Nonmagnetic Nanostructures for the Electrical

Letter pubs.acs.org/NanoLett

Ferromagnetic/Nonmagnetic Nanostructures for the Electrical Measurement of the Spin Hall Effect Van Tuong Pham,†,‡ Laurent Vila,*,†,‡ Gilles Zahnd,†,‡ Alain Marty,†,‡ Williams Savero-Torres,†,‡ Matthieu Jamet,†,‡ and Jean-Philippe Attané*,†,‡ †

CEA, INAC, SPINTEC, 17 avenue des Martyrs, 38054, Grenoble, France Université Grenoble Alpes, F-38000, Grenoble, France

‡

S Supporting Information *

ABSTRACT: Spin−orbitronics is based on the ability of spin−orbit interactions to achieve the conversion between charge currents and pure spin currents. As the precise evaluation of the conversion efficiency becomes a crucial issue, the need for straightforward ways to observe this conversion has emerged as one of the main challenges in spintronics. Here, we propose a simple device, akin to the ferromagnetic/nonmagnetic bilayers used in most spin−orbit torques experiments, and consisting of a spin Hall effect wire connected to two transverse ferromagnetic electrodes. We show that this system allows probing electrically the direct and inverse conversion in a spin Hall effect system and measuring both the spin Hall angle and the spin diffusion length. By applying this method to several spin Hall effect materials (Pt, Pd, Au, Ta, W), we show that it represents a promising tool for the metrology of spin−orbit materials. KEYWORDS: Spintronics, spin−orbitronics, spin Hall effect, nanowire devices

P

nonmagnetic channel is required to transfer the spins from the source to the detector,3,22−24 which multiplies interfaces and thus render delicate the quantitative extraction of the conversion rate. In this Letter, we propose a simple way to probe electrically the direct and inverse conversion in SHE systems, using a system akin to the ferromagnetic/nonmagnetic bilayers used in most spin−orbit torque experiments.10,11 By applying it to several SHE materials, and by demonstrating that it allows to measure both the spin Hall angle and the spin diffusion length, we show that this method represents a promising tool for the metrology of SO materials. The spin-charge conversion device proposed here is illustrated in Figure 1a and consists simply of a SHE wire connected to two transverse ferromagnetic electrodes. The device is designed so that the easy axis of magnetization is parallel to the ferromagnetic electrodes. Two electrical measurement schemes can be used. The first one, shown in Figure 1a and b, corresponds to the measurement of the direct SHE. The charge current flowing in the SHE wire generates a spin accumulation at the top surface of the SHE material, which is probed using the ferromagnetic electrodes. The second measurement scheme, shown in Figure 1c, corresponds to the inverse SHE. The flow of a charge current along the

ure spin currents correspond to the case of spin up and spin down electrons in equal number, flowing in opposite directions so that there is a transfer of angular momentum without overall charge current flow. Spin−orbit (SO) interactions can be used to achieve the conversion between charge currents and pure spin currents: the direct (charge to spin) or inverse (spin to charge) conversions can occur by spin Hall Effect (SHE) in the bulk of metals,1−3 semiconductors,4,5 and superconductors,6 by the Rashba effect in 2D electron gas7,8 or in topological insulators.9 The angular momentum carried by pure spin currents can be used to excite or to switch the magnetization, 10,11 and the promising use of SO interactions in spintronics has given birth to an expending field of research, the spin−orbitronics.12,13 The charge to spin conversion induced by SO effects can be observed using optical methods5,14,15 and ferromagnetic resonance techniques.8,16,17 Large efforts have also been devoted to develop purely electrical ways of detecting the conversion, primarily for the sake of simplicity and versatility, but also because the long-term objective is to implement SO effects into spintronic nanodevices. Direct ways to probe the conversion electrically are the H-shaped double Hall cross18,19 or the method proposed by Garlid et al.,20 but it remains limited to materials with long spin-diffusion lengths (e.g., semiconductors), which are generally associated with low conversion rates. The insertion of SO materials in lateral spin valves also allows observing the conversion in systems with large SO coupling, such as SHE heavy metals3 or Rashba interfaces.8,21 However, the nanodevice remains complex: a © XXXX American Chemical Society

Received: June 8, 2016 Revised: September 12, 2016

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DOI: 10.1021/acs.nanolett.6b02334 Nano Lett. XXXX, XXX, XXX−XXX

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Figure 2. Examples of SHE and ISHE signals in a Pt-based device, probed using CoFe electrodes (a and b) and NiFe electrodes (c and d). The SHE and ISHE measurement configurations correspond to Figure 1b and c, respectively. The Pt wire is 7 nm thick, and 400 nm wide (a and b) or 300 nm wide (c and d). The ferromagnetic electrodes are 15 nm thick and 50 nm wide. The electrodes are deposited on top of the SHE wire. The vertical arrows depict the magnetic state of the two ferromagnetic electrodes. The horizontal arrows indicate the field sweep direction.

1a. If the magnetization of a ferromagnetic electrode is along +X (or −X), the Fermi level of the electrode aligns with the electrochemical potential of the majority spins (or minority spins, respectively). When the magnetizations of the electrodes are parallel, there is no voltage difference between the electrodes, which are probing the same electrochemical potential. However, when they are antiparallel a voltage difference appears, corresponding to the difference between the spin-up and spin-down electrochemical potentials. This voltage is positive for positive fields, where the electrodes are in the head-to-head magnetic configuration. For negative fields, the antiparallel state is the tail-to-tail configuration; the electrodes now probe the opposite spins, and thus the measured difference of electrochemical potentials becomes negative. Note that, in this CoFe/Pt device, the amplitude of the spin signal is 8.0 ± 0.5 mΩ. This has to be compared to typical SHE signals measured in lateral spin valves, which are of the order of 0.1 mΩ or lower (i.e., 2 orders of magnitude smaller3,22−24) because of the spin relaxation in the channel and at the interfaces. The spin signal obtained in the ISHE configuration is shown in Figure 2b. Apart from the sign, which depends only on how the voltmeter is set up, it is similar to what is obtained in the SHE measurement, with exactly the same spin signal amplitude. The equivalence of the SHE and ISHE measurements, predicted by the Onsager reciprocal relations, has been verified in all our samples. The case of the ISHE configuration can be understood by considering that when the magnetizations of the electrodes are antiparallel, a spin current is injected in the SHE material. This spin current is then converted into a voltage by ISHE. For negative fields, and in the antiparallel configuration, the spin current is still injected, but its spin direction is reversed, which leads to a change of sign of the ISHE voltage. Figure 2c and d corresponds to the SHE and ISHE signals when using Ni81Fe19 electrodes instead of CoFe. The observed behavior is identical, although with a lower spin signal

Figure 1. (a) Measurement principle and scheme of the conversion device. Two ferromagnetic electrodes are connected on top of a SHE nanowire. The magnetization within the ferromagnetic electrodes, represented by black arrows, is along the X direction. A charge current Jc flows along SHE wire (in the Y direction), and generates a spin current Js along the Z direction, as down-spin and up-spin electrons are deflected along the positive and negative Z direction, respectively. Consequently, a spin accumulation appears at the edges of the SHE wire, which can be probed by the ferromagnetic electrodes. (b and c) SEM images of the device, with schemes of the measurement setup for the SHE (b) and ISHE (c) detections.

ferromagnetic electrodes induces the injection of a spin current within the SHE wire. This spin current is then converted by ISHE in a charge current along the SHE wire, so that in the open circuit conditions used here this generates a voltage between the two ends of the SHE wire. An example of spin signal obtained in the SHE configuration is given in Figure 2a, using a device with a Pt wire and Co60Fe40 electrodes. The ratio RSHE between the measured voltage and the constant applied current is measured as a function of the magnetic field applied along the X-axis, which corresponds to the easy axis of the ferromagnets, and thus to the quantification axis. The CoFe electrodes are designed so that they possess different switching fields. The variations of the resistance in the loop are due to the magnetization switching of the electrodes. This can be understood as follows: at any point of the SHE material, the relationship between the local charge current and local pure spin current is,1 JS = ΘSHEJC × s

(1)

where JC, JS, and s denote the charge and spin current density vectors, and the spin-polarization vector of the spin current, respectively. This leads to a spin accumulation at the surface, with majority spins along the X direction as illustrated in Figure B

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Nano Letters amplitude that we attribute to the fact that the effective spin polarization of CoFe is higher.25 The eventuality of being misled by an artifact has been studied carefully. One might expect that parasitic effects such as extraordinary Hall effect (EHE), anisotropic magnetoresistance, or thermal-related effects such as spin Nernst and spin Seebeck could appear in this configuration.26 In CoFe, the EHE is small, but nonetheless leads to the appearance of a signal with the same symmetry. As shown in the Supporting Information (SI), it is possible to calculate the contribution due to EHE, and the SHE contribution is found to be dominant in systems with high spin hall angles. In a control experiment using Ti, which is a light metal in which the SHE is negligible, the observed signal is found to be equal to the calculated EHE contribution (cf. SI). In this study, we took the EHE contribution into account to extract the exact value of the spin Hall angle (cf. Methods). Also, the anisotropic magnetoresistance and the planar Hall effect can be large in NiFe. In our experiments it can lead to an additional contribution that is symmetric in field, which disappears when the field is well-aligned with the ferromagnetic electrodes axis. We also show in the SI that thermal effects can be neglected. Finally, the normal Hall effect could lead to the appearance of a signal with the same symmetry, as in the antiparallel configuration the stray field produced in the SHE material by the ferromagnetic electrodes possess a component along Z. However, this stray field remains localized at the vicinity of the electrodes tips, and estimations of this effect show that it remains much smaller than the SHE (see SI). Lots of efforts have been recently devoted to develop an accurate measurement method of the spin transport parameters of SHE materials, i.e., the spin diffusion length λ and the spin Hall angle ΘSHE. To extract these parameters from our experiments, numerical finite elements method (FEM) simulations have been performed, using a two-current drift diffusion model (see Methods), and taking into account the presence of the EHE in the ferromagnetic electrodes. Figure 3 presents the main results of these simulations. Figure 3a shows that in the ISHE configuration the current lines are deflected into the SHE material. The corresponding spin accumulation μ for the parallel and antiparallel states are shown in Figure 3b and c, respectively. In both cases, a gradient of the electrochemical potential appears where the current gets into or out of the SHE wire. This gradient, which corresponds to a spin current, possesses a component along the Z direction. As the magnetization is along X, the ISHE generates a charge current density along the Y direction that will be detected by the voltmeter. In the parallel magnetization state (Figure 3b), the spin accumulations are of opposite signs, so that the generated current densities cancel out. In the antiparallel state (Figure 3c), the spin accumulations are symmetric, the ISHE generated current densities add up, and as seen in the experiments a voltage difference appears between the ends of the SHE wire. Figure 3d shows the spin accumulation in the SHE configuration, when the charge current flows along the SHE wire. The ferromagnetic electrodes are in contact with the spin accumulation that takes place at the top surface of the SHE wire. In the antiparallel state of magnetization, a voltage difference appears between the two ferromagnetic electrodes, which probe different electrochemical potentials. In order to deepen the understanding of the spin-charge conversion in this device, we derived an analytical expression, obtained in the framework of a 1D spin diffusion model (details

Figure 3. Results of 3D FEM simulations for ISHE are presented in panels a, b, and c. Panel a is a cross section of the device along the XZ plane, showing the geometry of the current lines. The current flows from the ferromagnetic electrode to the SHE wire and then to the second electrode (along X direction). Note that the current circumvents the lateral edges of the SHE wire, which are supposed to be insulating (previous transport experiments indeed showed that the interfaces that are not etched during our nanofabrication process remain insulating). Panels b and c are cross sections showing the spin accumulation μ (i.e., half the difference between electrochemical potentials). The spin current is proportional to the gradient of this spin accumulation. In our ISHE measurement setup we are only sensitive to the Z component of the spin current. In the parallel case (b), the spin accumulation pattern is antisymmetric, and the Z component of the spin current is in average equal to zero. In the antiparallel case (c), the spin accumulation pattern is symmetric, the Z component of the spin current is nonzero, which leads to the appearance of an ISHE signal. (d) Results of 3D FEM simulations for the SHE configuration. The charge current is applied along the SHE wire (Y direction) and induces a pure spin current along the Z direction. The resulting spin accumulation at the top surface of the SHE material is then probed by the ferromagnetic electrodes and leads to a voltage difference only in the antiparallel case. The figures illustrate the case for a Pt\CoFe device. As all the equations used for the simulations are linear, the voltage values correspond to an injected current arbitrarily set at 1 A. The dimensions are shown in panel b.

of the derivation are given in Section S1 of Supplementation Information). The amplitude of the spin signal varies according to eq 1: ΔR SHE/ISHE =

×

ΔV = I

1 ρN λN

(1 −

1 tanh(hN /λN) ρN λN

2pF ΘSHEλN

(

hN ρN

+

hF ρF

)w

1 cosh(hN / λN)

+

N

−

hF g ρF

)

1 tanh(hF /λF) ρF*λF

(2)

where wN/F, hN/F, and g are the widths, the thicknesses of the nanowires, and the gap between the electrodes, and pF, λ and ρ are the spin polarization, spin diffusion length, and resistivity, respectively. Subscripts F and N correspond to the ferromagnetic and nonferromagnetic layers, respectively. Note that it is also possible to add to this 1D model the contribution of the EHE in the electrodes (see Supporting Information), C

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spread in the literature between 1.2 and 12.0 nm, it is difficult to claim good agreement with previously reported values).3,23,27−30 Note however that the value of ρPtλPt = 0.84 ± 0.17 fΩ·m2 is close to what has been measured in several recent studies; for example, the values of 0.77, 0.63, 0.61, and 0.80 fΩ· m2 are shown in refs 27−30, respectively. Figure 4a also exhibits the expected variations of spin signal according to the 3D numerical simulations. Simulations were realized with varying Pt thicknesses. If we assume that λPt = 3.0 nm, the calculated curves reproduce the experimentally observed behavior for a value of the spin Hall angle of ΘSHE = 19%. For the 1D model, if we assume again that λPt = 3.0 nm, the best ΘSHE value to reproduce the experimentally observed behavior is around 10%. The proposed method for studying the spin to charge conversion has been applied to several other SHE systems: Pd, Au, Ta, and W. The main results are summarized in Table 1 and in Figure 4b. The observed spin signals in those systems are similar to those observed in the NiFe/Pt and CoFe/Pt systems. In particular, we observe a decrease of the spin signal amplitude with the width of the SHE wire wN (Figure 4b). This can be understood by considering the SHE configuration: the spin accumulation at the top surface depends on the current density. For a given applied current, the current density and thus the signal will decrease when increasing the channel width. This can be expected from the wN dependence in eq 2. For Ta samples, and despite trials with numerous nanofabrication processes and geometries, the obtained magnetoresistances are flat with a relatively large noise (± 2.0 mΩ). As the device resistance is reproducible from sample to sample, our interpretation is that the EHE and SHE contributions roughly cancel out, so that the signal is smaller than the noise. This assumption, that has to be taken cautiously, leads to a SHE angle of −2.7%, with a large error bar of 3%. As expected from previous studies, the spin Hall angle is smaller for Pd than for Pt3 and is even smaller for Au.30 The values of λN for Ta and W have been taken from studies where the materials possess similar resistivities32,31 (and similar growth conditions for W). Although reports have been made of a large negative spin Hall angle in Ta,10 we find here a negative but relatively small SHE angle (−2.7%), in agreement with recent measurements using lateral spin-valves, spin pumping or spin Hall magnetoresistance.3,32 The spin Hall angle in the W sample (−6.5%) is clearly negative and larger than that of Ta. Note that, for those two materials, the 1D model is inaccurate and has to be considered as not applicable: the comparison between 1D and 3D calculations shows that when ρN is too large the 1D model overestimates the EHE

even though comparison with 3D simulations show that the 1D model overestimate the EHE contribution for SHE materials with high resistivities. In eq 2, the spin signal amplitude is found to be linear in ΘSHE. If the spin diffusion length λN is also unknown, it is possible to extract it by studying the dependence of the spin signal with the thickness of the SHE layer hN. This study has been done for the Pt\CoFe system. Figure 4a and b shows the

Figure 4. (a) Spin signal amplitude vs Pt thickness in devices with CoFe electrodes: experimental results (symbols), 3D FEM simulations (dashed lines, calculated with λPt = 3.0 nm and ΘSHE = 19%), and 1D analytical model (solid lines, calculated with λPt = 3.0 nm and ΘSHE = 10%). The dependences are plotted for various channel widths. The maximal spin signal shall appear at a Pt thickness equal to two times the spin diffusion length. (b) Measured spin signal amplitude vs channel width, for different materials. The sign of the reported signal corresponds to the sign of the spin Hall angle of the SHE material. Experimentally, the sign of the measured voltage actually depends on the stacking order (i.e., F/N versus N/F stacks) and of the ISHE or DSHE measurement setup.

experimental dependence of the spin signal amplitude on the Pt thickness. According to eq 2, a maximum of the spin signal amplitude appears for hN ∼ 2λN, which leads to λPt = 3.0 ± 0.6 nm (note that as the spin diffusion length values of Pt are Table 1. Extracted Material Parametersa system

λF (nm)

λN (nm)

ρF (μΩ·cm)

ρN (μΩ·cm)

pF

ΘEHE (%)

NiFe/Pt CoFe/Pt CoFe/Pd CoFe/Au CoFe/Ta CoFe/W

3.525 3.525 3.525 3.525 3.525 3.525

3.0 ± 0.6 3.0 ± 0.6 133 3530 1.832 1.431

30 20.5 20.5 20.5 20.5 20.5

28 28 21 4.2 200 135

0.2625 0.5825 0.5825 0.5825 0.5825 0.5825

0.32 0.63 0.63 0.63 0.63 0.63

ΘSHE (1D-analytical) (%) 4.6 10.0 4.0 2.5

± ± ± ±

0.5 0.5 0.5 0.3

ΘSHE (3D-FEM) (%) 7.5 19 4.5 1.5 −2.7 −6.5

± ± ± ± ± ±

0.5 0.5 0.5 0.3 3.0 1.0

a

The polarization and the spin diffusion length of the ferromagnetic materials have been taken from the literature on electrical transport in lateral spin valves. The error bars on ΘSHE do not take into account the uncertainty on the values of λF, λN, and pF and are only related to the experimental uncertainty of the proposed technique (noise level and reproducibility from device to device). D

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Nano Letters contribution, since the lateral spread of the current is not taken into account in the 1D model. Even for Pt, which is considered to be the reference SHE material, the measurement of spin Hall angles remains an important metrology problem,27 which underlines the need for new measurement tools such as the method proposed here. For instance, the importance of interfacial effects can be observed when comparing NiFe(25)/Pt(10) and NiFe(25)/Cu(3)/ Pt(10) samples in Figure 4b. If all interfaces were transparent to the spin current, and as the sheet resistance of the sample with the Cu layer is 24% smaller (3.9 Ω/sq vs 5.1 Ω/sq), the sample with Cu should have a 24% smaller signal. This is in contrast with the observation shown in Figure 4b of a slight enhancement of 17% with less than 10% of the error margin (in average) of the signal for the samples having the insertion of the Cu layer in between NiFe and Pt. These results underline the role of the interface, that can be responsible for spin reflection33 and/or to spin relaxation,29 especially in the NiFe/ Pt system.33,34 The proposed device could help investigating these effects, using different material combinations and different insertion layers. In this study, as interface effects are not taken into account in our data analysis, the calculated values of SHE angles have to be understood as effective values, i.e., taken as lower bounds of the intrinsic values. In conclusion, we have proposed a simple electrical device in which it is possible to realize the conversion between charge and spin currents by SHE. The observed behavior can be reproduced roughly using a 1D-analytical model and more precisely using 3D-FEM simulations. We showed that it allows to extract the spin-dependent transport properties of the SHE material. Beyond its relative simplicity, the main interest of the proposed method is that the interconversion between spin and charge currents is done using a device akin to the ferromagnetic/nonmagnetic bilayers on which most spin− orbit torques experiments rely. In standard spin−orbit torque experiments the produced spin current is observed indirectly, through its effect on magnetization. The proposed technique should thus help shedding light in the role of the SHE in spin− orbit torques. Finally, the same design could in principle be used to study the conversion in Rashba materials7,8 and in topological insulators.9 The samples have been fabricated by conventional e-beam lithography, e-gun deposition, and lift-off processes on thermally oxidized SiO2 substrates. In most cases, the SHE nanowire is patterned before the ferromagnetic electrodes. A nucleation pad is patterned at the end of one of the ferromagnetic electrodes, so that the ferromagnetic electrodes have different switching fields. The transport measurements were performed using a lock-in amplifier working at 352 Hz, with an applied current of 100 or 200 μA. The resistivities of the different materials and the EHE angles of the ferromagnetic materials have been measured using patterned Hall crosses (cf. Table 1). The FEM simulations were carried out within the framework of a two spin-current drift diffusion model,35 with collinear magnetization of the electrodes along the easy axis of the ferromagnetic wires. For a magnetization axis along X, the current densities for spin up and spin down electrons can be written:

J↑⃗ / ↓

⎛1 0 0 ⎞ ⎜ ⎟ ±ΘSHE ⎟ 1 ± p ∇⃗μ 1 = ⎜0 ↑/↓ ⎜ ⎟ 2ρ 1 ⎠ ⎝ 0 ∓ΘSHE

Jc⃗ = J↑⃗ + J↓⃗

(3) (4)

⃗ and μ↑/↓ are the current densities and electrowhere J↑/↓ chemical potentials of spin up and down electrons, respectively. Equations 3 and 4 imply that in the ferromagnet the extraordinary Hall angle is ΘEHE = pFΘFSHE, where ΘFSHE is the spin Hall angle of the ferromagnetic materials. In the SHE material, the polarization in eq 3 is zero. Apart from the nonetched lateral edges of the SHE wire, the ferromagnet/normal metal interfaces are assumed to be transparent, without spin memory loss (i.e., the probability of spin flip events at the interface is null), and thus the electrochemical potentials are continuous along the entire device. The boundary conditions are of Neumann type and account for the current imposed to the device at the contact interfaces. The simulations were done using the free softwares GMSH36 for geometry construction, mesh generation, and postprocessing, and with the associated solver GETDP.37 The wires and the channel were taken long enough (i.e., more than 3 times the spin diffusion length in the considered material, and much larger than the nanowire widths) so that the spin accumulation vanishes at their ends. In the 3D FEM simulations, the polarization and the spin diffusion length of the ferromagnetic materials are taken from the literature and our own results on electrical transport in lateral spin-valves (cf. Table 1 for references). The spin diffusion lengths of the SHE materials are either measured (Pt) or taken from the literature. The resistivities and the AHE have been measured directly on hall crosses patterned close to the devices, so that finally the only free parameter of the FEM simulations is the spin Hall angle. The extracted spin Hall angle is the value that reproduces the observed spin signal amplitude. The derivation of the 1D analytical calculation is shown in the Supporting Information.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.6b02334. Development of two 1D analytical models: the first one describing the spin current/charge current conversion by ISHE, and the second one calculating the contribution of the EHE to the signal; discussion on the questions of spincaloritronic effects and of the normal Hall effect; results of the experiments on Ta and Ti (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (L.V.). *E-mail: [email protected] (J.-P.A.). Fax: (33) 4 38 78 21 27. Author Contributions

J.P.A. and L.V. planned and managed the project. V.T.P. performed the experiments, with the help of L.V., G.Z., A.M., W.S.T., M.J., and J.P.A. Simulations were made by V.T.P. and by A.M., who proposed the original experiment. Finally, V.T.P., E

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(19) Hankiewicz, E. M.; et al. Manifestation of the spin Hall effect through charge-transport in the mesoscopic regime. Phys. Rev. B: Condens. Matter Mater. Phys. 2004, 70 (24), 24130. (20) Garlid, E. S.; Hu, Q. O.; Chan, M. K.; Palmstrøm, C. J.; Crowell, P. A. Electrical measurement of the direct spin Hall effect in Fe/In x Ga 1− x As heterostructures. Phys. Rev. Lett. 2010, 105, 156602. (21) Isasa, M.; Martínez-Velarte, M. C.; Villamor, E.; Morellón, L.; De Teresa, J. M.; Ibarra, M. R.; Vignale, G.; Chulkov, E. V.; Krasovskii, E. E.; Hueso, L. E.; Casanova, F. Detection of inverse Rashba-Edelstein effect at Cu/Bi interface using lateral spin valves. arXiv preprint arXiv:1409.8540, 2014. (22) Niimi, Y.; Kawanishi, Y.; Wei, D. H.; Deranlot, C.; Yang, H. X.; Chshiev, M.; Valet, T.; Fert, A.; Otani, Y. Giant spin Hall effect induced by skew scattering from bismuth impurities inside thin film CuBi alloys. Phys. Rev. Lett. 2012, 109, 156602. (23) Kimura, T.; Otani, Y.; Sato, T.; Takahashi, S.; Maekawa, S. Room-temperature reversible spin Hall effect. Phys. Rev. Lett. 2007, 98, 156601. (24) Wei, D. H.; Niimi, Y.; Gu, B.; Ziman, T.; Maekawa, S.; Otani, Y. The spin Hall effect as a probe of nonlinear spin fluctuations. Nat. Commun. 2012, 3, 1058. (25) Zahnd, G.; Vila, L.; Pham, T. V.; Marty, A.; Laczkowski, P.; Torres, W. S.; Beigné, C.; Vergnaud, C.; Jamet, M.; Attané, J. P. Comparison of the use of NiFe and CoFe as electrodes for metallic lateral spin-valves. Nanotechnology 2016, 27, 035201. (26) Bauer, G. E.; Saitoh, E.; van Wees, B. J. Spin caloritronics. Nat. Mater. 2012, 11, 391−399. (27) Nguyen, M.-H.; Ralph, D. C.; Buhrman, R. A. Spin torque study of the spin Hall conductivity and spin diffusion length in platinum thin films with varying resistivity. Phys. Rev. Lett. 2016, 116, 126601. (28) Liu, Y.; Yuan, Z.; Wesselink, R. J. H.; Starikov, A. A.; van Schilfgaarde, M.; Kelly, P. J. Direct method for calculating temperature-dependent transport properties. Phys. Rev. B: Condens. Matter Mater. Phys. 2015, 91, 220405. (29) Rojas-Sánchez, J. C.; Reyren, N.; Laczkowski, P.; Savero, W.; Attané, J. P.; Deranlot, C.; Jamet, M.; George, J.-M.; Vila, L.; Jaffrès, H. Spin pumping and inverse spin hall effect in platinum: the essential role of spin-memory loss at metallic interfaces. Phys. Rev. Lett. 2014, 112, 106602. (30) Isasa, M.; Villamor, E.; Hueso, L. E.; Gradhand, M.; Casanova, F. Temperature dependence of spin diffusion length and spin Hall angle in Au and Pt. Phys. Rev. B: Condens. Matter Mater. Phys. 2015, 91, 024402. (31) Kim, J.; Sheng, P.; Takahashi, S.; Mitani, S.; Hayashi, M. Giant spin Hall magnetoresistance in metallic bilayers. arXiv preprint arXiv:1503.08903, 2015. (32) Hahn, C.; De Loubens, G.; Klein, O.; Viret, M.; Naletov, V. V.; Youssef, J. B. Comparative measurements of inverse spin Hall effects and magnetoresistance in YIG/Pt and YIG/Ta. Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 87, 174417. (33) Zhang, W.; Han, W.; Jiang, X.; Yang, S. H.; Parkin, S. S. Role of transparency of platinum-ferromagnet interfaces in determining the intrinsic magnitude of the spin Hall effect. Nat. Phys. 2015, 11, 496− 502. (34) Liu, Y.; Yuan, Z.; Wesselink, R. J. H.; Starikov, A. A.; Kelly, P. J. Interface Enhancement of Gilbert Damping from First Principles. Phys. Rev. Lett. 2014, 113, 207202. (35) Kim, T. S.; Lee, B. C.; Lee, H. W. Effect of ferromagnetic contacts on spin accumulation in an all-metallic lateral spin-valve system: Semiclassical spin drift-diffusion equations. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 78, 214427. (36) Geuzaine, C.; Remacle, J.-F. Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities. J. Numer. Methods Eng. 2009, 79, 1309. (37) Geuzaine, C. GetDP: a general finite-element solver for the de Rham complex. Proc. Appl. Math. Mech. 2007, 7, 1010603.

L.V., A.M., and J.P.A. took care of the data analysis and wrote the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The devices were fabricated in the Platforme Technologie Amont in Grenoble, and we acknowledge the support of the Renatec network. This work was supported by the “ANR- 13BS10-0005-01” SOspin project.

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REFERENCES

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DOI: 10.1021/acs.nanolett.6b02334 Nano Lett. XXXX, XXX, XXX−XXX