Persistent currents and spin torque caused by percolated quantum spin Hall state

Motivated by recent experiments, we investigate the quantum spin Hall state in 2D topological insulator/ferromagnetic metal planar junctions by means of a tight-binding model and linear response theory. We demonstrate that whether the edge state Dirac cone is submerged into the ferromagnetic subbands and the direction of the magnetization dramatically affect (i) how the edge state percolates into the ferromagnet and (ii) the spin-momentum locking of the edge state. Laminar flows of room temperature persistent charge and spin currents near the interface are uncovered. In addition, the current-induced spin polarization at the edge of the 2D topological insulator is found to be dramatically enhanced near the impurities. The current-induced spin polarization in the ferromagnet is mainly polarized in the out-of-plane direction $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{z}}$, rendering a current-induced spin torque that is predominantly fieldlike $\ensuremath{\propto}\mathbf{S}\ifmmode\times\else\texttimes\fi{}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{z}}$.