Oxygen Vacancies Nucleate Charged Domain Walls in Ferroelectrics

We study the influence of oxygen vacancies on the formation of charged 180° domain walls in ferroelectric ${\mathrm{BaTiO}}_3$ using first principles calculations. We show that it is favorable for vacancies to assemble in crystallographic planes, and that such clustering is accompanied by the formation of a charged domain wall. The domain wall has negative bound charge, which compensates the nominal positive charge of the vacancies and leads to a vanishing density of free charge at the wall. This is in contrast to the positively charged domain walls, which are nearly completely compensated by free charge from the bulk. The results thus explain the experimentally observed difference in electronic conductivity of the two types of domain walls, as well as the generic prevalence of charged domain walls in ferroelectrics. Moreover, the explicit demonstration of vacancy driven domain wall formation implies that specific charged domain wall configurations may be realized by bottom-up design for use in domain wall based information processing.

Figure 1

Properties of the unrelaxed CDWs in a $1\times 1\times 16$ supercell. Top: schematic atomic structure with exagerated displacements. The blue arrows indicate the direction of polarization; green, blue and red spheres indicate Ba, Ti, and O atoms, respectively. The dots indicate positions of Ti atoms in the individual unit cells. Second from top: polarization profile of the supercell. Second from bottom: bound ${\rho }_b$ and smoothed free ${\rho }_{\mathrm{f}}$ charge density. Bottom: electrostatic potential energy $v(z)$ averaged over the plane orthogonal to $z$ and total charge density $\rho$ obtained from a sliding window average.

Figure 2

Left: projected band structure of the unrelaxed $1\times 1\times 16$ supercell with no vacancies. Right, the projected density of states resolved in individual unit cells.

Figure 3

Top: Schematic illustration of the vacancy migration that leads to domain wall formation in a $3\times 3\times 8$ supercell. The crosses indicate the lowest formation energy positions at each BaO plane. Below, we show the energy cost $\mathrm{\Delta }{E}_{i\alpha }$ for the $i$th vacancy at position $\alpha$ (see text) given that $i-1$ vacancies are situated at their optimal positions. $P_{z,i\alpha }$ is the polarization profile of the supercell with $i$ vacancies at their optimal positions. The bottom panel shows the smoothed free (${\rho }_f$) charge density profiles for the relaxed supercell with one, two, and three vacancies at the central BaO plane.