  An effort based on the kinetic model allowed by Landau-Ginzburg-Devonshire
theory is presented here. The formation of vortex, antivortex states in
ferroelectric films are reported and theoretically explained. Phase transition
in toroidal moment is observed. Vortex-antivortex-vortex (V-AV-V) triplet is
generated by applying inhomogeneous transverse static localized fields in x-y
plane. A specific boundary condition is used to keep the spirit of vortex state
i.e. the net polarization across the boundary is always zero. %This is neither
a periodic nor an open circuit electric boundary condition.
