Interplay of proximity-induced spin interactions and correlated phenomena in multilayer graphene systems

We conducted a theoretical investigation on the impact of proximity-induced spin-orbit and exchange coupling on the correlated phase diagrams of rhombohedral trilayer graphene (RTG) and Bernal bilayer graphene (BBG). Using emph{ab initio}-fitted effective models of RTG and BBG encapsulated by transition metal dichalcogenides (spin-orbit proximity effect) and ferromagnetic Cr$_2$Ge$_2$Te$_6$ (exchange proximity effect), we explored potential correlated phases at different displacement fields and doping by incorporating Coulomb interactions within the random-phase approximation. Our findings reveal a diverse spectrum of spin-valley resolved Stoner and intervalley coherence instabilities induced by the spin proximity effects. For instance, we observed the emergence of a spin-valley-coherent phase due to valley-Zeeman coupling. Additionally, proximity-induced exchange coupling removed the spin phase degeneracies by biasing the spin direction, enabling a magneto-correlation effect.