Observation of the inverse spin Hall effect in silicon

Abstract

The spin–orbit interaction in a solid couples the spin of an electron to its momentum. This coupling gives rise to mutual conversion between spin and charge currents: the direct and inverse spin Hall effects. The spin Hall effects have been observed in metals and semiconductors. However, the spin/charge conversion has not been realized in one of the most fundamental semiconductors, silicon, where accessing the spin Hall effects has been believed to be difficult because of its very weak spin–orbit interaction. Here we report observation of the inverse spin Hall effect in silicon at room temperature. The spin/charge current conversion efficiency, the spin Hall angle, is obtained as 0.0001 for a p-type silicon film. In spite of the small spin Hall angle, we found a clear electric voltage due to the inverse spin Hall effect in the p-Si film, demonstrating that silicon can be used as a spin-current detector.

Introduction

Silicon is a group IV semiconductor having the diamond structure. This material has had a crucial role in exploring the physics of semiconductors. Silicon has been broadly viewed as an ideal host also for spintronics owing to its low atomic mass, crystal inversion symmetry, and near lack of nuclear spin, resulting in the exceptionally long spin lifetime^1,2,3.

Along with long spin lifetimes, key elements for spintronics are generation and detection of spin currents^{4,5,6,7,8,9,10,11}. A promising method is the utilization of the direct and inverse spin Hall effects (DSHE/ISHE), which convert a charge current into a spin current and vice versa^{12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30}. However, the underlying origin of the spin Hall effects is the spin–orbit interaction and, thus, it is natural to expect that the spin Hall effects are not accessible in a material that shows long spin lifetimes, such as silicon. Generation of spin currents from an electric field through the spin–orbit interaction, the DSHE, was first observed in gallium arsenide (GaAs) using optical detection techniques, a Kerr-microscopy and a two-dimensional light-emitting diode^17,18. Although these optical techniques have had a crucial role for investigating the physics of the DSHE^{17,18,19,21,28}, the application range of the techniques is limited to direct bandgap semiconductors with strong spin–orbit interaction; the indirect bandgap of silicon precludes using these techniques, making it difficult to explore the DSHE in silicon along with its very weak spin–orbit interaction.

The spin–orbit interaction responsible for the DSHE also causes the conversion of a spin current into an electric field, the ISHE^25,26,27, which could offer a way to circumvent the above obstacle in exploring the spin Hall effects. The ISHE enables the electric measurement of the spin/charge conversion through the spin–orbit interaction, as demonstrated, for example, in platinum and gallium arsenide^22,25,26,29. The electric field E_ISHE generated by the ISHE from a spin current j_s with the spin-polarization vector σ is described as²⁵

where is the spin Hall angle, σ_SHE and σ_N are the spin Hall conductivity and electric conductivity, respectively, and ρ_N is the electric resistivity. Equation (1) shows that the magnitude of the electric field due to the ISHE is proportional to the resistivity ρ_N of the material, indicating that the ISHE enables sensitive detection of spin currents especially in high-resistivity materials, such as semiconductors.

Although spin injection efficiency into semiconductors is drastically limited by the impedance mismatch problem³¹, recent advances revealed that efficient spin injection is possible using hot-electron injection³², tunnel barriers^33,34, and spin pumping³⁵. In particular, the generation of spin currents from magnetization precession^36,37, a recently discovered method utilizing spin pumping, enables high-density spin current injection into a macroscopic area³⁵, which is difficult to achieve by other methods. This is beneficial for enhancing the electric voltage due to the ISHE; V_ISHE is proportional both to the spin current density j_s and length w_F of the sample along E_ISHE. The combination of the spin pumping and ISHE has been observed and is a well-established technique in metallic systems³⁸. This has also been applied to semiconductors with strong spin–orbit interaction, enabling the observation of the ISHE in heavily doped n- and p-type GaAs³⁵. In this work, we experimentally demonstrate that the combination of the ISHE and spin pumping provides a route for exploring the spin/charge current conversion in high-resistivity materials with weak spin–orbit interaction by showing successful measurement of the ISHE in silicon at room temperature.

Results

Detection of inverse spin Hall effect in silicon

Figure 1a shows a schematic illustration of the sample used in this study. The sample is a Ni₈₁Fe₁₉/B-doped Si (Ni₈₁Fe₁₉/p-Si) film with a doping concentration of N_A=2×10¹⁹ cm⁻³ (see Methods). Two ohmic contacts were attached on the p-Si layer (Fig. 1a,b). Here the current-voltage characteristic shown in Figure 1c shows an almost ohmic behaviour at the Ni₈₁Fe₁₉/p-Si interface, suggesting strong dynamical exchange interaction J_ex between the magnetization in the Ni₈₁Fe₁₉ layer and carrier spins in the p-Si layer³⁵.

Figure 1: Experimental set-up.

(a) A schematic illustration of the Ni₈₁Fe₁₉/p-Si film used in this study. H represents an external magnetic field. (b) Current-voltage (I–V) characteristic measured for the Ni₈₁Fe₁₉/p-Si film, where the two electrodes are attached to the AuPd layers. w_F is the length of the Ni₈₁Fe₁₉ layer. (c) I–V characteristic measured for the Ni₈₁Fe₁₉/p-Si film. The two electrodes are attached to the Ni₈₁Fe₁₉ layer and AuPd layer, respectively.

We measured the ferromagnetic resonance (FMR) signal and electric-potential difference V between the electrodes attached to the p-Si layer to detect the ISHE³⁵; in the FMR condition, the spin pumping driven by the dynamical exchange interaction injects pure spin currents into the p-Si layer. This spin current gives rise to an electric voltage V_ISHE through the ISHE in the p-Si layer. During the measurements, the Ni₈₁Fe₁₉/p-Si sample was placed at the centre of a TE₀₁₁ microwave cavity with the frequency of f=9.45 GHz, where the microwave magnetic field was applied along the y direction (Fig. 1a). An external static magnetic field H was applied along the film plane as shown in Figure 1a. All of the measurements were performed at room temperature.

Figure 2a,b shows the DC electromotive force signals measured for the Ni₈₁Fe₁₉/p-Si film at various microwave excitation power, when the external magnetic field H is applied along the film plane at θ=0 and θ=180° (see the insets), respectively. Here θ is the out-of-plane angle of H. In the V spectra, clear electromotive force signals are observed around the ferromagnetic resonance field H_FMR (compare the V spectra with the FMR spectra shown in Fig. 2c,d). Figure 2c,d shows that the microwave absorption intensity I is identical for θ=0 and 180°. In contrast, importantly, the magnitude of the electromotive force V is clearly changed by reversing the magnetic field direction as shown in Figure 2a,b; this distinctive behaviour of V is the key feature of the ISHE induced by the spin pumping³⁵.

Figure 2: Observation of ISHE in silicon.

(a) Field (H) dependence of the electromotive force V measured for the Ni₈₁Fe₁₉/p-Si film when θ=0 at different microwave excitation powers. The external magnetic field is applied along the film plane. Here the background voltage due to the microwave irradiation is subtracted from the V spectra. The inset shows a schematic illustration of the experimental set-up when θ=0. (b) H dependence of V measured for the Ni₈₁Fe₁₉/p-Si film when θ=180° at different microwave excitation powers. (c) H dependence of the FMR signal dI(H)/dH measured for the Ni₈₁Fe₁₉/p-Si film when θ=0 at 200 mW microwave excitation (see the inset to a). I is the microwave absorption intensity. The solid circles are the experimental data. The solid curve shows the fitting result using the first derivative of a Lorentz function. (d) H dependence of dI(H)/dH for the Ni₈₁Fe₁₉/p-Si film when θ=180° at 200 mW microwave excitation (see the inset to b). (e) H dependence of V for the Ni₈₁Fe₁₉/p-Si film when θ=0. The solid circles are the experimental data. The solid curve shows the fitting result using with the parameters V_s=3.50 μV and V_as=−0.41 μV. (f) H dependence of V measured for the Ni₈₁Fe₁₉/p-Si film when θ=180°. The solid curve shows the fitting result with the parameters V_s=1.76 μV and V_as=0.41 μV. (g) The spectral shape of the symmetric V_s (H) and asymmetric V_as (H) components of the electromotive force V (H). (h) Microwave power P_MW dependence of ΔV_s, where . The solid circles are the experimental data. The solid line shows the linear fit to the data.

The electromotive force observed here is the combination of the ISHE in the p-Si layer, the ordinary Hall effect (OHE) in the p-Si layer, the anomalous Hall effect (AHE) in the Ni₈₁Fe₁₉ layer, and heating effects. The direct contribution from the ISHE in the p-Si layer can be extracted as follows (see Methods). The OHE and AHE voltages can be ruled out from the observed electromotive force by fitting the V spectra using a combination of symmetric (absorption shape) and asymmetric (dispersion shape) functions²⁵, , where H_FMR is the resonance field. Figure 2e,f is the fitting result for the V spectra at 200 mW for θ=0 and θ=180°, respectively, showing that the observed V spectra are well reproduced with V_s=3.50 μV and V_as=−0.41 μV for θ=0 and V_s=1.76 μV and V_as=0.41 μV for θ=180°. What is notable is that the Hall voltage due to rectification changes its sign across H_FMR as shown in Figure 2g (ref. 25). In contrast, the electromotive force due to the ISHE is proportional to the microwave absorption intensity³⁸. Here V_s is attributed to both the ISHE in the p-Si layer and heating effects³⁵. To eliminate the heating effects arising from the microwave absorption from the V spectra, we define , as the ISHE voltage due to the spin pumping changes its sign by reversing H whereas the electromotive force due to the heating effects is independent on the H direction. In Figure 2h, we show the microwave power P_MW dependence of ΔV_s. ΔV_s increases linearly with P_MW, as expected for the ISHE induced by the spin pumping³⁸. ΔV_s signal disappears when an in-plane magnetic field is applied parallel to the direction across the electrodes, supporting that ΔV_s is attributed to the ISHE in the p-Si layer because of equation (1).

Spin precession and inverse spin Hall effect

To further buttress the above result, we measured the out-of-plane magnetic field angle θ dependence of ΔV_s, which provides further evidence that the observed ΔV_s signals are attributed to the ISHE induced by the spin injection in the p-Si layer. Here the out-of-plane magnetic field angle θ is defined in Figure 3a. As shown in Figure 3a, when H is applied oblique to the film plane, the magnetization precession axis is not parallel to H because of the demagnetization field in the Ni₈₁Fe₁₉ layer. The relation between the external magnetic field angle θ and the angle of magnetization–precession axis φ can be obtained using the Landau–Lifshitz–Gilbert equation with the measured values of the resonance field H_FMR shown in Figure 3b (ref. 38). The θ dependence of φ for the Ni₈₁Fe₁₉/p-Si film is shown in Figure 3c. In Figure 3d,e, we show the dI/dH and V_s(H) signals for the Ni₈₁Fe₁₉/p-Si film at different θ. As shown in Figure 3e, ΔV_s disappears when the external magnetic field is applied perpendicular to the film plane; the θ dependence of ΔV_s shows the drastic variation of ΔV_s around θ=90° (Fig. 3f). Here the spin-polarization vector σ of the spin current injected into the p-Si layer is parallel to the magnetization–precession axis. Therefore, the spins of the spin current precess around the axis parallel to H, as shown in Figure 3a. This is described in the Bloch equation with spin diffusion and precession in the p-Si layer:

Figure 3: Angular dependence of ISHE signal and spin precession.

(a) A schematic illustration of the Ni₈₁Fe₁₉/p-Si film when the external magnetic field H is applied oblique to the film plane. M denotes the static component of the magnetization. θ and φ show the magnetic field angle and magnetization angle, respectively. (b) Magnetic field angle θ dependence of the FMR field H_FMR measured for the Ni₈₁Fe₁₉/p-Si film. The filled circles represent the experimental data. The solid curve is the numerical solution of the Landau–Lifshitz–Gilbert equation with the saturation magnetization 4πM_s=0.852T. (c) Magnetic field angle θ dependence of the magnetization angle φ for the Ni₈₁Fe₁₉/p-Si film estimated using the Landau–Lifshitz–Gilbert equation with the measured values of H_FMR. (d) Magnetic field angle θ dependence of the FMR signal dI(H)/dH measured for the Ni₈₁Fe₁₉/p-Si film at 200 mW. (e) Magnetic field angle θ dependence of the symmetric component of the electromotive force V_s (H) extracted by a fitting procedure from the measured V spectra for the Ni₈₁Fe₁₉/p-Si film at 200 mW. (f) Magnetic field angle θ dependence of ΔV_s. The solid circles are the experimental data. The solid curve is the theoretical curve obtained from equation (5) with τ_sf=9 ps. The dashed curve is the theoretical curve for τ_sf=0. The error bars represent the 90% confidence interval. The inset shows the θ dependence of ΔV_s calculated from equation (5) with τ_sf=20 ps (the red curve), τ_sf=10 ps (the blue curve), and (the black curve).

where m(x, t) is the magnetization of carriers in the p-Si layer; γ_c and τ_sf are the gyromagnetic ratio and spin relaxation time of carriers in the p-Si layer, respectively; D_N is the diffusion constant in the p-Si layer; e_x and e_z are the unit vector parallel to the x and z axes, respectively (Fig. 3a); δ(x) is the delta function and is the spin current density with the spin orientation direction p and flow direction q at the interface x=0. Thus and , where the spin current density j_s generated by the spin pumping at the interface in the FMR condition is given by³⁸,

Here is the spin mixing conductance, γ and M_s are the gyromagnetic ratio and saturation value of the magnetization M, respectively; α is the Gilbert damping constant; h is the microwave magnetic field; and ω=2πf is the angular frequency of the magnetization precession. By solving equation (2) for the equilibrium condition (∂m/∂t=0), we obtain

where and ; is the spin diffusion length of the Si layer; and are the real and imaginary part of , respectively. Because the spin current flows along the x direction, the electric field induced by the ISHE, E_ISHE(x), is proportional to . As shown in Figure 4a, decays because of the spin relaxation in the p-Si layer; the charge current density j_c(x) generated by the ISHE also depends on x, which induces short circuit currents in the Ni₈₁Fe₁₉ and p-Si layers³⁸. Equivalent circuit models of the Ni₈₁Fe₁₉/p-Si film are shown in Figure 4b,c (see Methods). Therefore, we obtain the angular dependence of the ISHE signal V_ISHE in the presence of spin precession as³⁵

Figure 4: Spin current relaxation.

(a) The spin current density generated by the spin pumping for τ_sf=9 ps. Here is the spin current density at the interface when the external magnetic field is applied along the film plane (θ=0). The parameters used for the calculation are shown in the text. (b) An equivalent circuit model of the Ni₈₁Fe₁₉/p-Si film. R_F is the electrical resistance of the Ni₈₁Fe₁₉ layer. (c) A simplified equivalent circuit model of the Ni₈₁Fe₁₉/p-Si film. (d) The spin relaxation time τ_sf dependence of the ISHE signal V_ISHE at θ=80° calculated from equation (5).

where d_N is the thickness of the p-Si layer. From equation (5), the electromotive force without taking into account spin precession () is given by , which is valid for materials where the spin relaxation time is very fast, such as Pt (ref. 38). Here, calculated θ dependence of ΔV_s is shown in the inset of Figure 3f for (the black curve), τ_sf=10 ps (the blue curve), and τ_sf=20 ps (the red curve) with 4πM_s=0.852 T. As τ_sf increases, spin precession reduces the electromotive force; the drastic variation of ΔV_s around θ=80° for becomes gentle for τ_sf=10 ps and τ_sf=20 ps owing to spin precession. The experimentally measured θ dependence of ΔV_s is well reproduced using equation (5) with τ_sf=9±3 ps as shown in Figure 3f, where ΔV_s is obtained from Figure 3e. This is the direct evidence of the observation of the ISHE in the p-Si layer; the ΔV_s signal cannot be attributed to the ISHE in the Ni₈₁Fe₁₉ layer, as the spin relaxation time in Ni₈₁Fe₁₉, τ_sf=9 fs, is so fast that is satisfied (see the dashed curve in Fig. 3f), where τ_sf is obtained from the spin diffusion length³⁹ λ_F=3 nm and diffusion constant⁴⁰ D_F=10 cm² s⁻¹. This result also supports that magnetogalvanic effects, that is, the OHE and AHE, and heating effects are irrelevant to ΔV_s.

Discussion

The above experimental results allow estimation of the spin Hall conductivity of the p-Si layer. In the FMR condition, when the magnetic field is applied along the film plane, the magnitude of the ISHE signal V_ISHE is obtained from equation (3) with the equivalent circuit model of the spin-pumping-induced ISHE where short-circuit currents in the Ni₈₁Fe₁₉ layer are taken into account³⁸: . Here w_F, d_F and σ_F are the length defined as in Figure 1b, thickness and electric conductivity of the Ni₈₁Fe₁₉ layer, respectively. Using the parameters for the Ni₈₁Fe₁₉/p-Si film, w_F=2.0 mm, D_N=3.23 cm² s⁻¹, d_N=4 μm, d_F=10 nm, σ_N=2×10² Ω⁻¹ cm⁻¹, σ_F=1.5×10⁴ Ω⁻¹ cm⁻¹, 4πM_s=0.852T, α=0.0088, h=0.16 mT, τ_sf=9 ps, and ΔV_s=0.87 μV, we find m⁻². Here the spin mixing conductance can be obtained from the enhancement of the FMR spectral width due to the spin pumping⁴¹. The spin mixing conductance of the Ni₈₁Fe₁₉/p-Si film is estimated from the FMR spectral width for the Ni₈₁Fe₁₉/p-Si film and a Ni₈₁Fe₁₉/SiO₂ film as m⁻². Thus we obtain the spin Hall angle for the p-Si layer θ_SHE≈1×10⁻⁴, which corresponds to the spin Hall conductivity σ_SHE≈2×10⁻² Ω⁻¹ cm⁻¹. These values are much smaller than those for doped GaAs²⁸, showing that this approach enables highly sensitive electric measurement of the ISHE. The successful measurement of the ISHE in silicon is attributed to its high electric resistivity, which is essential for large voltage generation due to the ISHE, and the high-density spin injection into macroscopic area by the spin pumping.

Although spin injection into n-type Si has been reported by several groups^33,34,42,43, there is only one report of room-temperature spin injection into p-type Si, using tunnel contacts³⁴. The successful observation of the ISHE in the Ni₈₁Fe₁₉/p-Si film now confirms this by a different approach, namely dynamical spin injection. The present experiment shows that the spin relaxation time in the p-Si layer is τ_sf=9 ps. Here in the direct Ni₈₁Fe₁₉/p-Si contact, the spin relaxation time near the interface may be reduced because of the coupling of the spins in the p-Si layer to the Ni₈₁Fe₁₉ layer⁴⁴. The spin relaxation time obtained using the electrical spin injection is τ_sf=270 ps for p-Si with the doping concentration of N_A=4.8×10¹⁸ cm⁻³ (ref. 34). Therefore, the spin relaxation time in p-Si obtained by both the electrical and dynamical spin injection is much longer than the momentum relaxation time ~5 fs in the p-Si layer⁴⁵; understanding the hole spin relaxation in p-type Si remains a challenge.

We showed that silicon has the potential to be used not only as a spin-current-transmission path^43,46 but also as a spin-current detector in spite of its weak spin–orbit interaction. Although the spin/charge current conversion efficiency is not large in the p-Si layer, the spin Hall effects in silicon can now be further explored; the combination of the spin pumping and ISHE paves the only way for quantitative exploration of the spin–orbit coupling effect in silicon for different doping density and dopant type. This approach provides also a way to extract the spin relaxation time τ_sf; as shown in Figure 4d, the magnitude of the electromotive force due to the ISHE is strongly dependent on τ_sf under the oblique magnetic field, especially when τ_sf is of the order of 10 ps. Furthermore, the approach presented here, thanks to the high-density spin injection, opens the way for exploring the spin Hall effects in a wide range of materials, including high-resistivity materials with weak spin–orbit interaction. This extends the range of potential materials for spin-current detector without magnetic materials.

Methods

Sample preparation

The sample used in this study is a Ni₈₁Fe₁₉/B-doped Si (Ni₈₁Fe₁₉/p-Si) film with a doping concentration of N_A=2×10¹⁹ cm⁻³. Two 30-nm-thick AuPd electrodes were sputtered on a silicon-on-insulator substrate (Fig. 1a) in an Ar atmosphere. After the sputtering, the silicon-on-insulator substrate was annealed at 400 °C for 10 min in a high vacuum, which yields ohmic contacts to the p-Si layer (Fig. 1b). The 10-nm-thick Ni₈₁Fe₁₉ layer was then deposited on the p-Si layer by electron-beam evaporation in a high vacuum. Immediately before the evaporation, the surface of the p-Si layer was cleaned by Ar-ion etching. The surface of the Ni₈₁Fe₁₉ layer and AuPd contact is of a 1.0×2.0-mm² rectangular shape and of a 1×0.5-mm² rectangular shape, respectively. The distance from the AuPd contact to the Ni₈₁Fe₁₉ layer is ~300 μm.

Electric voltage due to inverse spin Hall effect

The observed electromotive force in the Ni₈₁Fe₁₉/p-Si film is the combination of the ISHE in the p-Si layer, the OHE in the p-Si layer, the AHE in the Ni₈₁Fe₁₉ layer, and heating effects. The direct contribution from the ISHE in the p-Si layer can be extracted as follows: the OHE in the p-Si layer induces a DC electromotive force from an AC charge current due to a microwave electric field and an AC stray field due to precessing magnetization. This rectified voltage changes its sign across the resonance field, that is, the sign of the electromotive force when H<H_FMR is opposite to that when H>H_FMR, as the phase of magnetization precession shifts by π at resonance. Therefore, the shape of the electromotive force due to the OHE is asymmetric as shown in Figure 2g. Here a microwave magnetic field cannot create a detectable DC OHE voltage, since the direction of the microwave magnetic field is parallel to the direction across the electrodes (the y direction; Fig. 1a). Furthermore, the microwave magnetic field is independent of the FMR. The shape of the electromotive force due to the AHE is also asymmetric, because it is a rectified voltage induced by the combination of a charge current due to a microwave electric field and precessing magnetization³⁸. In contrast to the rectified voltage due to the OHE and AHE, the electromotive force due to the ISHE is proportional to the intensity of microwave absorption⁴⁷. This indicates that the shape of the electromotive force due to the ISHE is symmetric as shown in Figure 2g, and, thus, the electromotive force due to the OHE and AHE can be eliminated from the observed electromotive force. The electromotive force due to the sample heating is induced by the Seebeck effect, which is independent on the magnetic field direction. The Seebeck effect in the Ni₈₁Fe₁₉/p-Si film is induced by a lateral temperature gradient along the film plane due to small but finite misalignment of the position of the Ni₈₁Fe₁₉ layer with respect to the substrate. In fact, the magnitude of the symmetric component of V that does not change the sign with reversal of H depends strongly on samples. A longitudinal temperature gradient, that is, a temperature gradient perpendicular to the film plane, may induce a voltage through the Nernst effect. Although the Nernst effect induces a H-dependent voltage, Figure 3f clearly shows that this effect is irrelevant to the ΔV_s signals; the variation of ΔV_s cannot be reproduced by the cross product of a longitudinal temperature gradient and the external magnetic field. The θ dependence of ΔV_s is well reproduced using equation (5) with the spin relaxation time τ_sf=9 ps for P_MW=100, 150 and 200 mW. All errors and error bars represent the 90% confidence interval.

Equivalent circuit model

As shown in Figure 4a, decays because of the spin relaxation in the p-Si layer; the charge current density j_c(x) generated by the ISHE also depends on x, which induces short circuit currents in the Ni₈₁Fe₁₉ and p-Si layers³⁸. Here a total charge current generated by the ISHE is , where d_N is the thickness of the p-Si layer. By dividing the p-Si layer into n layers, an equivalent circuit of the Ni₈₁Fe₁₉/p-Si film is obtained as shown in Figure 4b, where R_F is the electrical resistance of the Ni₈₁Fe₁₉ layer. The electrical resistance and the charge current generated by the ISHE of the ith layer satisfy and , where R_N is the electrical resistance of the p-Si layer. It is straightforward to convert the circuit shown in Figure 4b into that shown in Figure 4c. Thus, the electromotive force due to the ISHE is obtained as . This result shows that V_ISHE is proportional to the total charge current I_N generated by the ISHE; the electromotive force due to the ISHE in the Ni₈₁Fe₁₉ layer is negligibly small because of the extremely short spin diffusion length³⁹ and small spin Hall angle⁴⁸.