Ginzburg soft mode conception and ferroelectricity in ultrathin films

It was shown recently that ferroelectricity and switching of the spontaneous polarization exist even in one monolayer (5-17 Angstrom) of the ferroelectric copolymer P[VDF-TrFE]. Ferroelectric properties were found in the ultrathin perovskite-like PZT films with a thickness of 12 Angstrom (three unit-cell parameters). Moreover, the simulation model, based on first principles, has shown that the critical size of perovskite ferroelectrics is three elementary cells. On the other hand the Ginzburg soft mode conception for displacive ferroelectrics supposed the existence of the low frequency vibration mode omega(0) (soft mode) and the corresponding long vibration wavelength lambda(0). Therefore the mechanism of the ferroelectric phase transition, connected with the soft mode, leads to the existence of a critical thickness of the film l(cr) congruent to lambda(0). At l(cr) < lambda(0) the mechanism of the ferroelectricity is not caused, by the soft mode. We show that in the ultrathin ferroelectric films the soft mode does not exist.