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 previously mysterious experiments. 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 new switching mechanism, which consists of an inhomogeneous rotational motion of the polarization and leads to an extended vortex state. The vortex appearance exhibits characteristic properties of a first-order field-induced phase transition: three critical electric fields and the possibility of hysteresis behavior. 
Laurent Baudry and Ana\"is Sen\'e and Igor A. Luk'yanchuk and Laurent   Lahoche and James F Scott
cond-mat.mtrl-sci