First‐principles study of the (001) surface of cubic PbTiO ₃

We present first‐principles calculations on the (001) surfaces of cubic PbTiO 3 with PbO and TiO 2 terminations. The cleavage energy, surface energy, surface grand potential, surface relaxation and surface electronic structure have been investigated by using the projector‐augmented wave method under generalized gradient approximation (GGA). The results show that surface energy of a TiO 2 ‐terminated surface is a little lower than that of a PbO‐terminated one, thus allowing both terminations to coexist. The PbO‐termination is stable in O‐ and Pb‐rich environments, while on the contrary, the TiO 2 ‐termination is stable in O‐ and Pb‐poor conditions. In addition, the surface rumpling S of a PbO‐terminated surface is slightly larger than that of a TiO 2 ‐terminated one. The relaxations dominantly take place on the outermost three layers, and an oscillatory (− + −) damping (|Δ d 12 | > | Δ d 23 | > | Δ d 34 |) relaxation phenomenon appears for both terminations. The band gaps of both PbO‐ and TiO 2 ‐terminations are slightly lower than that of the bulk. Moreover, the DOS curves of each layer show that for the TiO 2 ‐termination, the top of the valence band of the first and third TiO 2 layers moves toward Fermi level.