Opposite current-induced spin polarizations in bulk-metallic ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ and bulk-insulating ${\mathrm{Bi}}_2{\mathrm{Te}}_2\mathrm{Se}$ topological insulator thin flakes

One of the most fundamental and exotic properties of three-dimensional (3D) topological insulators (TIs) is spin-momentum locking (SML) of their topological surface states (TSSs), promising for potential applications in future spintronics. However, other possible conduction channels, such as a trivial two-dimensional electron gas (2DEG) with strong Rashba-type spin-orbit interaction (SOI) and bulk-conducting states that may possess a spin Hall effect (SHE), can coexist in 3D TIs, making determining the origin of the current-induced spin polarization (CISP) difficult. In this work, we directly compared the CISP between bulk-insulating ${\mathrm{Bi}}_2{\mathrm{Te}}_2\mathrm{Se}$ (BTS221) and bulk-metallic ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ thin flakes using spin potentiometry. In the bulk-insulating BTS221, the observed CISP has a sign consistent with the expected helicity of the SML of the TSS, but an opposite sign to its calculated bulk spin Hall conductivity. However, compared to BTS221, an opposite CISP is observed in the bulk-metallic ${\mathrm{Bi}}_2{\mathrm{Se}}_3$, consistent with both the expectations of its Rashba-Edelstein effect of the band-bending induced 2DEG and bulk intrinsic spin Hall Effect (SHE). If one assumes a representative occupation of the Rashba band of $3\times {10}^{13}\mathrm{c}{\mathrm{m}}^{-2}$ in ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ with a relevant relaxation time of 100 fs, the contribution to the CISP could be more dominated by the bulk intrinsic SHE. Our results provide an electrical way to distinguish the TSS from other possible conducting channels in spin transport measurements on 3D TIs, and open ways for the potential applications in charge-spin conversion devices.

Figure 1

Schematic illustrations of possible states that could give current-induced spin polarization on surfaces of 3D topological insulator materials and the circuit layout used in the spin potentiometric measurements. (a) Schematic illustration of topological surface state, band-bending induced Rashba-type two-dimensional electron gas near the top surface, and bulk spin Hall effect in 3D TIs. The red, black, and blue spheres with arrows representing the current-induced spin polarization due to TSS, 2DEG, and bulk SHE, respectively. The schematics of the Fermi surface of TSS (in red) and Rashba 2DEG (in gray) are shown in (a). Schematic device structures and circuit layouts used in the spin potentiometric measurements: (b) Hall-probe like and (c) four-terminal geometries. The TI surface defines the x-y plane and the surface normal $z$ direction. The two outside nonmagnetic (e.g., Au) contacts are used to apply a dc bias current ($I$), and the middle ferromagnetic (e.g., Py or Co) contact is magnetized by an in-plane magnetic field $B$ along its easy axis ($y$, with $-y$ defining the positive $B$ and positive $M$ directions).

Figure 2

Current-induced spin polarizations with opposite signs in bulk-insulating ${\mathrm{Bi}}_2{\mathrm{Te}}_2\mathrm{Se}$ (BTS221) and bulk-metallic ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ thin flakes. (a) Optical image of a typical BTS221 device (device A, a 40-nm-thick flake). The corresponding circuit layout is shown in Fig. 1. (b), (c) Voltage (Δ$V$) measured by an FM (Py, electrode “2”) spin detector as a function of the in-plane magnetic field ($B$) at bias currents $I=75\mu \mathrm{A}$ (b), and −75 μA (c), where a linear background has been subtracted from all the traces. The purple arrow represents the extracted spin signal $\delta V=\mathrm{\Delta }{V}_{+M}–\mathrm{\Delta }{V}_{-M}$. Here, $\mathrm{\Delta }{V}_{+M}$ and $\mathrm{\Delta }{V}_{-M}$ are the representative voltages measured before and after the magnetization switching of the FM spin detector near the coercive field. Insets of (b), (c) are the schematic band structures of TSS under positive and negative bias currents, respectively. (d) Optical image of a representative ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ device (device B, a 35-nm-thick flake). (e), (f) Voltage (Δ$V$) measured by a Co (electrode “2”) spin detector as a function of the in-plane $B$ field at bias currents $I=10\mu \mathrm{A}$ (e), and −10 μA (f). The raw data of the voltage traces are vertically shifted to be centered at zero. For (b), (c), (e), and (f), the directions of the bias current $I$, current-induced spin polarization $s$ at the top surface (inferred from the sign of the spin signal), and magnetization $M$ of the FM are labeled by the corresponding arrows. The arrows on the data traces indicate magnet field sweep directions. All the measurements were performed at $T=1.6\mathrm{K}$.

Figure 3

Current and temperature dependences of the spin signal measured on bulk-insulating BTS221. (a) The voltage measured by the Py spin detector on device A as a function of the in-plane magnetic field at different bias currents. The voltage traces have been vertically offset to have their central values aligned. (b) The spin signal δV as a function of the applied bias current. All the measurements are performed at $T=1.6\mathrm{K}$. (c) The spin signal δV as a function of temperature ranging from 1.6 to 125 K measured at a bias current of +100 or −100 μA.

Figure 4

Gate dependence of the spin signal measured on the bulk-insulating BTS221. (a) The voltage measured by the Py spin detector on device A as a function of the in-plane magnetic field at different back-gate voltages ($V_g$) and bias currents of 20 μA (top panels) and −20 μA (bottom panels), respectively. The voltage traces have been vertically offset to have their central values aligned. (b) Spin signal δV as a function of $V_g$ for both positive (red squares) and negative (black triangles) bias currents. (c) Back-gate dependence of the voltage $\left(V_0\right)$ measured between electrodes “2” and “3” at zero $B$ field at a bias current of $I=20\mu \mathrm{A}$ applied between electrodes “1” and “5.” Insets are the schematics of the band structure of TI with the corresponding Fermi levels at the most positive and negative gate voltages. All the measurements were performed at $T=1.6\mathrm{K}$.

Figure 5

Current and temperature dependences of the spin signal measured on bulk-metallic ${\mathrm{Bi}}_2{\mathrm{Se}}_3$. (a) The voltage measured by a Co spin detector on device B as a function of the in-plane magnetic field at different bias currents, where the voltage traces have been vertically offset to have their central values aligned. (b) The spin signals δV as a function of the applied bias current $I$. All the measurements were performed at $T=1.6\mathrm{K}$. (c) The spin signal δV as a function of the temperature ranging from 1.6 to 80 K.

Figure 6

The calculated intrinsic spin Hall conductivity in the bulk of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ and BTS221. (a) The coordinate system based on the crystal structure of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ and BTS221 used in the calculations. (b) The intrinsic SHC ${\mathit{\sigma }}_{\mathit{ij}}^{\mathit{k}}$ of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ and BTS221 crystals as a function of the Fermi energy $\left(E_{\mathrm{F}}\right)$. Here, we consider i, j, and $k$ along the z, x, and $y$ axes as the directions of spin current, charge current, and spin polarization, respectively.