Out-of-plane carrier spin in transition-metal dichalcogenides under electric current*

Broken spatial inversion symmetry allows a nonequilibrium spin polarization to be induced by electric currents, which in two-dimensional systems is conventionally analyzed using Rashba model, leading to in-plane spin polarizations. We propose the out-of-plane carrier spin can emerge in ferromagnetic transition-metal dichalcogenides monolayer, by symmetry arguments and first-principles calculations. An intrinsic spin-orbit coupling in the monolayer provides valley-contrasting Zeeman-type spin splitting for generating the vertical induced spin. The current direction can be exploited to tune the induced spin, accompanied with valley polarization. The exotic spin accumulation paves an accessible way for perpendicular magnetization switching and electric control of valleys.