Origin and evolution of surface spin current in topological insulators

The Dirac surface states of topological insulators offer a unique possibility for creating spin polarized charge currents due to the spin-momentum locking. Here we demonstrate that the control over the bulk and surface contribution is crucial to maximize the charge-to-spin conversion efficiency. We observe an enhancement of the spin signal due to surface-dominated spin polarization while freezing out the bulk conductivity in semiconducting ${\mathrm{Bi}}_{1.5}{\mathrm{Sb}}_{0.5}{\mathrm{Te}}_{1.7}{\mathrm{Se}}_{1.3}$ below $100\mathrm{K}$. Detailed measurements up to room temperature exhibit a strong reduction of the magnetoresistance signal between $2\text{and}100\mathrm{K}$, which we attribute to the thermal excitation of bulk carriers and to the electron-phonon coupling in the surface states. The presence and dominance of this effect up to room temperature is promising for spintronic science and technology.

Figure 1

Device schematic and electrical characterization. (a) Dirac cone of the topological surface state with spin-momentum locking (SML) and spin polarized nontopological surface states (dashed lines). (b) Schematic of a TI with FM tunnel contacts. The direction of spin current in ${\mathrm{Bi}}_{1.5}{\mathrm{Sb}}_{0.5}{\mathrm{Te}}_{1.7}{\mathrm{Se}}_{1.3}$ (BSTS) is defined by the charge current direction due to SML. (c) Colored scanning electron micrograph of a fabricated device with $\mathrm{Co}\text{/}{\mathrm{TiO}}_2$ contacts on an exfoliated BSTS flake $(1\mu \mathrm{m}$ scale bar). (d) Temperature dependence of the BSTS channel resistance transitioning from metallic (colored background) to semiconducting (white background) behavior. Inset: measurement configuration.

Figure 2

Weak antilocalization (WAL) and Shubnikov–de Haas (SdH). (a) Temperature dependence of the phase coherence length. (b) Angle dependence of the WAL signal plotted against the out-of-plane magnetic field component at $2\mathrm{K}$. (c) Resistance dependence on $B^{-1}$ at $2\mathrm{K}$ measured at $I=1\mu \mathrm{A}$ shows SdH oscillations. (d) The position of the oscillation's maxima extrapolates to $n\left(0\right)=\beta =0.52$.

Figure 3

Electrical detection of SML. Schematics of the magnetoresistance measurements between current-induced BSTS surface spins, $S_{\uparrow }$ in (a) and $S_{\downarrow }$ in (b), and magnetization $\left(\vec{M}\right)$ of the detector FM contact [13]. (c) Spin signal shows a hysteretic switching at $2\mathrm{K}$ for a bias current of $+50\mu \mathrm{A}$. The arrows show the magnetic field sweep directions up (red) and down (black). (d) Reversing the current direction $(-50\mu \mathrm{A}$ locking to $S_{\downarrow })$ results in a spin signal with an inverted hysteretic switching. (e) Bias current dependence of the spin signal amplitude $\mathrm{\Delta }V=({\mu }_{\uparrow }-{\mu }_{\downarrow })/-e$ measured at $10\mathrm{K}$ for BSTS.

Figure 4

Temperature dependence of SML signal. (a) Temperature dependence of the spin signal amplitude $R_S=\mathrm{\Delta }V/I$ for BSTS compared with ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ [13] and correlated with the channel's metal-semiconductor transition (colored background: SML; white background: SBC). The solid lines are guides to the eye. (b) Temperature dependence of the surface contribution factor $\eta =G^S/\left(G^S+G^B\right)$ and the surface spin polarization $P_S$.

Figure 5

Characterization of BSTS. (a) Atomic force micrograph of a $70\mathrm{nm}$ thick BSTS flake. Inset: height profile along the dashed line. (b) Raman spectrum of a $70\mathrm{nm}$ BSTS flake.

Figure 6

Characterization of ferromagnetic tunnel junctions. Temperature dependence of the contact current-voltage characteristic (top panel) and resistance curves (bottom panel). The nonlinearity indicates a good tunnel barrier with a weak temperature dependence.

Figure 7

Hall measurement in BSTS. (a) The Hall voltage measured in BSTS using a bias current of $10\mu \mathrm{A}$ at room temperature and $5\mathrm{K}$. (b) Temperature dependence of the Hall charge carrier concentration $n$ and mobility $\mu$. Insets: optical microscope image of Hall device and measurement schematic.

Figure 8

Weak antilocalization (WAL). Magnetoconductance measurements of BSTS with applied perpendicular magnetic field showing WAL up to $55\mathrm{K}$ measured at $I=5\mu \mathrm{A}$. A background without WAL signal measured at $70\mathrm{K}$ has been subtracted.

Figure 9

Temperature dependence of SML signal. Spin signal measured at different temperatures at $20\mu \mathrm{A}$ for BSTS.

Figure 10

Comparison of various data sets of SML measurements from literature. The temperature dependences of the spin resistance observed in several TI compounds published since the first report of electrical SML detection by Li et al. [5], various reports on ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ (Liu et al. [8], Dankert et al. [13], and Li et al. [27]), in $({\mathrm{Bi}}_{0.53}{\mathrm{Sb}}_{0.47}{)}_2{\mathrm{Te}}_3$(Tang et al. [7]) and ${\mathrm{Bi}}_{1.5}{\mathrm{Sb}}_{0.5}{\mathrm{Te}}_{1.7}{\mathrm{Se}}_{1.3}$ (this paper and Ando et al. [6]).

Figure 11

Spin-momentum locking in $p$-type ${\mathrm{Sb}}_2{\mathrm{Te}}_3$. (a) Hall measurement showing $p$-type doping. SML measured at opposite bias polarities of (b) $500\mu \mathrm{A}$ and (c) $-10\mu \mathrm{A}$.