Polarization vortex domains induced by switching electric field in ferroelectric films with circular electrodes

We describe ferroelectric thin films with circular electrodes and develop a thermodynamic theory that explains exotic experimental results previously reported. It is found to be especially useful for restricted geometries such as microstructures for which boundary conditions are well known to play an important role in ferroelectric properties. We have explored a switching mechanism that consists of an inhomogeneous rotational motion of the polarization and leads to a vortex state. The vortex appearance exhibits characteristic properties of a first-order field-induced phase transition with three critical electric fields and the possibility of hysteresis behavior.