π - ADDI

3.5. Fe substitutionals: competition between intra-atomic interactions and metal-carbonhybridization 79antibondingp −d z z 2MnS=3 µ BFeS=0 µ Bnon−bonding d∆ε AdFigure 3.11: Scheme of the electronic levels near E F for Mn and Fe substitutionals in graphene as deduced fromour model of bonding and GGA calculations. ∆ϵ Ad is the energy cost to promote an electron to the antibondingA p z -d z 2 hybridization level from the non-bonding 3d states. The magnitude of ∆ϵ Ad , relative to that of thespin-splitting ∆ S of these defect levels, is crucial to determine the spin state of these impurities.The band structure for both configurations of Zn substitutionals can be found in Fig. 3.9.Again they confirm the model presented in Fig. 3.8. The distorted Zn [Fig. 3.9 (g)] breaks thedegeneracy of the E sp-d levels: one of them appears fully occupied ∼0.8 eV below E F , whilethe other appears a few tenths of eV above E F . For the C 3v Zn impurity both E sp-d bandsare degenerate and the splitting between majority and minority levels is ∼0.71 eV. Table 3.1shows the Mulliken population analysis of the spin moment for the C 3v Zn systems. As in thecase of the noble metals the contribution from the three nearest carbon neighbors is the mostimportant. However, the contribution of Zn is somewhat larger and the total spin moment ismore delocalized with a contribution form the rest of the graphene layer of ∼0.66 µ B . Weshould note that here we have one additional electron as compared to the noble metal systems.3.5 Fe substitutionals: competition between intra-atomic interactionsand metal-carbon hybridizationWe have already pointed out that Fe substitutionals in graphene occupy a rather special placeat the border between two well defined regimes (see Fig. 3.3): (i) the strong 3d character of thedefect levels nearby E F and large spin moments found for V, Cr and Mn impurities, and (ii)