Main

Tunnelling spectroscopy is one of the most widely used experimental techniques to study electronic structures14. Conventional tunnelling spectroscopy measures the longitudinal tunnelling current to extract material parameters such as the electronic density of states (DOS) and band gap. In this Letter we show that by measuring the transverse current or voltage generated from spin-polarized tunnelling carriers, one can probe transport properties related to the spin–orbit interaction, in particular the spin Hall effect. Furthermore, the SHE signal from hot electrons can be detected by applying finite bias voltages.

To inject spin polarized current into the normal metal (NM), we pattern the NM/oxide/ferromagnet (FM) stacks into the shape shown in Fig. 1a. We apply the charge current between leads 1 and 3 and measure the voltage between 2 and 4. In the presence of the inverse SHE (ISHE), the spin angular momentum σ, injected spin current density js and generated charge current density jc satisfy the relationship3 jc ∼ σ × js. Therefore, a transverse voltage is expected to arise in the y direction when spins aligned in-plane along the x direction are injected into the NM and diffuse along the z axis (Fig. 1b). At zero d.c. bias, the ISHE voltage of the device in Fig. 1a can be written as15,16 (see also the Supplementary Information). Here ρ is the resistivity of the spin Hall (SH) metal, θSH is the SH angle, defined as the ratio between the orthogonally related charge current density and the spin current density, and js = Pjin represents the spin current density, where P and jin denote the spin polarization and injected charge-current density. a, b, w and t are dimensions defined in Fig. 1a. The shunting factors, b/w and (λsf/t) tanh(t/2λsf), take into account that the ISHE develops only in the region under the tunnel barrier and decays over a thickness of λsf whereas the charge current flows across the entire channel cross-section of width w and thickness t. As jin = I13/(ab), we arrive at the following expression for the transverse resistance:

Figure 1d shows the circuit for detecting the transverse resistance (Methods). Because of imperfect alignment in the photolithography, there exists a parasitic voltage on top of the ISHE signal, which we compensate with a resistance bridge. Because of its geometric nature, the parasitic resistance remains constant with magnetic field, and the SH resistance has been observed to be independent of its sign or magnitude in all devices.

Figure 1: Overview of the device and the circuit for SHE tunnelling spectroscopy measurements.
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a, Schematic of the devices used in the SHE tunnelling spectroscopy experiment. The lateral dimensions of the tunnel junction are defined by a and b. w and t represent the width and thickness of the SH metal channel. b,c, Illustration of the generation of transverse current for SH metals (b) and 2D electron states with spin–orbit splitting (c). In SH metals, the spin polarized hot electrons are deflected sideways after they are injected from the FM electrode. For 2D states, the majority and minority electrons tunnel into different sub-bands with different parallel wavevectors. In b, the direction of the electric field is defined by the convention that under a positive bias electrons tunnel into states above the Fermi surface of the NM. d, Schematic of the circuit used in the experiment.

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Figure 2a shows the ISH resistance (dV/dI)13,24 curve of a Ta/MgO/CoFeB sample. A hysteretic loop develops when we sweep the magnetic field along the x direction (0°), and vanishes when we sweep along the y direction (90°), consistent with the symmetry of the ISHE. The coercivity of ∼20 Oe agrees with the switching field of the CoFeB layer (Supplementary Information). Figure 2b shows the transverse resistance (dV/dI)24,13 measured in the direct SHE (DSHE) configuration, in which we apply the current between leads 2 and 4 and measure the voltage between leads 1 and 3. We can see that the magnitude of the signals agrees well between the DSHE and ISHE configurations, as is expected from the Onsager reciprocal relation. In the DSHE, the voltage across the barrier is induced by spin accumulation at the Ta surface (see inset of Fig. 2b). Using the model of ref. 15, we can write the DSHE-induced voltage as V13 = (θSHPρλsf/wt) ⋅ I24tanh(t/2λsf), the same as the ISHE equation (Supplementary Information).

Figure 2: SHE signal from the Ta/MgO/CoFeB sample.
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a,b, Transverse resistance dV/dI measured in the ISHE (a) and DSHE (b) configurations. The fields are applied along the x (0°) and y (90°) directions in each case. The junction area is ∼3 × 4 μm2 and the resistance–area product is ∼100 kΩ μm2. The differential ISH resistance dVISH/dI is defined as one half of the field-dependent signal. Inset of b, schematic illustration of the spin accumulation induced by the DSHE at the NM/oxide interface. The red and green curves represent the spin-dependent chemical potentials for the majority and minority spins, respectively. c, ISH resistance (dV/dI)13,24 measured at two different d.c. biases when the field is swept along 0°. d, The differential ISH resistance dVISH/dI as a function of the applied d.c. voltage. Two similar devices are shown. The dashed lines represent Taylor polynomial fits for the two samples. The error bars represent the standard deviation of results from ten scans.

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Figure 3a gives the ISHE data of a device with an AlOx tunnel barrier (Ta/AlOx/CoFeB). At zero bias (black circles in Fig. 3a), the magnitude of the signal is about half that of the MgO device (1.3 mΩ versus 2.6 mΩ). This can be explained by the different values of spin polarization across those two barriers. From the tunnelling magnetoresistance (TMR) of standard magnetic tunnel junctions (MTJs) made of these two barriers, we determined P(MgO) ∼ 0.60 ± 0.05 and P(AlOx) ∼ 0.38 ± 0.05 (Supplementary Information), roughly consistent with the difference in the ISH resistances.

Figure 3: SHE signal from the Ta/AlOx/CoFeB sample.
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a, ISH resistance (dV/dI)13,24 measured at VDC = −420 mV, 0 mV and +420 mV, with the field swept along the x direction (0°). The junction area is ∼4 × 4 μm2 and the resistance–area product is ∼20 kΩ μm2. b, Differential ISH resistance dVISH/dI as a function of the applied d.c. voltage. The error bars represent the standard deviation of results from ten scans.

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Besides Ta, we also measured samples made from Pt. Previous studies showed that both metals have a strong SHE but their signs are opposite8,10,16. As shown in Fig. 4a (ISHE) and 4b (DSHE), the transverse resistances of the Pt/MgO/CoFeB sample indeed exhibit opposite signs to those of the Ta samples. This fact also indicates that the measured signal must originate from the NM layer rather than from magneto-transport effects in the CoFeB layer, which would have resulted in the same sign in transverse resistance (Supplementary Information). To extract the SH angles, we note that all the parameters in equation (1) can be determined relatively precisely in our experiment except for λsf. Large discrepancies exist in the values of λsf reported from different experiments. To account for this uncertainty, we use a wide range for λsf in our calculation (1–2.7 nm for Ta (refs 16, 17) and 1.5–10 nm for Pt (refs 16, 18), which reflects the lower and higher bounds of λsf reported in the recent literature). With those numbers and with the spin polarization calculated from the TMR of standard MTJs, the SH angles are determined to be: |θSH(Ta)| = 0.05–0.11 and |θSH(Pt)| = 0.04–0.09 (Supplementary Information). Note that as the quality of the tunnelling barrier in the standard MTJs with two CoFeB electrodes is probably higher compared with that in the NM/oxide/FM junctions, we may have overestimated the spin polarization of our devices. Therefore, the values of the SH angle reported above should be treated as the lower bound of the actual values of the SH angle at the Fermi level. The magnitude of the SH angles has long been a heatedly debated topic in the study of the SHE (ref. 18). Large SH angles that are close to the spin polarization of FM metals usually need to be assumed to explain the magnetic dynamics observed in the SH spin torque experiments8,11,12,13. Also, electrical transport measurements have reported much smaller values (for example, 0.004 for Ta and 0.02 for Pt; ref. 16). In this Letter, by employing a pure transport approach, we obtained results that are consistent with previous SH torque studies, verifying the SH origins of those experiments. In contrast to previous transport experiments using non-local spin valves16, our devices inject spin-polarized current directly into the NM through a tunnel barrier. We thus avoid the complexity of dealing with the loss of the spin current across multiple interfaces and through diffusive metals. Therefore, we believe that SH tunnelling spectroscopy provides a simple and accurate measurement technique for determining SH angles.

Figure 4: SHE signal from Pt/MgO/CoFeB sample and voltage dependence of ISHE resistance from W and Ir samples.
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a,b, Transverse resistance dV/dI measured in the ISHE (a) and DSHE (b) configurations for the Pt sample. The device has dimensions of ∼4 × 5 μm2 and the resistance–area product is ∼200 kΩ μm2. In 90°scans, the small residual resistances at low field in the dV/dI versus H curves are due to the domains aligned along the easy axis (0°) that are not fully compensated, reflecting the multi-domain nature of the CoFeB electrode. c, ISH resistance (dV/dI)13,24 of the Pt sample measured at VDC = −500 mV, 0 mV and +540 mV. d–f, Absolute value of the differential ISH resistance dVISH/dI as a function of the applied d.c. voltage in Pt (d), W (e) and Ir (f) samples. The error bars represent the standard deviation of results from ten scans. Two devices are shown for each material. Inset of d, schematic illustration of the tunnel junction under a d.c. bias voltage of V. P(ɛ − eV) and θSH(ɛ) represent the spin polarization and the spin Hall angle for electrons with the corresponding energy, respectively.

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The use of tunnelling electrons has another important advantage—it enables us to apply a finite d.c. bias across the junction and measure the voltage dependence of the ISHE signal. Under finite bias, if the spin relaxation length (λsf) is much smaller than the hot-electron attenuation length (λat), the measured ISHE signal would mainly come from energetic electrons. In the other extreme, if λsf ≫ λat, the energetic electrons would relax back to the Fermi level before they contribute to the SHE, and thus we would expect to see very little signal variation to reflect the energy dependence of the SHE. When the two length scales are comparable (λsf ∼ λat), the observed tunnelling spectra would consist of a superposition of the SHE from both energetic and equilibrium electrons, which would retain the energy dependence of the SHE, albeit with energy-broadened spectral features. According to previous ballistic electron emission experiments, λat is usually between a few to a few tens of nm for tunnelling electrons in transition metals19,20. Meanwhile, λsf is around 1–10 nm for heavy metals such as Pt and Ta (refs 17, 18, 21). Therefore, the two quantities are at least comparable to each other in our studies and the measured signal should contain energy-dependent information from the SHE. Figure 2c shows the differential ISH resistance dVISH/dI of Ta/MgO/CoFeB under different d.c. biases. The voltage dependence of dVISH/dI over the range ±700 mV is summarized in Fig. 2d. We can see that dVISH/dI decays rapidly under negative bias, but increases under positive bias until the signal saturates around 400 mV. On the other hand, the Pt/MgO/CoFeB sample demonstrates a much more symmetric bias-voltage dependence (Fig. 4c, d). We have also measured devices made of W (Fig. 4e) and Ir (Fig. 4f) thin films. At zero d.c. bias, the sign and magnitude of the SH angles of these two materials (Supplementary Information) agree with previous experiments and calculations10,22. At finite bias, the W samples show a distinct bias asymmetry compared with Ta and Pt, and the spectral peak is located near the Fermi level, whereas the Ir samples show a monotonic increase in dVISH/dI with bias voltage within the voltage range of the experiment. We note that, compared with Ta/MgO/CoFeB, the Ta/AlOx/CoFeB sample shows a very similar bias asymmetry in dVISH/dI (Fig. 3a, b). The faster drop in the dVISH/dI(V) value under negative bias in the AlOx sample is consistent with a stronger voltage dependence of spin polarization across the AlOx tunnel barriers (Supplementary Fig. 2c, d). The fact that devices made from amorphous AlOx barriers and coherent MgO barriers show similar spectral features also indicates that the major contribution to the voltage dependence of dVISH/dI(V) may not come from the effect of tunnelling matrix elements.

Under finite bias, the DOS and tunnelling probability of tunnelling electrons may both change with the applied voltage. Correspondingly, the tunnelling current and the induced transverse voltage would also vary. In our experiment, however, the nonlinearity of the I–V characteristics has been taken into account by normalizing the ISH voltage against the applied a.c. current. Therefore, the voltage dependence of current does not contribute to the voltage dependence of dVISH/dI. Another factor that can contribute to the voltage dependence is the spin polarization P(V). In our experiment, P(V) alone cannot explain the drastically different bias asymmetries observed in devices made using different 5d transition metals, which have nominally the same barrier and FM electrode. Moreover, the voltage-dependent spin polarization in standard MTJs can be estimated using their TMR value, which provides a guideline for estimating P(V) of the NM/oxide/FM junctions. It can be shown that the variation of P is relatively small (≤30%; Supplementary Information), not enough to account for the comparatively large changes in the ISH signal (≥50% in Pt, even larger in Ta, Ir, and W). Although the above discussions strongly indicate that the SHE is not fully masked by the energy dependence of the other factors, a quantitative determination of the energy-dependent SH angle requires more experimental data on the voltage dependence of the spin polarization and the spin/energy relaxation length, as well as a rigorous treatment which takes into account the band structure of both electrodes and the tunnelling matrix of the barrier.

A comparison can be made between the measured voltage-dependent SHE signal and theoretical calculations based on the band structures of the materials. For Pt, results in Fig. 4d qualitatively agree with previous calculations9,10 in which the intrinsic SH conductivity was shown to peak close to the Fermi surface. This is consistent with the fact that, for the intrinsic SHE in Pt, the dominant contribution comes from the avoided crossings of the nearly degenerate bands located near the Fermi level, where the uncompensated Berry curvature gives rise to a large SH conductivity9. For other metals, further first-principles calculations using the same crystalline structures as those of our films (for example, the β phase for Ta) are necessary to explain the voltage dependence found in the tunnelling spectra.

Besides the SHE, which is generally calculated using the bulk electronic structure of the corresponding material, spin–orbit interactions can also induce splitting in localized surface states, as observed in many heavy-element metals23,24,25 by means of angle resolved photoemission spectroscopy (ARPES). A similar transverse voltage26 can be generated as a result of spin-momentum locking (Fig. 1c). Our energy-dependent dVISH/dI measurement provides a method to distinguish between those two mechanisms. For example, in Pt, previous calculations and experiments show that the bottom of surface bands is located ∼300 meV above the Fermi surface25,27. Within the resolution of our experiment, we observe no sharp transition or change of slope around that energy level. Moreover, we can compare the dVISH/dI(V) tunnelling spectra of W (Fig. 4e) and Ir (Fig. 4f) with the ARPES spectra, in which the spin–orbit-interaction-induced surface band splitting has been observed earlier23,24. That the spectral peaks in dVISH/dI(V) do not agree with the location of the surface bands observed by ARPES in these metals indicates that the tunnelling transverse signal should be mainly attributed to the SHE in the projected bulk bands. Moreover, the consistency between the SH angles measured in our experiment and those in NM/FM bilayer spin–orbit torque measurements also implies that the anti-damping torque observed in those experiments shares the same bulk band origin.

The SHE spectra provide guidelines for further improving the magnitude of the SHE by means of electronic structure engineering, for example, by adjusting the Fermi surface position through alloying or chemical compound formation. Because of the impedance matching capability of the tunnel junctions, besides metals, the SHE tunnelling spectroscopy can also be used to investigate semiconductors. It will be particularly useful for probing spin–orbit interactions in topological insulators or two-dimensional (2D) electron gases where surface states dominate. In the former case, the capability of applying finite biases will enable the detection of electrons close to the Dirac point.

Methods

Sample fabrication.

The full stacks of substrate/SH metal (7)/oxide tunnel barrier (1.5–2.5)/Co20Fe60B20 (4)/Ta (5)/Ru (5) (units in nm) were first deposited by sputtering and then patterned into the shape shown in Fig. 1a by a combination of photolithography and ion beam etching. The etching stops slightly below the SH metal/oxide interface. The CoFeB layer has in-plane anisotropy because of the chosen thickness. Post-deposition annealing was used to optimize the tunnelling spin polarization. Top contacts made from a layer of Ta(5 nm)/Cu(90 nm)/Pt(20 nm) were deposited after the side of the tunnel junction was encapsulated with SiO2. The resistance–area (RA) product of tunnel barriers in our samples ranges between 20 kΩ μm2 and 300 kΩ μm2. The tunnel junctions have rectangular shapes with their easy axis aligned along the x direction. The lateral dimensions of tunnel junctions vary between 3 and 8 um and the channel width of the SH metal is 8 μm.

Circuit and measurement scheme.

In the circuit, we used an audio transformer to inject d.c. and a.c. currents simultaneously into the tunnel junction. The a.c. current is provided by the internal oscillator of the lock-in amplifier. The frequency of the a.c. current IAC was set to be around 1 kHz. The amplitude of IAC was read out by measuring the voltage of the serial sensing resistor Rsense = 10 Ω and was maintained around 10 μA in our experiments. For our 8 kΩ devices, this corresponds to a ∼80 mV a.c. voltage across the junction at zero d.c. bias, which determines the energy resolution of our technique. To avoid electrical breakdown of the tunnel junction, another serial resistor Rlimit was used to limit the a.c. voltage distribution on the device. To measure the transverse a.c. voltage, we first amplified the signal between leads 2 and 4 through a pre-amp, so that the floated voltage is converted into a signal relative to the ground. Then we connected the output of the pre-amp to one end of the input channel of a lock-in amplifier and the resistor bridge to the other end of the lock-in input to compensate for parasitic signals due to misalignment. The absolute value of the parasitic resistance is <20 Ω for Ta and <4 Ω for Pt, W and Ir. Both positive and negative values have been observed for devices on different chips, indicating randomness in the pattern misalignment. We measured the ISH voltage as a function of the applied sensing current IAC within a wide range and a good linear dependence was observed. This excludes the possibility that the observed signal comes from thermal effects (Supplementary Information). For energy dependence measurements, we use a d.c. current source to provide the bias voltage. The d.c. voltage of the device was measured with a voltmeter connected in parallel with the output of the current source. As the resistance of Rsense is much smaller than that of the device, the measured voltage is approximately the same as the voltage drop across the junction. All the measurements were done at room temperature.