Table 1 Results for the atomic structure of the graphene/metal interface models and for the clean metal surfaces: \(E_{\mathrm {int}}\) (in meV/C-atom) is the interaction energy, defined as \(E_{\mathrm {int}} = E_{\mathrm {gr/metal}} - (E_{\mathrm {gr}} + E_{\mathrm {metal}})\), where \(E_{\mathrm {gr/metal}}\) is the total energy of the graphene/metal system, and \(E_{\mathrm {gr}}\) and \(E_{\mathrm {metal}}\) are the energies of the fragments at the same coordinates as in the graphene/metal system; \(d_0\) (in Å) is the mean distance between the graphene overlayer and the interface metal layer; \(d_1\) (in Å) is the mean distance between the interface metal layer and the second metal layer; \(d_2\) (in Å) is the mean distance between the second and third metal layers; \(m_{\mathrm {Mn}}\) (\(\mu _{\mathrm {B}}\)) is the interface Mn spin magnetic moment; \(m_{\mathrm {C}}\) (in \(\mu _{\mathrm {B}}\)) is the interface carbon spin magnetic moment (several values for the nonequivalent carbon atoms are indicated); \(E_D-E_F\) (in meV) is the position of the Dirac point with respect to the Fermi energy.

From: Intercalation of Mn in graphene/Cu(111) interface: insights to the electronic and magnetic properties from theory