Effect of surface state hybridization on current-induced spin-orbit torque in thin topological insulator films

We investigate the thickness optimization for maximum current-induced spin-orbit torque (SOT) generated by topological surface states (TSS's) in a bilayer system comprising of a ferromagnetic layer coupled to a thin topological insulator (TI) film. We show that by reducing the TI thickness, two competing effects on the SOT are induced: (i) the torque strength is stronger as the bulk contribution is decreased; (ii) on the other hand, the torque strength becomes suppressed due to increasing hybridization of the surface states. The latter is attributed to the opposite helicities of the coupled TSS's. We theoretically model the interplay of these two effects and derive the optimal TI thickness to maximize the spin torque, which is estimated to be about 3-5 nm for typical Bi₂Se₃ films.