Ab initio study of ferroelectric domain walls in ${\mathrm{PbTiO}}_3$

We have investigated the atomistic structure of the 180° and 90° domain boundaries in the ferroelectric perovskite compound ${\mathrm{PbTiO}}_3$ using a first-principles ultrasoft-pseudopotential approach. For each case we have computed the position, thickness and creation energy of the domain walls, and an estimate of the barrier height for their motion has been obtained. We find both kinds of domain walls to be very narrow with a similar width of the order of one to two lattice constants. The energy of the 90° domain wall is calculated to be $35{\mathrm{m}\mathrm{J}/\mathrm{m}}^2,$ about a factor of 4 lower than the energy of its 180° counterpart, and only a miniscule barrier for its motion is found. As a surprising feature we detected a small offset of 0.15–0.2 eV in the electrostatic potential across the 90° domain wall.