Swapping exchange and spin-orbit induced correlated phases in proximitized Bernal bilayer graphene

Ex-so-tic van der Waals heterostructures take advantage of electrically tunable layer polarization to swap proximity exchange and spin-orbit coupling in the electronically active region. Perhaps the simplest example is Bernal bilayer graphene (BBG) encapsulated by a layered magnet from one side and a strong spin-orbit material from the other. Taking WS2/BBG/Cr2Ge2Te6 as a representative ex-so-tronic device, we employ realistic ab initio inspired Hamiltonians and effective electron-electron interactions to investigate the emergence of correlated phases within the random phase approximation. We find that exchange and spin-orbit coupling induced Stoner and intervalley coherence instabilities can be swapped for a given doping level, allowing one to explore the full spectrum of correlated phases within a single device.