Spin-orbit coupling induced spin-transfer torque and current polarization in topological-insulator/ferromagnet vertical heterostructures.

We predict an unconventional spin-transfer torque (STT) acting on the magnetization of a free ferromagnetic (F) layer within N/TI/F vertical heterostructures, which originates from strong spin-orbit coupling on the surface of a three-dimensional topological insulator (TI), as well as from charge current becoming spin polarized in the direction of transport as it flows perpendicularly from the normal metal (N) across the bulk of the TI layer. The STT vector has both in-plane and perpendicular components that are comparable in magnitude to conventional torque in F'/I/F (where I stands for insulator) magnetic tunnel junctions, while not requiring additional spin-polarizing F' layer with fixed magnetization, which makes it advantageous for spintronics applications. Our principal formal result is a derivation of the nonequilibrium Green function-based formula and the corresponding gauge-invariant nonequilibrium density matrix, which makes it possible to analyze the components of the STT vector in the presence of arbitrary strong spin-orbit coupling either in the bulk or at the interface of the free F layer.