Direct visualization of current-induced spin accumulation in topological insulators

Charge-to-spin conversion in various materials is the key for the fundamental understanding of spin-orbitronics and efficient magnetization manipulation. Here we report the direct spatial imaging of current-induced spin accumulation at the channel edges of Bi2Se3 and BiSbTeSe2 topological insulators as well as Pt by a scanning photovoltage microscope at room temperature. The spin polarization is along the out-of-plane direction with opposite signs for the two channel edges. The accumulated spin direction reverses sign upon changing the current direction and the detected spin signal shows a linear dependence on the magnitude of currents, indicating that our observed phenomena are current-induced effects. The spin Hall angle of Bi2Se3, BiSbTeSe2, and Pt is determined to be 0.0085, 0.0616, and 0.0085, respectively. Our results open up the possibility of optically detecting the current-induced spin accumulations, and thus point towards a better understanding of the interaction between spins and circularly polarized light.


Supplementary Note 1. Materials characterization
The temperature dependent resistivity, carrier concentration and mobility of 9-nm-thick Bi 2 Se 3 film were obtained from four probe and Hall measurements. As shown in Supplementary   Fig. 2a, the almost constant sheet resistivity when the temperature is below 30K suggests the surface dominated transport behavior, which is a typical characteristic of Bi 2 Se 3 . Supplementary   Fig. 2b indicates that our sample is electron doped with a sheet carrier concentration ( D n 2 ) of D n 2 ~ 14.3 × 10 13 cm -2 and carrier mobility (  ) of ~ 45.5 cm 2 V -1 s -1 at room temperature.
We then performed Hall measurements on BiSbTeSe 2 sample. As shown in Supplementary Fig. 3b, the negative Hall slope indicates that our BSTS sample is electron doped.
The sheet carrier concentration at room temperature is determined to be ~ 4.8 × 10 13 cm -2 , which is in a similar range compared with previous studies 1,2 .

Supplementary Note 2. Hanle analysis
The Hanle effect denotes the precession of spins when applying an external magnetic field (B ext ) perpendicular to the spin direction. The frequency of the spin precession is known as

Supplementary Note 3. Spin Hall angle estimation in Bi 2 Se 3 and BiSbTeSe 2
The spin Hall angle is defined as sh  P , the optically excited electron density rate G , and the total electron density n e .
The spin lifetime s  can be estimated to be ~ 3.3 ± 0.13 ps from Hanle measurements (Fig. 3d).
The optically excited electron density can be written as   where I is the laser intensity. The initial out-of-pane spin polarization P 0 in Bi 2 Se 3 is estimated to be ~ 0.1. 5 Thus the carrier spin polarization P can be calculated to be (7.10 ± 0.28) × 10 -3 .
The transverse voltage V T is 0.168 ± 0.03 mV under a bias current of 0.5 mA (Fig. 3f). Thus, the spin Hall angle θ sh is calculated to be ~ 0.0085 ± 0.0016.
In the case of BiSbTeSe 2 , the spin lifetime is calculated to be 18.6 ± 1.5 ps from the Hanle measurements (Fig. 4e) and the resistivity is decided to be 1.6 × 10 -4 Ω·m from transport measurements. The absorption coefficient and reflectance in BiSbTeSe 2 are α = 2 × 10 4 cm -1 and R = 0.21, respectively. We can get n ~ 1.79 × 10 23 m -3 . We use the initial spin polarization value P 0 ~ 0.25 to estimate the carrier spin polarization P 6 . The transverse voltage V T is 2.8 ± 0.4 mV under a bias current of 0.12 mA (Fig. 4f). The spin Hall angle in BiSbTeSe 2 can be estimated to be ~ 0.0616 ± 0.0101.

Supplementary Note 4. The contribution of TSS and BS to spin accumulation in Bi 2 Se 3
We first discuss the contribution of TSS, 2DEG and BS to the out-of-plane accumulation in 9 QL Bi 2 Se 3 . We employ the multi-channel model to estimate the spin current generated from topological surface states (TSS), 2DEG and bulk states (BS). The thickness of TSS and 2DEG in According to recent reported spin Hall angles measured by ST-FMR and spin pumping, the spin Hall angle (θ sh ) originated from TSS is between 0.047 and 3.5 12,13 while θ sh originated from bulk states is between 0.0093 and 0.43 14,15 . For simplicity, we consider θ sh originated from TSS and bulk states with 0.047 13 and 0.01944 15 , respectively. Thus, the ratio of spin current density flowing in TSS to that in BS is estimated to be J s-TSS :J s-BS = 3.57:3.88. We then convert the spin current density to the spin current by considering the thickness of the TSS and BS. The ratio of the spin current flowing in TSS to that in BS is estimated to be I s-TSS :I s-BS = 1:2.06, indicating that there is a considerable bulk spin Hall contribution to the spin accumulation in 9 QL Bi 2 Se 3 at room temperature.
We have then performed the thickness dependence study on Bi 2 Se 3 at room temperature.
As shown in Supplementary Fig. 5, HDP shows a relatively constant value ~ 4 µV for 9, 10 and 20 QL devices, and starts to increase below 9 QL, reaching a maximum of ~ 12.6 µV at 7 QL.
Previous reports showed that negligible bulk states are expected when the thickness of Bi 2 Se 3 is below 8 QL 16 . We thus attribute the HDP measured on 7 QL and 8 QL to TSS. While in the case of 9, 10 and 20 QL devices, the smaller HDP signal could be due to a considerable bulk state contribution.

Supplementary Note 5. The contribution of TSS and BS to spin accumulation in BiSbTeSe 2
The thickness of TSS in BiSbTeSe 2 was reported to be ~ 2.5 nm 17 . The estimated spin diffusion length in BSTS2 is estimated ~ 5.82 ± 1.67 nm. In order to estimate the charge current flowing in TSS and BS, we use the carrier concentration to estimate the current flowing in TSS and BS by employing I TSS = n TSS µ TSS eEW and I BS = n BS µ BS eEW where W and E are the channel width and electric field (same for TSS and BS), respectively. We assume µ TSS = µ BS since the linearity of the Hall curve as shown in Supplementary Fig. 3. The carrier concentration of bulk and surface was calculated using the model reported previously 18

Supplementary Note 6. Spin Hall angle estimation in Pt
In order to estimate the spin Hall angle in Pt, we first performed Hanle measurements and the result is shown in Supplementary Fig. 6a.  Fig. 6b). The spin Hall angle in Pt is thus estimated to be ~ 0.0085 ± 0.0006.