  The role of the surface during polarization switching in constrained
ferroelectrics is investigated using the time-dependent Ginzburg-Landau theory.
The model incorporates the elastic and electrostrictive effects in the form of
a long-range interaction that is obtained by eliminating the strain fields
subject to the elastic compatibility constraint. A square shaped finite sized
constrained ferroelectric system with vanishing surface polarization is
considered. Computer simulations of the hysteresis reveal that the corners of
the constrained square act as nucleation sources for $90^{o}$ domain
structures.
  It is also found that no nucleation of $90^{o}$ domain structure takes place
in a system with semi-infinite (corner free) geometry. For the corner free
case, the polarization switches by $180^{o}$ reorientations and a front of the
reverse domains emerges from the surface, eventually sweeping over the entire
system. Size dependence of the hysteresis loops is also studied.
