Magnetic mediation effect of a C impurity in a Mn-doped Zn₁₂O₁₂ nanocluster : a case of multiple exchange interactions

The stability and exchange interaction mechanism of a doped Zn₁₂O₁₂ cluster with Mn and C atoms were investigated by first-principles calculations. For the Mn-doped Zn₁₂O₁₂ cluster, it is identified that a superexchange interaction deriving the hybridization between the Mn 3d²_x - ²_y and O 2p_xy orbitals dominates the Mn(up arrow)-Mn(down arrow) antiferromagnetic coupling, although a direct exchange interaction deriving the Mn-Mn bonding is also found. In order to turn the Mn spin state in the Mn-doped Zn₁₂O₁₂ cluster, C doping is undertaken to change the magnetic interactions of these impurities. It is proved that the C incorporation into the Mn-doped Zn₁₂O₁₂ cluster destroys the short-ranged antiferromagnetic coupling, where multiple exchange interactions take over, including the direct exchange interaction and the kinetic p-d exchange interaction partially due to the geometric distortion and surface effect with dangling bonds (sp²-like hybrids). It is concluded that the kinetic p-d exchange interaction plays a dominant role in Mn/C-doped Zn₁₂O₁₂ clusters.