Origin of sawtooth domain walls in ferroelectrics

Abstract Domains and domain walls are among the key factors that determine the performance of ferroelectric materials. In recent years, a unique type of domain walls, i.e., the sawtooth shaped domain walls, has been observed in BiFeO$_{3}$ and PbTiO$_{3}$. Here, we build a minimal model to reveal the origin of these sawtooth shaped domain walls. Incorporating this model into Monte-Carlo simulations shows that (i) the competition between the long-range Coulomb interaction (due to bound charges) and short-range interaction (due to opposite dipoles) is responsible for the formation of these peculiar domain walls and (ii) their relative strength is critical in determining the periodicity of these sawtooth shaped domain walls. Necessary conditions to form such domain walls are also discussed.