We use a combination of conventional density functional theory (DFT) and post-DFT methods, which include the local density approximation plus Hubbard $U$ ($\text{LDA}+U$), PBE0, and self-consistent $\mathit{GW}$, to study the electronic properties of Ni-substituted PbTiO${}_3$ (Ni-PTO) solid solutions. We find that LDA calculations yield unreasonable band structures, especially for Ni-PTO solid solutions that contain an uninterrupted NiO${}_2$ layer. Accurate treatment of localized states in transition-metal oxides such as Ni-PTO requires post-DFT methods. $B$-site Ni/Ti cation ordering is also investigated. The $B$-site cation arrangement alters the bonding between Ni and O, and therefore strongly affects the band gap ($E_g$) of Ni-PTO. We predict that Ni-PTO solid solutions should have a direct band gap in the visible light energy range, with polarization similar to the parent PbTiO${}_3$. This combination of properties makes Ni-PTO solid solutions promising candidate materials for solar energy conversion devices.

• Received 11 February 2011

DOI:https://doi.org/10.1103/PhysRevB.83.205115