Scattering-induced and highly tunable by gate damping-like spin-orbit torque in graphene doubly proximitized by two-dimensional magnet Cr2Ge2Te6 and monolayer WS2

Graphene sandwiched between semiconducting monolayers of ferromagnet\nCr$_2$Ge$_2$Te$_6$ and transition-metal dichalcogenide WS$_2$ acquires both\nspin-orbit (SO), of valley-Zeeman and Rashba types, and exchange couplings.\nUsing first-principles combined with quantum transport calculations, we predict\nthat such doubly proximitized graphene within van der Waals heterostructure\nwill exhibit SO torque driven by unpolarized charge current. This system\nlacking spin Hall current, putatively considered to be necessary for efficient\ndamping-like (DL) SO torque that plays a key role in magnetization switching,\ndemonstrates how DL torque component can be generated solely by skew-scattering\noff spin-independent potential barrier or impurities in purely two-dimensional\nelectronic transport due to the presence of proximity SO coupling and its spin\ntexture tilted out-of-plane. This leads to current-driven nonequilibrium spin\ndensity emerging in all spatial directions, whose cross product with proximity\nmagnetization yields DL SO torque, unlike the ballistic regime with no\nscatterers in which only field-like (FL) SO torque appears. In contrast to SO\ntorque on conventional metallic ferromagnets in contact with three dimensional\nSO-coupled materials, the ratio of FL and DL torque can be tuned by more than\nan order of magnitude via combined top and back gates.\n