Electronic structure and lattice distortion in PbMg$_{1/3}$Nb$_{2/3}$O$_3$

We investigated the local structural distortions of PMN(PbMg$_{1/3}$Nb$_{2/3}$O$_3$) within the density functional theory using the linearized augmented plane-wave method. Structural relaxations were performed on 30 atom unit cells with B-cations arranged in 1:1 chemical ordering along [111]. The direction and magnitude of Mg and Nb off-centering within O$_6$ octahedral cages and Pb within its cage as well as electronic structures were examined. The results are discussed in terms of the Nb 4d - O 2p and Pb 6p - O 2p hybridizations and their interplay. A significant role is found for the on-site Ewald potential of different Nb sublattices, which is correlated with the off-centering. \\ \\ $\dag$This work was supported by ONR and DOE.