A hexadomain vortex in tetragonal ferroelectrics

We study internal flux closures in tetragonal ferroelectric crystals using a phase-field model and demonstrate the existence of a stable polarization vortex of six domains. This hexadomain vortex exhibits a threefold rotation axis and appears as a minimum energy equilibrium state over a narrow range of aspect ratios in freestanding cuboidal nanodots. Square polarization vortices of four domains represent lower energy solutions for a wide range of aspect ratios. The hexadomain vortex offers significant potential in memory storage applications as it has eight stable states.