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The spin Hall effect (SHE) was predicted 40 years ago1,2. Theorists Dyakonov and Perel proposed that an unpolarized electrical current should lead to a transverse spin current in systems

with the relativistic spin–orbit coupling. In their picture, spin–orbit coupling enters SHE via the Mott scattering of electrons on unpolar-ized impurities, which results in spatial separation of electrons with opposite spins. The effect has a Hall symmetry, because the polariza-tion axis of the spins is perpendicular to the plane of the transverse spin current and the driving longitudinal electrical current. Concepts for the experimental detection of the phenomenon were introduced by Hirsch3 and Zhang4 almost 30 years after the original theoretical

Spin Hall effect devicesTomas Jungwirth1,2*, Jörg Wunderlich1,3 and Kamil Olejník1,3

The spin Hall effect is a relativistic spin–orbit coupling phenomenon that can be used to electrically generate or detect spin currents in non-magnetic systems. Here we review the experimental results that, since the first experimental observation of the spin Hall effect less than 10 years ago, have established the basic physical understanding of the phenomenon, and the role that several of the spin Hall devices have had in the demonstration of spintronic functionalities and physical phenomena. We have attempted to organize the experiments in a chronological order, while simultaneously dividing the Review into sections on semiconductor or metal spin Hall devices, and on optical or electrical spin Hall experiments. The spin Hall device studies are placed in a broader context of the field of spin injection, manipulation, and detection in non-magnetic conductors.

work. Hirsch proposed a device in which a spin current is generated by SHE in one part and injected into another part where it is detected by the inverse spin Hall effect (iSHE). In iSHE, the spin current gen-erates a transverse current of charge and when accumulated at the edges of the sample the charge can be detected electrically3. Relying on both SHE and iSHE simultaneously for observing the phenom-enon turned out to be experimentally challenging, and the method was realized only recently5. The proposal3 that SHE has an inverse counterpart has, nevertheless, played a key role in establishing the basic physics of the phenomenon and in utilizing the effect as a tool for both the electrical injection and electrical detection of spin cur-rents in non-magnetic materials.

Zhang4 suggested that the edge spin accumulation produced by SHE could be detected electrically using an attached ferromagnetic probe6. The method is based on measuring the dependence of the electrochemical potential at the detection ferromagnetic electrode on the relative orientation of the magnetization of the electrode, and the accumulated spins in the non-magnetic system underneath it. It took several years to demonstrate the viability of this method7. Nevertheless, in a broader context, the idea of connecting SHE with the more mature field, which utilizes ferromagnets for injection and detection of spins in non-magnetic systems, has fuelled numerous important studies of spin Hall devices.

The experimental discovery of SHE was prompted by theoreti-cal work that approached the SHE physics from a different angle. Inspired by studies of the intrinsic nature of the closely related anomalous Hall effect in ferromagnets8,9, Murakami et al.10 and Sinova et al.11 predicted that a spin-dependent transverse deflection of electrons in non-magnetic systems can originate directly from the relativistic band structure of the conductor without involving the Mott scattering. The intrinsic SHE proposal triggered an intense the-oretical debate, which is summarized in several review articles12–20. Unlike Hirsch3 and Zhang4 who considered the extrinsic, scatter-ing induced SHE1 and electrical detection schemes designed for metals, the intrinsic SHE proposals focused on semiconductors and suggested that the optical activity of these materials be utilized for detecting SHE. In particular, the circularly polarized electrolumines-cence was suggested in ref. 10 and the magneto-optical Kerr effect in refs 10,11. These methods were used in the first measurements of the SHE phenomenon. Kato et al.21 employed a magneto-optical Kerr microscope to scan the spin polarization across the channel (Fig. 1), whereas Wunderlich et al.22 used coplanar p–n diodes to detect cir-cularly polarized electroluminescence at opposite edges of the spin Hall channel (Fig. 2; ref. 23). Remarkably, Wunderlich et al. ascribed the observed signal to the intrinsic SHE whereas Kato et al. to the extrinsic SHE.

1Institute of Physics ASCR, v.v.i., Cukrovarnická 10, 162 53 Praha 6, Czech Republic, 2School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK, 3Hitachi Cambridge Laboratory, Cambridge CB3 0HE, UK. *e-mail: jungw@fzu.cz

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Figure 1 | Observation of SHE by the magneto-optical Kerr microscope. a,b, Two-dimensional images of spin polarization density ns (a) and reflectivity (b), for the unstrained GaAs sample measured at temperature 30 K and applied driving electric field 10 mV μm−1. Arbitrary units are used for ns as the measured Kerr rotation signal is not calibrated to the corrresponding spin density for this measurement. Figure reproduced with permission from ref. 21, © 2004 AAAS.

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Following the discovery of SHE, experiments with optical spin detection have explored the basic phenomenologies of the extrinsic and intrinsic SHEs21–30, as well as demonstrating the potential of SHE as a spin-current source25. A two-colour optical excitation technique with perpendicular linear polarizations of the incident laser beams was used to detect iSHE in a semiconductor31. The spin-current source produced by laser excitation is transferred, owing to iSHE, into a transverse electrical current, resulting in a spatially dependent charge accumulation that was detected by the optical transmission signal of a probe laser beam. Very recently, these all-optical meas-urements in an intrinsic semiconductor were performed on time-scales shorter than the scattering time, and have provided the most direct demonstration of the intrinsic spin Hall signal32. The seminal two-colour optical injection work31 was performed almost simulta-neously with the first experiments on iSHE in metals utilizing spin injection from a ferromagnetic contact33,34. The experiments demon-strated the potential of iSHE for optical and electrical spin detection.

A distinct approach for observing iSHE generated by an optically injected spin current in a semiconductor is based on the absorption of circularly polarized light. The roots of this technique can be traced back to experiments in which a circularly polarized beam at the normal incidence to the surface of a bulk semiconductor was used to excite spin-polarized photo-electrons35,36. These electrons diffuse in the vertical direction from the surface and after aligning their spins along an axis parallel to the surface by an applied magnetic field (by Hanle precession), an electrical voltage was detected in the transverse in-plane direction35. (Alternatively, the vertically spin-polarized electrons can be accelerated in the in-plane direction by an applied electrical bias to also yield a transverse in-plane voltage36.) Because in these experiments the source of spin current is accom-panied by a diffusive or drift charge current, and the Hall signal is measured across the optically excited spin-polarized region of the semiconductor, the geometry is halfway between the anomalous Hall effect in a ferromagnet and iSHE. Recently, the same type of a copla-nar p–n diode as used in ref. 22, but now operated as a photo-cell, has allowed the optical spin generation and electrical spin detection regions of the semiconductor to be separated37. The inverse spin Hall

Figure 2 | Observation of SHE by the circularly polarized electroluminescence of coplanar p–n diodes. a, Schematic of the lateral p–n junction with the channel current Ip and the diode current ILED for detecting spin accumulation. b, Light emission from the p–n junction recorded by a charged-coupled device camera. The black dashed line shows the position of the p–n junction. c, Electron microscope image of the microdevice with symmetrically placed p–n diodes at both edges of the 2D hole gas channel. d,e, Emitted light polarization of recombined light in the p–n junction for the channel and diode current flow indicated by arrows in (c). Figure reproduced with permission from ref. 23, © 2005 APS.

effect induced by the pure spin-current was eventually observed in these devices by draining the p–n junction electrical current before the Hall cross38. The work showed that iSHE can be combined with spin-precession phenomena in electrically controllable Rashba and Dresselhaus spin–orbit fields. (This is the type of spin manipulation considered in the original Datta–Das spin-transistor proposal39.) It led to the demonstration of a tunable electrical polarimeter and a spin-transistor logic device37,38.

The pioneering works combining iSHE and SHE with the previ-ously known spin injection and detection techniques utilizing fer-romagnetic contacts were performed in metals, taking advantage of the compatibility of non-magnetic metal channels with conventional metal ferromagnets. In some cases7,34,40–42, the electrical spins were injected from a ferromagnetic contact6. In others, the ferromagnetic resonance spin-pumping method43–45 was used33,46–48. Metal spin Hall devices provided the first demonstration of the electrical measure-ment of SHE by an attached ferromagnetic contact7, as proposed originally by Zhang4, and showed that one non-magnetic metal elec-trode can generate SHE or iSHE, that is, can be used as an electrical spin injector or detector7,34,40–42. They also showed that extrinsic spin Hall angles can be large even at room temperature in metals with strong spin–orbit coupling. Experiments based on the ferromagnetic spin-pumping effect suggested that iSHE and SHE can be used as an electrical detector and generator of spin dynamics in magnetic microstructures33,46,49–51. The utility of a metal iSHE sensor led to the discovery of the spin Seebeck effect, opening a new experimental research area in the field of spin caloritronics52–55. Recently, an exper-iment in a metal–semiconductor hybrid structure was reported, which demonstrated the conversion of circularly polarized light absorbed in a semiconductor to an electrical signal in an attached metal iSHE sensor56.

In the past two years, semiconductor spin Hall devices have entered the realm of metals by not requiring light for their operation. This development started with an experiment5 that materialized the original idea of Hirsch3 for simultaneously employing SHE and iSHE to detect the phenomenon electrically. It is remarkable that not only was the experiment performed in a semiconductor but, also unlike

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the characteristic spin–orbit coupling energy Δso and momentum scattering time τ in the 3D semiconductor samples studied in ref. 21 yield Δsoτ/ħ ~10–3, that is, confirm the weak spin–orbit coupling regime of the samples. The required spatial resolution to observe SHE was therefore Ls ~1–10 μm, which is achievable by using Kerr rotation microscopy. The out-of-plane spin-polarization density ns measured by Kato et al.21 is shown in Fig. 1. Consistent with the SHE phenomenology, spin polarizations at opposite edges of the chan-nel have opposite sign. Further consistency checks performed in the experiments confirmed the proportionality of the amplitude of the observed signal to the driving longitudinal electrical current and, in agreement with the prediction of Dyakonov and Perel2, a diminish-ing SHE signal due to the Hanle spin precession in applied in-plane magnetic fields. The amplitude of the measured edge spin polariza-tions in ref. 21 reached ~0.1% (the measurements were performed at 50 K). By fitting the measured spin accumulation to the solution of the drift-diffusion equations4,3, the SHE-induced transverse spin current was estimated to be ejs ≈ 10 nA μm−2 for a source longitudi-nal charge current jc ≈ 50 μA μm−2. This corresponds to a spin Hall angle α = ejs/jc ≈ 2 × 10−4. In the weak spin–orbit coupling regime the spin–orbit splitting of the quasiparticle bands is smeared out by dis-order that favours the extrinsic SHE interpretation of the measured signal in ref. 21. The absence of the intrinsic SHE was confirmed by measurements in the strained InGaAs sample, which showed no dependence of the SHE signal on the strain-induced anisotropies of the spin–orbit-coupled band structure.

A microdevice with two coplanar light-emitting diodes used by Wunderlich et al.22,23 to detect SHE is shown in Fig. 2. Devices were patterned from a semiconductor heterostructure that comprised a modulation p-doped AlGaAs/GaAs heterojunction on top of the structure, 90 nm of intrinsic GaAs, and an n-doped AlGaAs/GaAs heterojunction underneath. In the unetched part of the wafer, the top heterojunction was populated by 2D holes of a sheet density 2 × 1012 cm−2, whereas the 2D electron gas at the bottom heterojunc-tion was almost depleted. The n-side of the coplanar p–n junction was formed by removing the p-doped surface layer from part of the wafer,

the original proposal, the measured SHE–iSHE microdevice worked in the ballistic transport regime of the intrinsic SHE. Compared with metals, semiconductor spin-transport devices with ferromagnetic metal electrodes can suffer from the problem of resistance mismatch between semiconductors and common metal ferromagnets, which hinders efficient spin transport across the interface57. The introduc-tion of a highly resistive tunnel barrier between the ferromagnetic metal electrode and the semiconductor channel solves this prob-lem58,59, and ferromagnetic tunnel contacts were successfully used to detect the SHE-induced spin accumulation in a semiconductor60. Recently, a spin Hall device has been reported that utilizes electri-cal injection from a ferromagnet/semiconductor tunnel contact and demonstrates electrical spin detection by iSHE and by the ferromag-netic probe electrode61. Also, the device shows the possibility of mod-ulating the detector spin signal by electrically controlled drift of the spins. The resistance mismatch problem can also be tackled without introducing a tunnel barrier between the ferromagnetic metal and the semiconductor, as demonstrated recently in ref. 62, where a semi-conductor iSHE device is reported that has an ohmic contact between the ferromagnetic electrode and the semiconductor, and where spin injection is realized by ferromagnetic resonance spin pumping.

Optical spin Hall devices in semiconductorsFor imaging the SHE-induced edge spin accumulation by Kerr rota-tion microscopy, Kato et al.21 used unstrained n-GaAs and strained n-In0.07Ga0.93As three-dimensional (3D) epilayers, which were pat-terned into 300 × 77 μm2 and 300 × 33 μm2 channels, respectively. The wafers were doped to a low electron density of n = 3 × 1016 cm−3 to achieve long spin lifetimes of τs ~1–10 ns. This corresponds to a spin diffusion length of Ls = (Dτs)1/2 ~1–10 μm, where D is the diffusion constant. In his seminal theoretical work, Zhang4 showed by solving the spin-dependent drift-diffusion equations for a finite width chan-nel that Ls defines the length scale of the edge spin accumulation. The analysis based on the drift-diffusion equations, which assumes well-resolved spin-up and spin-down transport channels3,4, is applicable only in the weak spin–orbit coupling limit, Δsoτ/ħ<<1. Estimates of

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Figure 3 | Observation of iSHE using the two-colour optical pump-and-probe technique. a, Illustration of orthogonally polarized ω and 2ω pulses producing a pure spin current (double headed arrow) along the ω beam polarization direction (x). The charge current due to iSHE (curved arrows) along ŷ leads to electron accumulation near one edge of the illuminated region. b, Measured charge accumulation due to iSHE. ΔN is the excess charge. Figure reproduced with permission from ref. 31, © 2006 APS.

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thereby populating the 2D electron gas. The 1.5- and 10-μm-wide channels in the experimental devices22,23 were formed in the unetched part of the epilayer with the 2D hole gas. The etched-off regions of the wafer outside the channel make the channel edges act as copla-nar p–n diodes with an effective recombination width of ~100 nm. The measured circular polarization of the electroluminescence peak (Fig. 2d,e) reverses sign when the sign of the SHE-generating elec-trical current along the 2D hole channel is reversed. Also consistent with the SHE phenomenology, opposite polarizations were detected at opposite edges of the 2D hole gas channel. The amplitude of the measured SHE signals (at 4 K) reached ~1% in these experiments. The 2D hole gas studied in refs 22,23 was in the strong spin–orbit coupling regime, Δsoτ/ħ ≈ 4, which favours the intrinsic SHE mecha-nism. A quantitative microscopic description of the measured edge-spin-accumulation signal was developed and further experimentally tested23. Theoretical analysis pointed out that the length scale of the edge spin accumulation is defined in the strong spin–orbit cou-pling regime by the spin–orbit precession length Lso = νFτso, where τso = ħπ/Δso is the precession time of the spin in the internal spin–orbit field and νF is the Fermi velocity. With increasing strength of the spin–orbit coupling, the edge-spin-accumulation region narrows down and, simultaneously, the amplitude of the spin polarization increases. For the experimental parameters of the 2D hole gas, Lso ~10 nm and the calculated amplitude of the edge spin polarization was 8%, in good agreement with the 1% polarization of the measured electroluminescence signal, which was averaged over the ~100 nm sensitivity range of the coplanar light-emitting diode. Measurements in a device with a 10 μm wide 2D hole gas channel confirmed the theoretical expectation that the SHE edge spin accumulation is inde-pendent of the channel width (for widths larger than Lso)23.

Subsequent magneto-optical measurements of SHE in the n-GaAs 3D epilayers have demonstrated experimentally that the SHE-induced spin accumulation is due to a transverse spin current, which can drive spin polarization tens of micrometres into a region in which there is minimal electric field25. The work proved experimen-tally that SHE can be used as a source of spin current generated in a non-magnetic system. A systematic doping dependence of the SHE angle was studied in n-GaAs 3D epilayers with electron densities n in

the range 1.8 × 1016–3.3 × 1017 cm−3 and the results were found to be

consistent with theoretical predictions for the extrinsic SHE30. The measured SHE angles of ~5 × 10−4–5 × 10−3 increased with increas-ing doping with a tendency to saturate at the high doping end of the studied set of samples at a value corresponding to ~1% edge spin polarization. It was concluded from this systematic analysis that the spin accumulation is reduced by an enhanced spin relaxation due to the Dyakonov–Perel spin-relaxation mechanism, whereas the spin current induced by SHE is enhanced with increasing n (ref. 30). The spin Hall effect was also observed in other semiconductor systems including n-ZnSe 3D epilayers26, and InGaN/GaN superlattices27.

The optically generated and detected iSHE was observed in an intrinsic GaAs (at 80 K) using a two-colour optical coherence con-trol technique with orthogonally polarized 1,430 nm and 715 nm fs pulses31. The method, shown in Fig. 3a, is based on quantum interfer-ence between absorption pathways for one- and two-photon absorp-tion connecting the same initial and final states, and allows for a pure spin-source current to be generated in an intrinsic semiconductor with no drift currents induced by an applied electric field, but rather with ballistic carriers decelerated by scattering. For generating a pure spin-current, a coherent pulse centred at frequency ω with phase ϕω is normally incident along the z direction and linearly polarized along the x direction that can be arbitrary with respect to the crystal axes as the effect is not strongly sensitive to the crystal orientation. A co-propagating 2ω pulse with phase ϕ2ω is linearly polarized along the orthogonal ŷ direction. Excited spin-up electrons are polarized along z and move preferentially in one direction along x, whereas spin-down electrons move in the opposite direction. Together they generate a spin current js

z ∝ cos(Δϕ), where Δϕ = 2ϕω−ϕ2ω. This pure spin-current is the source of a transverse charge current arising due to iSHE. The resulting charge accumulation was measured opti-cally by differential transmission, that is, the transmission with and without pump beams, of a linearly polarized probe pulse. Consistent with the iSHE phenomenology, the excess charge (ΔN) on one side and the deficit on the other side of the sample, shown in Fig. 3b, was observed along the direction perpendicular to the driving spin cur-rent. The ballistic nature of transport in these experiments in intrinsic GaAs has been fully exploited in recent femtosecond time-resolved

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Figure 4 | iSHE-based transistor. a, Schematic of the spin-injection Hall effect measurement set-up with optically injected spin-polarized electrical current propagating through the Hall bar and corresponding experimental Hall effect signals at crosses H1 and H2. The Hall resistances, RH = VH/IPH, where VH is the Hall voltage and IPH is the photocurrent for the two opposite helicities of the incident light are plotted as a function of the focused light spot position, that is, of the position of the injection point. VB is the p–n junction bias voltage, σ+ and σ− are the helicity of the polarized light. IPH is independent of the helicity of the incident light and varies only weakly with the light spot position. b, Same as (a) for iSHE in which the electrical current is closed before the first detecting Hall cross H1. c, Schematic of the spin Hall transistor and experimental Hall signals as a function of the gate voltage (VG) at a Hall cross placed behind the gate electrode for two light spot positions with a relative shift of 1 μm. The red and dashed black lines correspond to measurements with the relative shift of the laser spot of 1 μm. Figure reproduced with permission from ref. 38, © 2010 AAAS.

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measurements32. These measurements allowed the momentum scattering time τ ≈ 0.45 ps to be inferred, and with a much shorter time delay of the probe pulses, the transverse charge current could be observed in real time. The measurements showed that the charge current was generated well before the first scattering event, providing a direct demonstration of the intrinsic iSHE.

A traditional way of generating spin-polarized photo-carriers in semiconductors is by absorption of circularly polarized light63. Because of the optical selection rules, the out-of-plane spin polariza-tion of photo-carriers is determined in this technique by the helicity and degree of the circular polarization of vertically incident light. Wunderlich et al.37,38 used the same type of a lateral p–n diode they had used previously22,23 to utilize optical spin injection by a circularly polarized laser beam for observing the iSHE and for employing the effect in experimental opto-spintronic and spin-transistor devices. In their original SHE measurements22,23, the p–n junctions were fab-ricated along the edges of the 2D hole channel and under forward bias could detect the spin state of recombining electrons and holes through polarized electroluminescence. In their later work37,38, on the other hand, the spin Hall channel was fabricated in the etched part of the epilayer with the 2D electron gas, the channel was oriented perpendicular to the p–n junction, and the diode was under zero or reverse bias, operating as a photocell as shown in Fig. 4. The opti-cal activity of the lateral diode confined to a submicro metre deple-tion region, combined with a focused (~1 μm) laser beam, allowed for a well-localized injection of spin-polarized photo-electrons into

the planar 2D electron gas channel. The Hall signals were detected electrically on multiple Hall-crosses patterned along the channel. Two regimes of operation of the device were distinguished: One was referred to as the spin-injection Hall effect regime, in which the reverse-bias charge current is drained behind the Hall crosses at the opposite end of the channel from the p–n junction injection point (Fig. 4a). The other regime corresponds to the iSHE measurement, because in this case the charge current is drained before the Hall crosses, allowing only the pure spin-current to diffuse further in the channel (Fig. 4b). In both cases the measured transverse electrical signals were consistent with the spin Hall phenomenology37,38. The sign of the voltage was opposite for opposite helicities of the incident light, that is, opposite spin polarizations of injected photo-electrons. Moreover, the amplitude of the electrical signals was found to depend linearly on the degree of circular polarization of the light, render-ing the device an electrical polarimeter37. The electrical signals were observable over a wide temperature range with spin Hall angles of 10−3–10−2. The measured 2D electron gas was in the weak spin–orbit coupling regime, Δsoτ/ħ ~10−1, and the measured data were consist-ent with the extrinsic spin Hall mechanism37.

A distinct feature of the iSHE experiments in the 2D electron gas is the observed spin precession due to internal Rashba and Dresselhaus spin–orbit fields37,38. As the spin diffusion length scales approximately38 as Lso

2/w, it was possible to observe a few spin pre-cessions in channels of a width w = 1 μm for Lso ~1 μm of the stud-ied 2D electron gas. The corresponding oscillations of the spin Hall

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voltages were consistently observed by measuring at different Hall crosses along the channel or by shifting the laser spot, that is, the spin-injection point (Fig. 4). The lateral iSHE channels also allow top-gate electrodes to be placed in between the Hall crosses as shown in Fig. 4c. (The gates were formed by unetched regions of the wafer.) The strength of the Rashba and Dresselhaus spin–orbit fields and, therefore, also the spin precession can be manipulated electrically in the device as shown in Fig. 4c. To demonstrate an AND logic func-tionality, two gates were fabricated on top of the channel and the Hall electrical signal was measured at a cross placed behind both gates. Intermediate gate voltages on both gates represented the input value 1 and gave the largest electrical iSHE signal, representing the out-put value 1. When a large reverse gate voltage was applied to any of the two gates, representing input value 0, the electrical iSHE signal disappeared, that is, the output was 0.

Metal devices with ferromagnetic contactsValenzuela and Tinkham34 performed experiments (at 4 K) in which a spin current injected from a ferromagnetic electrode into a non-magnetic metal strip was detected by iSHE and by the non-local spin-valve effect using a ferromagnetic probe electrode. The elec-trical injection of the spin current results from a non-equilibrium spatially dependent splitting of spin-up and spin-down electrochem-ical potentials on either side of the electrically biased ferromagnet/normal metal contact6. In the device shown in Fig. 5, the ferromag-netic CoFe electrode FM1 is used to inject spin-polarized electrons through an Al2O3 tunnel barrier into an Al channel. The tunnel bar-rier is important because it enhances the polarization of the injected electrons. In Fig. 5b, the electrical current is directed from the injec-tion electrode FM1 to the left, away from the ferromagnetic CoFe electrode FM2, causing a pure spin-current to diffuse towards FM2. The non-local spin-valve voltage is then measured between the fer-romagnetic probe FM2 and the right side of the Al strip. The CoFe electrodes are magnetized in the plane at zero magnetic field owing to the strong thin-film shape anisotropy. The large positive non-local spin-valve voltage at zero magnetic field shown in Fig. 5d, cor-responds to parallel magnetizations of the injection and detection CoFe electrodes, that is, parallel spin polarization in the Al channel with the magnetization in the FM2 probe above it. The large nega-tive spin-valve voltage at zero field corresponds to the antiparallel configuration. At weak out-of-plane magnetic fields the polarization of the ferromagnetic electrodes remains in-plane and the measured spin-valve signal shows the in-plane component of the injected spins in the Al channel, which precesses owing to the Hanle effect. At large

magnetic fields, the CoFe magnetization is rotated out-of-plane and, correspondingly, the spin-valve signal saturates at the large positive value. Figure 5a,c shows spin injection and detection measurements when the electrical current is directed from the injection electrode FM1 to the right, away from the Al Hall cross, causing a pure spin-current to diffuse towards the cross. Consistent with the iSHE phe-nomenology, the measured transverse voltages on the Hall cross are proportional to the out-of-plane component of the spin polariza-tion of the injected spin current. The spin Hall angle ~1–3 × 10−4, obtained by fitting the measured Hall voltages to the solution of the diffusion equation for the injected pure spin-current, compares well with the theoretical estimates for the extrinsic iSHE in Al (ref. 34).

Kimura et al.7 studied iSHE and SHE in one NiFe/Cu/Pt structure whose geometry is shown in the insets of Fig. 6. First they used the NiFe electrode as a spin injector and measured iSHE in the Pt strip (Fig. 6a). Then the experimental geometry was inverted and the driv-ing electrical current was passed through the Pt strip, generating a transverse spin current by SHE in Pt. The spin current was detected by measuring the non-local spin-valve signal on the NiFe electrode (Fig. 6b). Same spin Hall conductivities were obtained from both the inverse and direct spin Hall measurements. The data provided experimental evidence of the utility of SHE and iSHE as a spin injec-tion and detection tool.

In parallel with the seminal study of iSHE driven by electrical spin injection from a ferromagnetic contact34, Saitoh et al.33 applied the ferromagnetic resonance spin-pumping method44 of spin injec-tion from NiFe into a Pt layer. The physical mechanism of the spin-pumping technique is in the transfer of angular momentum from the precessing magnetization to the conduction electrons. This transfer, which contributes to magnetization damping, polarizes the spins of conduction electrons and when a paramagnetic metal is connected to the ferromagnet the spin polarization may propagate into the metal as a pure spin-current. Spin pumping has a form of an enhanced Gilbert damping in the Landau–Lifshitz equation, jss ∝ m × ∂m/∂t. The polarization vector s of the spin current is perpendicular to the instantaneous magnetization direction m and to its time derivative (∂m/∂t). This means that the spin current has a time-independent component along the equilibrium magnetization direction (Fig. 7a).

The measured ferromagnetic resonance spectrum of the NiFe/Pt sample is compared with a reference NiFe sample in Fig. 7b. The spectral width of the NiFe/Pt sample is larger than that of the reference NiFe film, which demonstrates the presence of the spin-pumping effect in the NiFe/Pt. The induced voltage signal measured across the sample along an axis parallel to the NiFe/Pt interface

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Figure 6 | iSHE and SHE detection in a metal. a, The change in Hall resistance ΔRSHE = ΔVc / I due to iSHE at 77 K. The black and grey curves show measurements for the two opposite sweeps of the magnetic field. b, Spin-accumulation signal ΔVs / I generated by SHE at 77 K. Insets: measurement set-up. NiFe, Cu and Pt are in grey, pink and yellow, respectively. μ0H is the applied magnetic field, M is the magnetization of NiFe and Ie is the applied electrical current. Figure reproduced with permission from ref. 7 © 2007 APS.

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is shown in Fig. 7c. Saitoh et al.33 demonstrated that the signal is present only when the spin-polarization vector of the injected spin current has a component perpendicular to the measured electric field across the sample, consistent with iSHE.

Mosendz et al.47,48 applied the ferromagnetic resonance spin-pumping method to determine the spin Hall angles in a series of non-magnetic metals. Ando et al.46 demonstrated electrical detec-tion of a spin-wave resonance in nanostructured NiFe/Pt samples. By inverting the experiment, Liu et al.51 applied a microwave frequency charge current in the plane of a NiFe/Pt sample and observed the ferromagnetic resonance in NiFe. It was an all-electrical magnetic resonance experiment because the oscillating magnetization led to an oscillation of the bilayer resistance owing to the anisotropic mag-netoresistance of NiFe. The output d.c. voltage signal was generated across the sample from the mixing of the microwave current and the oscillating resistance, similar to the signal that arises from spin-transfer-torque-induced ferromagnetic resonance in spin valves and magnetic tunnel junctions51.

Semiconductor devices operating without lightBrüne et al.5 performed a non-local electrical measurement in nanoscale H-shaped structures built on high-mobility HgTe/(Hg,Cd)Te quantum wells with a top-gate electrode. The experiment was in the spirit of the original proposal of Hirsch3 for simultane-ously employing SHE and iSHE to detect the phenomenon electri-cally. The geometry of the microdevice64 and the measured iSHE signals are shown in Fig. 8a. The idea behind these transport meas-urements is as follows. When an electric current flows in one of the legs of the H-bar structure, a transverse spin current due to SHE is induced in the connecting part. Subsequently, this spin current produces, owing to iSHE, a non-local voltage difference in the oppo-site leg of the H-bar structure, which can be measured by a voltme-ter. Sweeping the gate voltage in the sample allowed the strength of the Rashba spin–orbit splitting to be varied by both the electrical field across the quantum well and the Fermi level position in the quantum well. In the sample it was possible to electrically tune the carrier density from strongly n-type, through insulating, down to a

p-type regime. This resulted in a strong modulation of the non-local voltage (Fig. 8a). In the p-regime, where the spin–orbit coupling is strong, the signal is at least one order of magnitude larger than in the weakly spin–orbit coupled n-regime. The H-structures consisted of legs 1 μm long and 200 nm wide, with the connecting part being 200 nm wide and 200 nm long. The estimated mean free path in the system was ≥2.5 μm, that is, the samples were well within the quasi-ballistic regime. Detailed numerical calculations confirmed that the observed spin Hall signals had the ballistic intrinsic origin5.

The hybrid semiconductor/metal-ferromagnet structures have for a long time suffered from the resistance mismatch problem57. As the spin transport relies on different conductivities for spin-up and spin-down electrons and is governed by the least conductive part of the device, the effects are weak in devices in which the non-magnetic semiconductor with equal spin-up and spin-down conductivities dominates the resistance of the device58. The introduction of a highly resistive tunnel barrier between the ferromagnetic metal electrode and the semiconductor channel can solve the problem58,59. (The tunnelling resistance is spin dependent because of the exchange-split bands on the ferromagnet side of the tunnel junction.)

Garlid et al.60 reported an all-electrical measurement of SHE in epitaxial Fe/InGaAs heterostructures with an n-type InGaAs semiconductor channel and a Schottky tunnel barrier at the Fe/InGaAs interface. A transverse spin current generated by an ordinary charge current flowing in the InGaAs was detected by measuring the spin accumulation at the edges of the channel. An important aspect of the experiment was the ability to tune the strength of the spin–orbit interaction between different samples by changing the In content, and to vary the conductivity of the samples. This allowed the different contributions to the spin Hall conductivity to be extracted. As expected in n-doped 3D semicon-ductors, the observed spin Hall conductivity was dominated by the extrinsic mechanism.

Olejnik et al.61 demonstrated the iSHE detection in a semi conductor combined with an electrical spin injection and manipulation. In a GaAs microchannel with an Fe Schottky injec-tion contact, the spin current in a lateral semiconductor channel

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Figure 7 | Observation of iSHE in a metal device with spin injection from a ferromagnet by the ferromagnetic resonance spin pumping. a, Schematic of the NiFe/Pt sample system used in the study and of the spin-pumping effect and iSHE. Jc is the charge current, Js is the spin current and σ is the spin orientation of injected electrons. b, Magnetic-field dependence of the ferromagnetic resonance (FMR) signal for the NiFe/Pt bilayer film and a Ni film. I is the microwave absorption intensity. c, Magnetic-field dependence of dV(H)/dH for the NiFe/Pt sample. V is the electrical-potential difference between the electrodes on the Pt layer. Figure reproduced with permission from ref. 33, © 2006 AIP.

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was detected by iSHE and the spin polarization was simultaneously measured using an additional Fe electrode. The spins in the chan-nel were manipulated by the Hanle spin precession induced by an applied magnetic field and by a drift induced by an applied electrical bias65. As shown in Fig. 8b–d, the output iSHE and non-local spin-valve signals are suppressed or enhanced depending on the electrical bias, that is, the device acts as an electrically controlled spin modula-tor. Qualitatively, the modulation of the spin signal can be explained by a shift of the injected spin polarization profile from the injection electrode in the direction towards the detection electrodes in the case of the positive drift current or away from the detectors in the case of the negative drift.

Electrical tuning of the spin signal in a semiconductor has also been recently demonstrated by Ando and colleagues62. In this exper-iment, spins were injected from NiFe into GaAs through a Schottky contact using ferromagnetic resonance spin pumping. Tuning of the spin-pumping efficiency was achieved by applying a bias voltage across the NiFe/GaAs Schottky barrier and interpreted as a conse-quence of a suppressed or enhanced spin coupling across the inter-face. The ferromagnet/semiconductor spin-pumping experiments in ref. 62 were also performed on samples with an ohmic contact between NiFe and GaAs. The measurements demonstrated that the resistance mismatch problem in ohmic metal/semiconductor spin-injection devices can be circumvented by using the ferromagnetic resonance spin-pumping technique.

OutlookExperiments in spin Hall devices performed so far have established the basic physics of SHE and iSHE, showed that the intrinsic and extrinsic mechanisms can contribute to the phenomenon, and that SHE and iSHE are universal to metal and semiconductor sys-tems (3D and 2D) with spin–orbit coupling. As the strength of the spin–orbit coupling increases, the spin current that arises from SHE increases. At the same time, however, the spin lifetime decreases. Finding the optimal compromise between these two counteract-ing effects of the spin–orbit coupling remains an important open

problem in the field. Research directions recently initiated5,37,38 are among the experiments that may contribute to a better understand-ing of this problem. They showed that spin Hall devices can operate in the ballistic regime, that is, when the typical dimensions of the device are smaller than the scattering mean free path5. Also, for the diffusive spin Hall devices it was pointed out that there are regimes in which spin coherence can be strongly enhanced38. One regime is when the width of the channel is comparable to or smaller than the precession length in the internal spin–orbit field66. In the other regime, the width of the channel is not relevant, and enhanced spin coherence occurs as a result of the single-particle transport analogue of the spin helix state67,66 realized at 2D Rashba and Dresselhaus spin–orbit fields of equal or similar strengths.

The utility of SHE and iSHE as an electrical spin injector and detector in non-magnetic systems can allow a variety of new spin-tronic functionalities to be explored. One of the recently proposed areas is opto-spintronics. It was shown, for example, that iSHE acts as a direct electrical detection tool for the polarization of light37,56, and because of the universality of the spin Hall phenomenon, the approach can be implemented in semiconductors active over a wide range of wavelengths. Other proposed applications include spin-photovoltaic cells, switches, invertors and interconnects. Several types of devices combining electrical spin detection by iSHE with electrical spin manipulation have been recently demonstrated, which makes spin transistors another potentially fruitful area of spin Hall research. Some devices are reported to act as a spin analogue of a field-effect transistor5,38,62. The gate electrode in these devices can control the spin–orbit coupling5,38 or the interfacial spin interac-tions62 by changing the electric field strength across the film or the Fermi level position. The device reported in ref. 61 is different as it uses an additional drift current to control the output spin signal. Finally we recall the research direction suggested by recent reports of the SHE-controlled magnetization dynamics49–51. These are the pure spin-current analogues of the spin-transfer-torque phenomena that have for decades played a key role in basic spintronics research and in bringing spintronics to commercial applications68.

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Figure 8 | Electrical spin Hall devices in semiconductors. a, Spin injection by SHE and detection by iSHE in a gated H-shaped device. Inset: schemtic showing the measurement set-up for current injection (I) and voltage probes (V). The black curve shows the non-local iSHE resistance signal. The blue curve indicates the residual voltage owing to current spreading. b–d, Semiconductor iSHE device with electrical modulation of the spin signal. Schematic showing the experimental set-up (b). Experimental non-local spin-valve (VNL) and iSHE (VH) signals in the in-plane field Bx measured at constant spin-injection bias current IB = 300 μA and at three different drift currents ID depicted in b (c,d). Figures reproduced from: a, ref. 5 © 2010 NPG; b–d, ref. 61.

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AcknowledgementsWe acknowledge support from EU grants ERC Advanced Grant 268066-0MSPIN and FP7-215368 SemiSpinNet, and from Czech Republic grant AV0Z10100521 Praemium Academiae.

Additional informationThe authors declare no competing financial interests. Reprints and permissions information is available online at http://www.nature.com/reprints. Correspondence should be addressed to T. J.

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