Nonlinear-linear transition of magnetoelectric effect in magnetic graphene nanoflakes on substrates

Linear magnetoelectric (ME) effect provides an ideal way to control magnetism by an external electric field and has long been pursued in spintronics. However, the essential conditions for linear ME effects are still not well understood, especially for the newly emerged metal-free ME systems. Here, using density functional theory calculations, we reveal a novel nonlinear-linear transition of the ME effect in graphene nanoflakes (GNFs) placed on substrates with different chemical activities. We show that the ME effect is nonlinear in a magnetic GNF on graphene substrate. Interestingly, the ME effect in the same GNF becomes highly linear with markedly increased ME coefficient when an h-BN sheet is inserted between the GNF and graphene layer. We reveal that the weak electronic hybridization between the GNFs and substrate is the essential mechanism for the linear ME behavior in the graphene-based magnets. The tunable nonlinear-linear transition in ME coupling opens up new opportunities to fabricate and manipulate high-quality ME devices.