Spin accumulation in topological insulator thin films—influence of bulk and topological surface states

Abstract

Current-induced spin torques in topological insulators (TIs) include both field-like torques as well as damping-like torques. In many experimental spin torque measurements, the Fermi energies are such that both of the topological surface states (TSSs) and the bulk states are occupied. In this work, we calculate the electric field-induced spin accumulation that leads to these torques in TI thin film systems, and account for the contributions of both of the TSSs as well as bulk states in the presence of interfacial band bending and disorder scattering. We analyze how the band structure of a TI thin film is affected by the film thickness, magnetization coupling, and band bending. The variation of the band structure due to these factors in turn affects the spin accumulation along both the in-plane and out-of-plane directions, and hence the induced spin torques. We show that the in-plane spin accumulation is influenced more by the TSS, whereas the bulk bands have a significant effect on the out-of-plane spin accumulation. The predicted variation of spin accumulation with sample thickness, and doping, substrate, and ferromagnetic material choices, mirrors the widely varying spin torque measurements in experiments.