Flexoelectricity and Ferroelectric Domain Walls: Landau Theory from Density-Functional Theory Calculations

Ising domain walls between two ferroelectric regions of a perovskite oxide with antiparallel polarization vectors are, in many of these materials, atomically thin. Despite of this, simple continuum Landau models where a thermodynamic potential is expanded as a function of strain, polarization, and the gradient of polarization give good predictions of wall energy, wall thickness, and atomic displacements. In the work presented in this talk, we developed Landau models for six different perovskites and we computed the coefficients of those models, some of which are related to the flexoelectric properties of the oxide. In the process, we addressed the role of some arbitrary choices that one faces regarding the definition of local strain, polar distortion pattern, and flexoelectric tensor, which have an impact in the predictions of the model--and we describe criteria that ensure physically meaningful results. The solutions produced in this way agree very well with our full density-functional theory calculations. Finally, we ellaborate on the extension of this theory to more complex ferroelectric domain walls, such as Néel- and Bloch-type ones.