Depolarization in modeling nano-scale ferroelectrics using the Landau free energy functional

We derived thermodynamically from first principles the free energy functional of a ferroelectric under an applied field E that contains the depolarization field E-d. We found that it is crucial to recognize the relationship between the total polarization and the applied field due to the depolarization field when expressing the free energy functional in the Landau form. Ad hoc formulations of ferroelectric models that overlooked this relationship effectively double-count the depolarization field, and thus cause serious overestimation of its effects. Examples are given in which the Curie temperature and the critical thickness of ferroelectricity, etc., can be overestimated this way by orders of magnitude.