LETTERS PUBLISHED ONLINE: 20 JULY 2014 | DOI: 10.1038/NPHYS3004 Spin Hall effect tunnelling spectroscopy Luqiao Liu * , Ching-Tzu Chen and J. Z. Sun The spin Hall effect (SHE) and its inverse have been widely used to generate and detect spin currents 1–8 . To date, most experiments focus only on characterizing electrons near the Fermi surface 4–8 , whereas the SHE, which originates from the spin–orbit interaction, is expected to be energy dependent 9,10 . Here, we report a tunnelling spectroscopy technique developed to measure the SHE under finite bias voltages. We studied the SHE for typical 5d transition metals. At zero d.c. bias, the obtained spin Hall angles confirm the results from spin-torque experiments 8,11–13 . At high bias, the transverse spin Hall signals of these materials exhibit very different voltage dependences. The SHE tunnelling spectra have important implications in pinpointing the mech- anisms of the SHE and provide guidelines for engineering high-SHE materials. Moreover, SHE tunnelling spectroscopy can be directly applied to two-dimensional surface states with strong spin–orbit coupling, such as Dirac electrons in topological insulators. Tunnelling spectroscopy is one of the most widely used experimental techniques to study electronic structures 14 . 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 j s and generated charge current density j c satisfy the relationship 3 j c ∼ σ × j s . 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 as 15,16 V 24 = ρθ SH j s a · (b/w) · (λ sf /t ) tanh(t /2λ sf ) (see also the Supplementary Information). Here ρ is the resistivity of the spin Hall (SH) metal, θ SH is the SH angle, defined as the ratio between the orthogonally related charge current density and the spin current density, and j s = Pj in represents the spin current density, where P and j in 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 (λ sf /t ) tanh(t /2λ sf ), take into account that the ISHE develops only in the region under the tunnel barrier and decays over a thickness of λ sf whereas the charge current flows across the entire channel cross-section of width w and thickness t . As j in = I 13 /(ab), we arrive at the following expression for the transverse resistance: dV 24 dI 13 = θ SH P ρ w · λ sf t · tanh(t /2λ sf ) (1) 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 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 V 13 = (θ SH P ρ λ sf /wt ) · I 24 tanh(t /2λ sf ), the same as the ISHE equation (Supplementary Information). Figure 3a gives the ISHE data of a device with an AlO x tunnel barrier (Ta/AlO x /CoFeB). At zero bias (black circles in Fig. 3a), the magnitude of the signal is about half that of the MgO device (1.3 m versus 2.6 m). This can be explained by the different values of spin polarization across those two barriers. From the tunnelling magne- toresistance (TMR) of standard magnetic tunnel junctions (MTJs) made of these two barriers, we determined P (MgO) ∼ 0.60 ± 0.05 and P (AlO x ) ∼ 0.38 ± 0.05 (Supplementary Information), roughly consistent with the difference in the ISH resistances. Besides Ta, we also measured samples made from Pt. Previous studies showed that both metals have a strong SHE but their signs are opposite 8,10,16 . 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 λ sf . Large discrepancies exist in the values of λ sf reported from different experiments. To IBM TJ Watson Research Center, Yorktown Heights, New York 10598, USA. *e-mail: lliu@us.ibm.com NATURE PHYSICS | VOL 10 | AUGUST 2014 | www.nature.com/naturephysics 561 © 2014 Macmillan Publishers Limited. All rights reserved.