Self-trapping of holes in p-type oxides: Theory for small polarons in MnO

Employing the $p$-$d$ repulsion to increase the valence band dispersion and the energy of the VBM is an important design principle for p-type oxides, as manifested in prototypical $p$-type oxides like Cu$_2$O or CuAlO$_2$ which show a strong Cu-$d$/O-$p$ interaction. An alternative opportunity to realize this design principle occurs for Mn(+II) compounds, where the $p$-$d$ orbital interaction occurs dominantly in the fully occupied $d^5$ majority spin direction of Mn. However, the ability of Mn to change the oxidation state from +II to +III can lead to a small polaron mechanism for hole transport which hinders p-type conductivity. This work addresses the trends of hole self-trapping for MnO between octahedral (rock-salt structure) and tetrahedral coordination (zinc-blende structure). We employ an on-site hole-state potential so to satisfy the generalized Koopmans condition. This approach avoids the well-known difficulty of density-functional calculations to describe correctly the localization of polaronic states, and allows to quantitatively predict the self-trapping energies. We find that the tetrahedrally coordinated Mn is less susceptible to hole self-trapping than the octahedrally coordinated Mn.