Effect of t_2g orbitals on domain walls in electron-doped perovskite ferroeletrics

Domain wall morphologies in ferroelectrics are believed to be largely shaped by electrostatic forces. Here, we show that in conducting domain walls, the morphology also depends on the details of the charge-carrier band structure. For concreteness, we focus on transition-metal perovskites like BaTiO₃ and SrTiO₃. These have a triplet of t_2g orbitals attached to the Ti atoms that form the conduction bands when electron doped. We solve a set of coupled equations---Landau-Ginzburg-Devonshire equations for the polarization, tight-binding Schrodinger equations for the electron bands, and Gauss' law for the electric potential---to obtain polarization and electron density profiles as a function of electron density. We find that at low electron densities, the electron gas is pinned to the surfaces of the ferroelectric by a Kittel-like domain structure. As the electron density increases, the domain wall evolves smoothly through a zigzag head-to-head structure, eventually becoming a flat head-to-head domain wall at high density. We find that the Kittel-like morphology at low density is protected by orbital asymmetry, while at high electron densities the high density of states of the multiorbital model effectively screens depolarizing fields and flattens the domain wall relative to single-orbital models.