n c e  A d v a n c e s  |  R e s e ar  c h  A r t i c l e6 of 7architectures that still rely on rare metals (e.g., in magnetic tunnel junctions), the introduction of Si/Al as a more “sustainable” mate-rial option broadens the landscape for spin current–based systems.Crucially, these materials generate spin currents without the heavy reliance on strong SOI, thus providing greater flexibility in device design. Our FOM analysis reveals that Si/Al gradient films can match—or even surpass—the performance of Pt-based struc-tures, not only in spin torque efficiency but also in energy efficiency. Measurements show a substantial reduction in write power relative to Pt, underscoring their potential for low-power spintronics.Looking forward, these findings suggest that compositional gra-dient strategies could be extended to other material systems. By le-veraging abundant elements like Si and Al, we present a promising pathway to high spin torque efficiency while maintaining an eye to-ward resource sustainability. This balance between performance and environmental consideration marks a promising direction for next-generation spintronic devices.MATERIALS AND METHODSSample preparationThe films were fabricated on thermally oxidized silicon substrates by magnetron sputtering at room temperature. The chamber base pres-sure before deposition was less than 5.0 × 10−4 Pa. The deposition pressure was 0.22 Pa with an argon (Ar) flow rate of 4.0 standard cubic centimeters per minute. The Al layer creation used radio fre-quency (RF) deposition at 13.56 MHz with a power density of 1.4 W/m2 and a deposition rate of 0.043 nm/s from a 99.9% pure Al target. The Si layer was deposited by RF sputtering with a power density of 3.5 W/m2 and a deposition rate of 0.062 nm/s from a Si target. The NiCu layer was deposited by dc sputtering with a power density of 1.4 W/m2 and a deposition rate of 0.2 nm/s from a 99.9% pure Ni95Cu5 alloy target. The SiO2 capping layer was deposited by RF sputtering with a power density of 3.5 W/m2 and a deposition rate of 0.044 nm/s from a 99.99% pure SiO2 target. The thin films were pat-terned into 10-μm-wide and 100-μm-long strips by photolithogra-phy and liftoff processes.An electrically shorted coplanar waveguide made from 70-nm-thick Au was connected to both ends of the strip to conduct the ST-FMR measurements. All measurements were conducted at room temperature.Electrical measurementsFor a dc Gilbert damping modulation of the ST-FMR spectrum, we applied 20-dBm continuous sinusoidal signals with a frequency of 20 GHz in the longitudinal direction (x axis) of the film by a signal generator. An in-plane external magnetic field was applied with an amplitude ranging from 0 to 2.0 T at a fixed angle of π/4 or 5π∕4 with respect to the x axis. For the linewidth modulation, we varied the dc in the range between −8 and 8 mA. We then measured the rectified dc voltage Vdc by a nanovoltmeter from a dc port of bias tee. The resulting spectra were fit by the expression Vdc = Vsfs(B) + Vafa(B), where fs(B) and fa(B) are the symmetric and antisymmetric Lorent-zian functions, respectively. The inverse SHE measurement used a general spin-pumping experiment setup. We applied a continuous sinusoidal signal with an amplitude of 20 dBm and a frequency of 5 GHz into the coplanar waveguide fabricated on the sample, which was patterned into a Hall-bar shape. The sample and coplanar wave-guide were insulated by the insertion of a 120-nm-thick SiO2 film. The external magnetic fields with amplitudes ranging from 0 to 2.0 T were applied in the x-y plane at an angle ranging between 0 and 2π from the x axis. The dc inverse spin Hall voltage was mea-sured using a nanovoltmeter.Electron microscopy characterizationWe prepared cross-sectional thin specimens for HAADF-STEM characterization using a focused ion beam with a Ga+ ion source on a FEI Helios G4 UX instrument. Before the milling process, a ∼5-nm-thick Au layer was deposited on the film surface to protect and enhance the conductivity of samples during milling. The lift-out lamellae were thinned to ∼100 nm at 30 kV with the current decreas-ing from 0.75 nA to 90 pA, followed by final polishing at 2 kV and 17 pA. HAADF-STEM and nanobeam electron diffraction images were obtained using a Cs-corrected FEI Titan G2 80-200 equipped with a Super-X EDS. The HAADF-STEM images were collected us-ing a convergence semiangle of 18 mrad and an inner-collection semiangle of 55 mrad. EDS mapping was performed using a Bruker Esprit analysis system with automatic drift correction during the collection process, which augments the reliability of the composi-tional analysis. Integrated line profiles were conducted across the heterostructure in EDS maps to enhance the signal-to-noise ratio. The Cliff-Lorimer analysis method was applied to quantify the EDS line-scan results.Supplementary MaterialsThis PDF file includes:Supplementary Text S1 to S7Table S1Figs. S1 to S8ReferencesREFERENCES AND NOTES  1. C . Chappert, A. Fert, F. N. Van Dau, The emergence of spin electronics in data storage. Nat. Mater. 6, 813–823 (2007).  2.  B. Tudu, A. Tiwari, Recent developments in perpendicular magnetic anisotropy thin films for data storage applications. Vacuum 146, 329–341 (2017).  3. L . Liu, C.-F. Pai, D. C. Ralph, R. A. Buhrman, Magnetic oscillations driven by the spin Hall effect in 3-terminal magnetic tunnel junction devices. Phys. Rev. Lett. 109, 186602 (2012).  4. V . E. Demicov, S. Urazhdin, H. Ulrichs, V. Tiberkevich, A. Slavin, D. Baither, G. Schmitz,  S. O. Demokritov, Magnetic nano-oscillator driven by pure spin current. Nat. Mater. 11, 1028–1031 (2012).  5.  Z. Duan, A. Smith, L. Yang, B. Youngblood, J. Lindner, V. E. Demidov, S. O. Demokritov,  I. N. Krivorotov, Nanowire spin torque oscillator driven by spin orbit torques. Nat. Commun. 5, 5616 (2014).  6.  J. E. Hirsch, Spin Hall effect. Phys. Rev. Lett. 83, 1834–1837 (1999).  7.  S. Zhang, Spin Hall effect in the presence of spin diffusion. Phys. Rev. Lett. 85, 393–396 (2000).  8.  S. O. Valenzuela, M. Tinkham, Direct electronic measurement of the spin Hall effect. Nature 442, 176–179 (2006).  9.  S. Maekawa, A flood of spin current. Nat. Mater. 8, 777–778 (2009).  10.  Y. K. Kato, R. C. Myers, A. C. Gossard, D. D. Awschalom, Observation of the spin Hall effect in semiconductors. Science 306, 1910–1913 (2004).  11. V . M. Edelstein, Spin polarization of conduction electrons induced by electric current in two-dimensional asymmetric electron systems. Solid State Commun. 73, 233–235 (1990).  12.  S. D. Ganichev, E. L. Ivchenko, V. V. Bel’kov, S. A. Tarasenko, M. Sollinger, D. Weiss,  W. Wegscheider, W. Prettl, Spin-galvanic effect. Nature (London) 417, 153–156 (2002).  13.  J. C. Rojas Sanchez, L. Vila, G. Desfonds, S. Gambarelli, J. P. Attane, J. M. De Teresa,  C. Magén, A. Fert, Spin-to-charge conversion using Rashba coupling at the interface between non-magnetic materials. Nat. Commun. 4, 2944 (2013).  14.  A. Manchon, H. C. Koo, J. Nitta, S. M. Frolov, R. A. Duine, New perspectives for Rashba spin–orbit coupling. Nat. Mater. 14, 871–882 (2015).  15. L . Liu, C.-F. Pai, Y. Li, H. W. Tseng, D. C. Ralph, R. A. Buhrman, Spin-torque switching with the giant spin Hall effect of tantalum. Science 336, 555–558 (2012).Downloaded from https://www.science.org at National Institute for Materials Science on May 11, 2025Horaguchi et al., Sci. Adv. 11, eadr9481 (2025)     9 May 2025S c i e n c e  A d v a n c e s  |  R e s e ar  c h  A r t i c l e7 of 7  16.  G. Allen, S. Manipaturuni, D. E. Nikonov, M. Doczy, I. A. Young, Experimental demonstration of the coexistence of spin Hall and Rashba effects in β-tantalum/ferromagnet bilayers. Phys. Rev. B 91, 144412 (2015).  17.  R. Yu, B. F. Miao, L. Sun, Q. Liu, J. Du, P. Omelchenko, B. Heinrich, W. Mingzhong, H. F. Ding, Determination of spin Hall angle and spin diffusion length in β-phase-dominated tantalum. Phys. Rev. Mater. 2, 074406 (2018).  18. C .-F. Pai, L. Liu, Y. Li, H. W. Tseng, D. C. Ralph, R. A. Buhrman, Spin transfer torque devices utilizing the giant spin Hall effect of tungsten. Appl. Phys. Lett. 101, 122404 (2012).  19.  Q. Hao, G. Xiao, Giant spin Hall effect and switching induced by spin-transfer torque in a W/Co40Fe40B20/MgO structure with perpendicular magnetic anisotropy. Phys. Rev. Appl. 3, 034009 (2015).  20.  W. Gerlach, O. Stern, Der experimentelle nachweis der richtung-squantelung im magneticfield. Z. Phys. 9, 349–352 (1922).  21.  W. Gerlach, O. Stern, Das magnetische moment des silber atoms. Z. Phys. 9, 353–355 (1922).  22.  M. Matsuo, Y. Ohnuma, S. Maekawa, Theory of spin hydrodynamic generation. Phys. Rev. B 96, 020401(R) (2017).  23.  R. Takahashi, M. Matsuo, M. Ono, K. Harii, H. Chudo, S. Okayasu, J. Ieda, S. Maekawa,  E. Saitoh, Spin hydrodynamic generation. Nat. Phys. 12, 52–56 (2016).  24. D . Kobayashi, T. Yoshikawa, M. Matsuo, R. Iguchi, S. Maekawa, E. Saitoh, Y. Nozaki, Spin current generation using a surface acoustic wave generated via spin-rotation coupling. Phys. Rev. Lett. 119, 077202 (2017).  25.  Y. Kurimune, M. Matsuo, S. Maekawa, Y. Nozaki, Highly nonlinear frequency-dependent spin-wave resonance excited via spin-vorticity coupling. Phys. Rev. B 102, 174413 (2020).  26.  S. Tateno, G. Okano, M. Matsuo, Y. Nozaki, Electrical evaluation of the alternating spin current generated via spin-vorticity coupling. Phys. Rev. B 102, 104406 (2020).  27. T he STAR Collaboration, Global Λ hyperon polarization in nuclear collisions. Nature 548, 62–65 (2017).  28.  H. Petersen, The fastest-rotating fluid. Nature 548, 34–35 (2017).  29.  G. Okano, M. Matsuo, Y. Ohnuma, S. Maekawa, Y. Nozaki, Nonreciprocal spin current generation in surface-oxidized copper films. Phys. Rev. Lett. 122, 217701 (2019).  30. T . An, B. Cui, L. Liu, M. Zhang, F. Liu, W. Liu, J. Xie, X. Ren, R. Chu, B. Cheng, C. Jiang, J. Hu, Enhanced spin current in Ni81Fe19/Cu-CuOx bilayer with top and sideways oxidation. Adv. Mater. 35, e2207988 (2023).  31. L . Liu, T. Moriyama, D. C. Ralph, R. A. Buhrman, Spin-torque ferromagnetic resonance induced by the spin Hall effect. Phys. Rev. Lett. 106, 036601 (2011).  32.  S. Kasai, K. Kondou, H. Sukegawa, S. Mitani, K. Tsukagoshi, Y. Otani, Modulation of effective damping constant using spin Hall effect. Appl. Phys. Lett. 104, 092408 (2014).  33.  O. Mosendz, V. Vlaminck, J. E. Pearson, F. Y. Fradin, G. E. W. Bauer, S. D. Bader, A. Hoffmann, Detection and quantification of inverse spin Hall effect from spin pumping in permalloy/normal metal bilayers. Phys. Rev. B 82, 214403 (2010).  34. C .-F. Pai, Y. Ou, L. H. Valelaleao, D. C. Ralph, R. A. Buhrman, Dependence of the efficiency of spin Hall torque on the transparency of Pt/ferromagnetic layer interfaces. Phys. Rev. B 92, 064426 (2015).  35.  S. Karimeddiny, D. C. Ralph, Resolving discrepancies in spin-torque ferromagnetic resonance measurements: Lineshape versus linewidth analyses. Phys. Rev. Appl. 15, 064017 (2021).  36. T .-Y. Chen, C.-W. Peng, W.-B. Liao, C.-F. Pai, “Characterization of spin-orbit torque efficiency in the RF regime for MRAM applications,” in 2021 IEEE International Symposium on Radio-Frequency Integration Technology (RFIT) (IEEE, 2021), pp. 1–6.  37.  M. Harder, Y. Gui, C. M. Hu, Electrical detection of magnetization dynamics via spin rectification effects. Phys. Rep. 661, 1–59 (2016).  38.  J. Sklenar, W. Zhang, M. B. Jungfleisch, H. Saglam, S. Grudichak, W. Jiang, J. E. Pearson,  J. B. Ketterson, A. Hoffmann, Unidirectional spin-torque driven magnetization dynamics. Phys. Rev. B 95, 224431 (2017).  39. T . Horaguchi, M. Matsuo, Y. Nozaki, Highly accurate evaluation of spin-torque efficiency by measuring in-plane angular dependence of spin-torque ferromagnetic resonance. J. Magn. Magn. Mater. 505, 166727 (2020).  40.  A. Hoffman, Spin Hall effects in metals. IEEE Trans. Magn. 49, 5172–5193 (2013).  41.  M. Matsuo, J. Ieda, K. Harii, E. Saitoh, S. Maekawa, Mechanical generation of spin current by spin-rotation coupling. Phys. Rev. B 87, 180402(R) (2013).  42. D . Go, D. Jo, T. Gao, K. Ando, S. Blügel, H.-W. Lee, Y. Mokrousov, Orbital Rashba effect in a surface-oxidized Cu film. Phys. Rev. B 103, L121113 (2021).  43.  A. Johansson, B. Göbel, J. Henk, M. Bibes, I. Mertig, Spin and orbital Edelstein effects in a two-dimensional electron gas: Theory and application to SrTiO3 interfaces. Phys. Rev. Res. 3, 013275 (2021).  44.  H. An, Y. Kageyama, Y. Kanno, N. Enishi, K. Ando, Spin–torque generator engineered by natural oxidation of Cu. Nat. Commun. 7, 13069 (2016).  45.  Y. Kageyama, Y. Tazaki, H. An, T. Harumoto, T. Gao, J. Shi, K. Ando, Spin-orbit torque manipulated by fine-tuning of oxygen-induced orbital hybridization. Sci. Adv. 5, eaax4278 (2019).  46. T . Gao, A. Qaiumzadeh, H. An, A. Musha, Y. Kageyama, J. Shi, K. Ando, Intrinsic spin-orbit torque arising from the Berry curvature in a metallic-magnet/Cu-oxide interface. Phys. Rev. Lett. 121, 017202 (2018).  47.  J. Kim, D. Go, H. Tsai, D. Jo, K. Kondou, H.-W. Lee, Y. Otani, Nontrivial torque generation by orbital angular momentum injection in ferromagnetic-metal/Cu/Al2O3 trilayers. Phys. Rev. B 103, L020407 (2021).  48.  H. Nakayama, T. Horaguchi, C. He, H. Sukegawa, T. Ohkubo, S. Mitani, K. Yamanoi,  Y. Nozaki, Spin-torque generation using a compositional gradient at the interface between titanium and tungsten thin films. Phys. Rev. B 107, 174416 (2023).  49. E . Saitoh, M. Ueda, H. Miyajima, G. Tatara, Conversion of spin current into charge current at room temperature: Inverse spin-Hall effect. Appl. Phys. Lett. 88, 282509 (2006).  50.  H. Zhao, E. J. Loren, H. M. van Driel, L. Smirl, Coherence control of Hall charge and spin currents. Phys. Rev. Lett. 96, 246601 (2006).  51.  Y. Tserkovnyak, A. Brataas, G. E. W. Bauer, Enhanced Gilbert damping in thin ferromagnetic films. Phys. Rev. Lett. 88, 117601 (2002).  52.  H. L. Wang, C. H. Du, Y. Pu, R. Adur, P. C. Hammel, F. Y. Yang, Scaling of spin Hall angle in 3d, 4d, and 5d metals from Y3Fe5O12/metal spin pumping. Phys. Rev. Lett. 112, 197201 (2014).  53.  K. Ando, S. Takahashi, J. Ieda, Y. Kajiwara, H. Nakayama, T. Yoshino, K. Harii, Y. Fujikawa,  M. Matsuo, S. Maekawa, E. Saitoh, Inverse spin-Hall effect induced by spin pumping in metallic system. J. Appl. Phys. 109, 103913 (2011).  54. E . Shikoh, K. Ando, K. Kubo, E. Saitoh, T. Shinjo, M. Shiraishi, Spin-pump-induced spin transport in p-type Si at room temperature. Phys. Rev. Lett. 110, 127201 (2013).  55.  P. Deorani, J. Son, K. Banerjee, N. Koirala, M. Brahlek, S. Oh, H. Yang, Observation of inverse spin Hall effect in bismuth selenide. Phys. Rev. B 90, 094403 (2014).  56.  Y. Wang, P. Deorani, K. Banerjee, N. Koirala, M. Brahlek, S. Oh, H. Yang, Topological surface states originated spin-orbit torques in Bi2Se3. Phys. Rev. Lett. 114, 257202 (2015).  57. L . Zhu, R. A. Buhrman, Maximizing spin-orbit-torque efficiency of Pt/Ti multilayers: Trade-off between intrinsic spin hall conductivity and carrier lifetime. Phys. Rev. Appl. 12, 051002 (2019).  58. L . Zhu, D. C. Ralph, R. A. Buhrman, Maximizing spin-orbit torque generated by the spin Hall effect of Pt. Appl. Phys. Rev. 8, 031308 (2021).  59.  P. M. Haney, H.-W. Lee, K.-J. Lee, A. Manchon, M. D. Stiles, Current induced torques and interfacial spin-orbit coupling: Semiclassical modeling. Phys. Rev. B 87, 174411 (2013).  60. T . Seki, Y.-C. Lau, S. Iihama, K. Takanashi, Spin-orbit torque in a NiFe single layer. Phys. Rev. B 104, 094430 (2021).  61.  M. Aoki, E. Shigematsu, R. Ohshima, T. Shinjo, M. Shiraishi, Y. Ando, Anomalous sign inversion of spin-orbit torque in ferromagnetic/nonmagnetic bilayer systems due to self-induced spin-orbit torque. Phys. Rev. B 106, 174418 (2022).  62.  A. Brataas, G. E. W. Bauer, P. J. Kelly, Non-collinear magnetoelectronics. Phys. Rep. 427, 157–255 (2006).Acknowledgments: We thank J. Uzuhashi for transmission electron microscopy observation. Funding: This work was supported by the following: JSPS KAKENHI Grant in Aid for  JSPS Fellows (19J21785 and 24KJ1955); Grant in Aid for Young Scientists (Start-up)  (22K20359); Grants in Aid for Scientific Research (20H01863, 21H04565, 24H00322, and 24H02233); Core Research for Evolutional Science and Technology, Japan Science and Technology Agency (JPMJCR19J4); The Priority Program of the Chinese Academy of Sciences, grant no. XDB28000000; and Spintronics Research Network of Japan (Spin RNJ). Author contributions: T.H. and Y.N. planned the study and wrote the manuscript. T.H. performed film deposition and fabricated the devices. C.H. and T.O. performed the microscopy experiments. T.H. and H.N carried out the measurements and analyzed the data with the help of Z.W., K.Y., S.M., H.S., and Y.N. T.H., J.F., M.M., and Y.N. performed the numerical calculation based on SVC theory. All the authors discussed the results and commented on the manuscript. Competing interests: The authors declare that they have no competing interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials.Submitted 24 July 2024 Accepted 7 April 2025 Published 9 May 2025 10.1126/sciadv.adr9481Downloaded from https://www.science.org at National Institute for Materials Science on May 11, 2025 Nanometer-thick Si/Al gradient materials for spin torque generation INTRODUCTION RESULTS Fabrication and structural analysis of Si/Al gradient materials Electric current–induced spin torque Origin of spin torque accompanied by Si/Al gradient materials Highly nonreciprocal SC generation in Si/Al gradient materials FOM for spin torque switching capability of Si/Al gradient materials DISCUSSION MATERIALS AND METHODS Sample preparation Electrical measurements Electron microscopy characterization Supplementary Materials This PDF file includes: REFERENCES AND NOTES Acknowledgments