Scattering-induced and highly tunable by gate damping-like spin-orbit torque in graphene doubly proximitized by two-dimensional magnet Cr$_2$Ge$_2$Te$_6$ and WS$_2$

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