A simplified treatment of the Landau theory of phase transitions for thin ferroelectric films

A simple analytical approximation based on Landau-Ginzburg theory is developed for ferroelectric thin films with continuous and first-order phase transitions. We show that the polarization profile can be conveniently modeled by a power series expansion that allows us to re-express the Landau-Ginzburg free energy as an effective Landau-Devonshire free energy. Simple expressions are obtained for the properties of ferroelectric films. It is found that the calculated properties based on our effective Landau-Devonshire theory are consistent with numerical results from the Landau-Ginzburg theory.