Structural, electronic, and magnetic properties of the Fe-, Co-, Ni-, and V-intercalated graphene bilayer sandwich (denoted by C2|M|C2, M = Fe, Co, Ni, and V) and graphene on hexagonal boron nitride (h-BN) bilayer sandwich (denoted by C2|M|BN, M = Fe, Co, Ni, and V) are studied by using density functional theory method. We find that both the graphene bilayer and graphene-h-BN bilayer in all the C2|M|C2 and C2|M|BN sandwiches favor AB stacking over AA stacking mode. The Fe, Co, and Ni atoms prefer to be located over the center of C–C bonds whereas V atoms prefer to be located above the C atoms on graphene, and they all prefer to be located above the N atoms on h-BN sheet, regardless of the stacking mode. The C2|Fe|C2, C2|Co|C2, C2|Fe|BN, and C2|Co|BN sandwiches of AB stacking are all ferromagnetic metals with the spin polarization of 86%, 67%, 65%, and 46% at the Fermi level, respectively. By contrast, both C2|Ni|C2 and C2|Ni|BN sandwiches of AB stacking are nonmagnetic semiconductors with bandgaps of 0.64...
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