Spin-transfer torque and spin-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 (SOC) 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 from the normal metal (N) across the bulk of the TI slab. Unlike conventional STT in symmetric F'/I/F magnetic tunnel junctions, where only the in-plane STT component is non-zero in the linear response, both the in-plane and perpendicular torque are sizable in N/TI/F junctions while not requiring fixed F' layer as spin-polarizer which is advantageous for spintronic applications. Using the nonequilibrium Born-Oppenheimer treatment of interaction between fast conduction electrons and slow magnetization, we derive a general Keldysh Green function-based STT formula which makes it possible to analyze torque in the presence of SOC either in the bulk or at the interface of the free F layer.