SUPPLEMENTARY INFORMATION

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1 SUPPLEMENTARY INFORMATION DOI: /NNANO Electrical detection of charge current-induced spin polarization due to spin-momentum locking in Bi 2 Se 3 by C.H. Li, O.M.J. van t Erve, J.T. Robinson, Y. Liu, L. Li and B.T. Jonker Ferromagnetic contacts The magnetic characteristics of the ferromagnetic (FM) detector contacts were determined by anisotropic magnetoresistance (AMR) measurements. The AMR was measured in a two terminal geometry in which current flows through the FM material. The resistance is measured as a magnetic field applied in-plane along the contact edge reverses the contact magnetization. A characteristic AMR signal appears in Figure SI-1 for an Fe contact, and sharp peaks occur at the coercive fields of ± 62 Oe as the magnetization reverses, with a variation of ± 5 Oe from contact to contact. Panel b) shows the corresponding AMR data for the Co contacts. The coercive field is much higher (150 Oe) and the peaks are much broader than those of the Fe, indicating that reversal of the contact magnetization occurs over a much broader range of applied field. Figure SI-1. Anisotropic magnetoresistance of the FM detectors at 10K. a) Fe contacts. The peaks observed at ± 65 Oe occur as the magnetization of the detector contact reverses with an in-plane applied magnetic field, and correspond to the coercive field. b) Co contacts. The coercive field is 150 Oe. AMR is a property of the FM metal contact, not of the TI. The red trace corresponds to increasing the applied magnetic field from negative to positive, and the black trace corresponds to decreasing the magnetic field. NATURE NANOTECHNOLOGY 1

2 Control experiments Control measurements were performed using only the non-magnetic reference contacts to determine any background contributions. The two-terminal magnetoresistance measurement at T = 8K with the +2 ma bias current flowing between two end Au / Ti contacts is shown in Figure SI-2, and shows a nearly linear magnetoresistance-like response ΔV 2T (μv) V! Magnetic field (Oe) Figure SI-2. Two terminal magnetoresistance measurement of the Bi 2 Se 3. The measurement geometry is shown by the inset, and the magnetic field is applied in-plane and perpendicular to the current direction. The data were obtained at T = 8K for a +2 ma bias current, and a linear background was subtracted. The red trace corresponds to increasing the applied magnetic field from negative to positive, and the black trace corresponds to decreasing the magnetic field. A second set of control measurements were performed using one of the non-magnetic Au/Ti contacts as the voltage detector. A fixed bias current flows between the two end contacts, and the voltage at the non-magnetic detector is recorded with a high-impedance voltmeter (> 1 Giga-ohm) as a function of an in-plane magnetic field applied orthogonal to the bias current direction in the TI. No current flows through the detector contact. These data are shown in 2

3 Figure SI-3 (T = 8K, +2 ma bias), and again show a nearly linear magnetoresistance-like response with no evidence for hysteretic behavior. V! Figure SI-3. Control measurement with non-magnetic detector. The measurement geometry is shown by the inset, and the magnetic field is applied in-plane and perpendicular to the current direction. A non-magnetic Au / Ti contact is used as the detector. No hysteretic behavior is measured. The data were obtained at T = 8K for a +2 ma bias current, and a linear background was subtracted. The red trace corresponds to increasing the applied magnetic field from negative to positive, and the black trace corresponds to decreasing the magnetic field. Additional control experiments were performed with a magnetic ohmic (rather than tunnel barrier) contact as the detector to determine whether local fringe fields due to domain walls, film roughness or contact edges produced any measureable signal which might mimic a spin voltage. Such fringe fields could lead to local Hall or other Lorentz force based effects. An ohmic contact will sense only the charge contribution and not the spin contribution as a consequence of the impedance mismatch issue between a metal and semiconductor. 1,2 These data are shown in Figure SI-4 for a Co detector and 0.5 ma bias current, and demonstrate that any such effects, if present, are within the noise of our measurements and much smaller than the spin voltage we measure on the magnetic tunnel barrier detector contacts. 3

4 Figure SI-4. Control measurement with magnetic (Co) ohmic detector. Anisotropic magnetoresistance and anomalous Hall effects The rectangular hysteresis loops shown in Figures 4b-4f exclude contributions from anisotropic magnetoresistance (AMR) which may arise due to possible current shunting by the magnetic detector contacts. In materials such as Fe and Co, the AMR is small (of order 0.1-1%), exhibits a cos 2 θ dependence upon the angle between the current and magnetization, a weak temperature dependence, and persists to room temperature. The data of Figures 4b-4f exhibit none of these characteristics, and we conclude any current flow in the detector is negligible. Thus there is also no mechanism to generate contributions from the anomalous Hall effect (AHE). Although the data of Figs 4g and 4h indeed resemble a cos 2 θ behavior, these data are from the same detector contact as that of Figs 4c-f (only the orientation of the magnetization has changed), and therefore we can also exclude AMR here. The behavior observed in Figures 4g and 4h is exactly as expected from bias current induced spin-momentum locking as the detector magnetization reverses for the orientation of bias current and magnetization used in these panels, and is discussed further below. Additional control experiments on Fe/Si and Fe/InAs samples show that even significant current flow in the planar magnetic detector contact does not produce a significant voltage signal for the top-to-bottom detector geometry we employ, ruling out contributions from AHE. These are discussed in detail below. 4

5 Raw data and background subtraction To illustrate the spin-dependent signal levels and the simple background subtraction employed, we show the raw data corresponding to Figure 3b in Figure SI-5. This is the voltage measured on contact Fe1 / Al 2 O 3 / Bi 2 Se 3 for a +2mA bias current as a function of magnetic field. The spindependent signal is clearly observed above the background voltage in the raw data. The dashed line shows the linear background which is subtracted its slope is taken to be the average of the slopes of the data for magnetic fields /H/ > 200 Oe. Figure SI-5. Raw data corresponding to Figure 3b. The spin signal is distinct from the background and readily observed in the raw data. The dashed line illustrates the linear background subtracted. Temperature dependence of the resistance for Bi2Se3 films The temperature dependence of the resistance for the 11 nm and 23 nm thick Bi 2 Se 3 films used is shown in Figure SI-6. The resistance smoothly decreases with decreasing temperature, indicating that the films are metallic in character, consistent with the measured electron density of n ~ cm -3. Figure SI-6. Temperature dependence of the Bi 2 Se 3 film resistance. 5

6 Hysteresis observed in Figures 4g and 4h The hysteresis observed in Figures 4g and 4h is a natural consequence of the process of magnetization reversal. The key issue to appreciate in all of these measurements is that the spin voltage measured is proportional to the dot product between the contact magnetization M and the TI spin polarization p (labeled s in the figure insets). In Figure 4g-h, at high +/- magnetic field, M is saturated and rigorously orthogonal to s, as the inset diagram shows the dot product and spin voltage are zero. As the magnetic field is swept from either large +/- values and crosses zero, M begins to rotate in-plane and necessarily has a non-zero projection on s this is the standard process of magnetizaton reversal in a thin film. The non-zero projection produces the spin voltage. As the applied magnetic field increases further from zero, it pulls M in the corresponding direction so that it eventually reverses. But this does not happen abruptly, it occurs over a field range of ~ 200 Oe, as shown explicitly by the Co anisotropic magnetoresistance data of Figure S1-b. During this reversal process, the contact breaks up into magnetic domains, which is why the magnitude of the spin voltage in Fig 4d and 4h is smaller than that of Fig 4b and 4f. In addition, in a film with domain pinning sites (e.g. sample edges) or anisotropy, the net magnetization reverses in the same sense with each field sweep cycle rather than randomly, particularly if the applied magnetic field direction is off by a few degrees from an easy magnetization axis of the sample. Therefore, the voltage does not average to zero with multiple field sweeps. This is textbook behavior. 3 Additional control experiments: Fe / Si and Fe / InAs(001) There is a remote chance that some fraction of the bias current applied to the Bi 2 Se 3 is shunted through the magnetic detector film due to interface roughness, and thus produce some spurious signal arising from an anomalous Hall effect (AHE) or anisotropic magnetoresistance (AMR) in the magnetic detector itself rather than from the topologically protected states of the Bi 2 Se 3. To address this concern, we fabricated samples consisting of Fe films on n-type Si(001) (n = 2 x cm -3 ), a low spin-orbit material, and n-type InAs(001) (n > cm -3 ), a high spin orbit material known to exhibit a surface two-dimensional electron gas (due to surface accumulation) and strong Rashba effects. The Fe contacts exhibit a linear I-V characteristic typical of an ohmic 6

7 contact. As a worst case scenario, we pass the bias current directly through the Fe film rather than through the underlying semiconductor using the contact geometry shown in Figure SI-7. The same voltage detection geometry and circuit is used as for the Bi 2 Se 3 samples. The magnetic field is applied in-plane and normal to the current direction, which is expected to provide best sensitivity to any AHE contributions. V Figure SI-7. Measurement geometry for control samples. Bulk wafers of Si and InAs were used. The Fe film was 20 (8) nm thick for the Si (InAs) sample. Fe n-siorinas(001) The results are shown for a bias current of +2mA at T = 15K in Figure SI-8 b-e, and compared with the data of Figure 3b (Fe / Al 2 O 3 / Bi 2 Se 3 ) which is repeated here as Figure SI-8a. Panel (b) shows the detector voltage vs in-plane magnetic field for the Fe/Si control sample, and panel (c) shows the same data with the voltage axis amplified by 10x. Panels (d) and (e) show the corresponding data for the Fe/InAs control sample. The data from the Fe/Si and Fe/InAs samples are very similar. We note two key points. First, even when the +2 ma bias current is applied directly through the Fe detector contact, any voltage signal is 10-fold smaller than that measured for the Fe/Al 2 O 3 /Bi 2 Se 3 sample of Figure 3b. Second, although weak hysteretic behavior is observed in Figures SI8 b-d, the loop is inverted about the vertical axis relative to the data of panel (a) for the Fe/Al 2 O 3 /Bi 2 Se 3 sample. Regardless of their origin, these signals are much smaller than and of opposite symmetry to those we attribute to spin-momentum locking in the topologically protected surface states of our Bi 2 Se 3 samples. These data collectively rule out contributions from AHE or AMR. 7

8 !" #"!" #"!"!"!"!" Figure SI-8. Data from Fe/Si and Fe/InAs control samples using the geometry of Figure SI-7. Panel (a) repeats the data of Figure 3b for the Fe/Al 2 O 3 /Bi 2 Se 3 sample at T = 8K. Panel (b) shows the detector voltage vs in-plane magnetic field for the Fe/Si control sample, and panel (c) shows the same data with the voltage axis amplified by 10x. Panels (d) and (e) show the corresponding data for the Fe/InAs control sample. The relative orientation of electron current and applied field are shown by the insets. 8

9 Two dimensional electron gas states and potential Rashba contribution The Bi 2 Se 3 surface is reported to exhibit downward band bending which leads to surface accumulation and potential formation of two dimensional electron gas (2DEG) states just below the bulk conduction band edge (~ 40 mev) 4 with unusually large Rashba spin-orbit coupling. 5,6 Some have reported that these 2DEG and Rashba states do not form until an adsorbate such as potassium is deposited onto the surface 7. Once formed, the Rashba states exist as spin-split pairs with momenta k 1 and k 2 at E F, k 1 < k 2 (taken along k x, for example), with the spin in-plane and at approximately right angles to the electron momentum. These bands can, in principle, also give rise to a current-induced spin polarization opposite that produced by the TI surface state bands 8,9,10 and may contribute to the voltages we measure here. However, we believe that this Rashba-induced polarization is small compared to that of the TI surface bands for our samples for the following reasons. First, the Rashba states exist as spin-split pairs with opposite spin directions at each momentum, and the resulting current-induced spin densities tend to cancel. 9 In contrast, a single TI surface band has only one spin state at each momentum with no cancellation. Second, a quantitative analysis 10 has shown that the spin polarization induced per unit bias current for TI spin-momentum locking is p(ti) = -2/π, and always larger in magnitude and opposite in sign than that induced by the Rashba spin-split pair given by p(rashba) = 2/π [(k 2 - k 1 ) / (k 2 + k 1 )]. Hong et al explicitly calculate these contributions for Bi 2 Se 3 using the giant spinorbit parameter obtained from photoemission, α = 0.79 ev angstrom, 7 and find that the voltage produced on the FM detector contact is significantly larger for TI spin-momentum locking than for the Rashba spin-split states. 10 They find further that the bias current-induced polarization is always larger for the TI surface states than for the Rashba states in both ballistic and diffusive transport regimes for all values of E F except at the minimum of the Rashba bands, where the TI and Rashba contributions are nearly equal. Third, the sign of the voltage we measure indicates that the TI spin-momentum locking contribution to the bias current induced spin polarization dominates. Following the model calculation of Hong et al, 10 the FM detector voltages V(M) we measure experimentally (Figures 3 and 4) are directly related to the current induced spin polarization by [V(M) - V(-M)] = I b R B P FM ( p. M u ), (bold case denotes a vector) where I b is the (hole) bias current in the +x 9

10 direction, R B is the ballistic conductance of the channel, and P FM is the transport spin polarization of the FM detector metal. M u is a unit vector along the detector magnetization M (positive along the +y axis), and p is the degree of spin polarization induced per unit bias current by both spin-momentum locking in TI surface states (along y) and Rashba spin-orbit coupling (along +y). We take the data of Figure 4e as a specific example to determine the sign of p we obtain in our measurements: [V(M) - V(-M)] is negative, I b and M u are positive, and therefore p must be negative, as expected for the TI surface spin-momentum locking contribution. In closing, we note that spin-momentum correlations are not unique to the Dirac surface states of topological insulators. In addition to the Rashba spin-split states mentioned above, photoexcited electrons in semiconductors are predicted to show unique spin-momentum correlations upon reflection at symmetry-breaking interfaces. 11 The topological protection offered by the Dirac surface states of materials such as Bi 2 Se 3 makes spin-momentum locking in these materials particularly attractive for potential device applications. References 1 Rashba, E.I., Theory of electrical spin injection: Tunnel contacts as a solution of the conductivity mismatch problem, Phys. Rev. B 62, R16267 (2000). 2 Schmidt, G. et al, Fundamental obstacle for electrical spin injection from a ferromagnetic metal into a diffusive semiconductor, Phys. Rev. B 64, R4790 (2000). 3 Cullity, B.D. and Graham, C.D., Introduction to Magnetic Materials (John Wiley & Sons, Hoboken, NJ, 2009). 4 Bianchi, M. et al, Coexistence of the topological state and a two-dimensional electron gas on the surface of Bi 2 Se 3, Nature Commun. 1:128 DOI: /ncomms1131 (2010). 5 King, P. D. C. et al, Large Tunable Rashba Spin Splitting of a Two-Dimensional Electron Gas in Bi 2 Se 3, Phys. Rev. Lett. 107, (2011). 6 Bahramy, M. S. et al, Emergent quantum confinement at topological insulator surfaces, Nature Commun. 3:1159 DOI: /ncomms2162 (2012). 10

11 7 Z.-H. Zhu et al, Rashba Spin-Splitting Control at the Surface of the Topological Insulator Bi 2 Se 3, Phys. Rev. Lett. 107, (2011). 8 Aronov, A. G. and Lyanda-Geller, Yu B., Nuclear electric resonance and orientation of carrier spins by an electric field, JETP Lett. 50, 431 (1989). 9 V. Yazyev, J. E. Moore, and S. G. Louie, Spin Polarization and Transport of Surface States in the Topological Insulators Bi 2 Se 3 and Bi 2 Te 3 from First Principles, Phys. Rev. Lett. 105, (2010). 10 Hong, S., Diep, V., Datta, S. and Chen, Y.P., Modeling potentiometric measurements in topological insulators including parallel channels, Phys. Rev. B. 86, (2012). 11 Qing, L., Song, Y. and Dery, H., Proximity effects of a symmetry-breaking interface on spins of photo-excited electrons, Phys. Rev. Lett. 107, (2011). 11