On the morphology of ferroelectric domains

Abstract

A theoretical model is proposed in order to explain the lamellar or spiked morphology of domains of opposite polarization observed in ferroelectric crystals in their polar phase. A nonconvex free energy is constructed, which has two isolated minima corresponding to states of opposite spontaneous polarization. The jump conditions for the electric field and polarization vector across domain walls assume a special form for this free energy. The electrostatic problem for a single domain of unknown shape and possibly curved walls is analyzed in two dimensions. The fields inside and outside are found explicitly. Metasbility then restricts the shape of the domain to be lamellar, i.e. slender, with small wall curvature, and terminating in sharp cusped ends along the polar axis. Thermodynamic considerations allow evaluation of the driving force at every wall point. This shows that such domains may elongate, but cannot thicken in the presence of moderate applied electric fields.