Magnetoelectric effect in graphene nanoribbons on substrates via electric bias control of exchange splitting.

We predict a magnetoelectric (ME) effect in graphene nanoribbons on silicon substrates by first-principles calculations. It is shown that a bias voltage can produce strong linear ME effect by driving charge transfer between the nanoribbons and substrate, thus tuning the exchange splitting of magnetic edge states; moreover, the bias induced n-to-p-type transition in the ribbon layer can switch the ME coefficient from negative to positive due to the unique symmetry of band structures. This mechanism is proven to be robust against variations in material and physical configurations, thus opening a new avenue for ME coupling in metal-free magnet systems of practical importance.