The topological surface states (TSS) in topological insulators (TIs) can exert strong spin-orbit torque (SOT) on adjacent magnetization, offering great potential in implementing energy-efficient magnetic memory devices. However, there are large discrepancies among the reported spin Hall angle values in TIs, and its temperature dependence still remains elusive. Here, the spin Hall angle in a modulation-doped Cr-Bi Sb Te (Cr-BST) film is quantitatively determined via both transport and optic approaches, where consistent results are obtained. A large spin Hall angle of ≈90 in the modulation-doped Cr-BST film is demonstrated at 2.5 K, and the spin Hall angle drastically decreases to 0.3-0.5 as the temperature increases. Moreover, by tuning the top TSS carrier concentration, a competition between the top and bottom TSS in contributing to SOT is observed. The above phenomena can account for the large discrepancies among the previously reported spin Hall angle values and reveal the unique role of TSS in generating SOT.
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