Nonlocal Measurement as a Probe of the Spin Hall Effect in Topological Insulators

Topological insulators (TIs) are promising candidates for alternative computing device designs. In particular, they have great potential for spintronic devices, where utilization of electron spin rather than charge would allow for lower-power and higher-performance computing in next-generation architectures. Efficient conversion between spin and charge signals is crucial to spintronic technology. TIs provide highly efficient spin-to-charge conversion, as a result of their unique topological properties. One way to electrically quantify conversion efficiency is with the spin Hall effect (SHE). Here, we present SHE measurements of the topological insulator ${\mathrm{Bi}}_2{\mathrm{Te}}_{2.5}{\mathrm{Se}}_{0.5}$. Because of the topological nature of this material, we can measure the SHE without the use of ferromagnetic injectors or detectors. Using the nonlocal resistance, we measure spin Hall angles up to 2.4 with spin lifetimes up to 9 ps. Furthermore, ferromagnet-free measurement allows for quick diagnostics of the spin properties without the need to fabricate multilevel devices.

Figure 1

Device design. (a) Optical image (inset image taken with a confocal laser microscope) of the ${\mathrm{Bi}}_2{\mathrm{Te}}_{2.5}{\mathrm{Se}}_{0.5}$ Hall bar. Avenue and contact arms are 0.25-µm wide and patterned by electron beam lithography. Spacings between adjacent contacts from 0.5 to 2 µm. (b) Schematic showing the geometry of the spin Hall measurement. Local charge current between the left two contacts produces a pure spin current in the channel through spin Hall effects. This spin current then produces a nonlocal voltage at the right set of contacts via the inverse spin Hall effect. Magnetic field is applied along the charge-current direction.

Figure 2

Nonlocal spin signal. (a) Characteristic R_NL(B) for I = +50 µA and Δx = 1.75 µm (points) with the associated fitting (line) to Eq. (1). (b) Nonlocal resistance, R_NL, versus bias current peaks at low current due to increased spin polarization at low currents. (c) Amplitude, ΔR_NL, of the nonlocal signal versus contact spacing at a fixed current of 10 µA. Signal strengthens up to 1.25 µm, likely due to a reduction in residual local background, and decreases at 2.5 µm.

Figure 3

Spin-parameter length and bias dependencies. (a) Spin Hall angle, (b) spin-diffusion length, and (c) spin lifetime as functions of contact spacing. Respective bias dependencies are given in the insets. Spin Hall angle, θ_SH, increases linearly with spacing. While low current increase tracks ΔR_NL, the increase between 1.25 and 2.5 µm can be attributed to a near-complete removal of lingering local backgrounds. (b) Spin-diffusion length, λ_s, is relatively constant with an anomalous peak at 1.25 µm, while (c) spin-relaxation time, τ_s, decreases steadily with increasing contact spacing. (d)–(f) All three parameters follow similar bias dependencies to that of ΔR_NL shown in (b), as a result of saturation of the spin signal and decreased spin-to-charge-conversion efficiency at higher bias currents.

Figure 4

Local resistance effects. (a) Local magnetoresistance (MR) of ${\mathrm{Bi}}_2{\mathrm{Te}}_{2.5}{\mathrm{Se}}_{0.5}$ thin film. WAL cusp is weakly visible over the background linear MR. Similar behavior is not present in Fig. 2, ruling out WAL as a contributing factor. (b) Measured nonlocal signal (black squares) along with expected nonlocal (blue) and local (red) contributions. Expected nonlocal contribution is calculated using average values of τ_s, λ_s, and θ_SH from data in Fig. 3. Ohmic contribution decreases much faster that what is measured, which more closely follows expected nonlocal behavior. (c) Temperature dependence of nonlocal resistance (black) and local resistance (red). Low-temperature decrease in R_NL disappears at 10 K when the signal in field-dependent data (inset) vanishes. Additional temperature data up to 20 K is given in the Supplemental Material [39] and demonstrates that the signal has disappeared completely.