A self-consistent approach to soft mode analysis in size driven ferroelectricity

The polarization distribution in a finite size system obtained through Landau phenomenology is shown to contain unphysical oscillatory parts [P. Khare, D. Sa, Solid State Commun. 150 (2010) 172]. Self-consistency in the solution has been used to remove such difficulty and the issue of soft mode in such system has been addressed. The temperature as well as the size dependence of the soft mode frequency is calculated and compared with the experiment. The extrapolation length for the size driven ferroelectricity is argued to behave in a way similar to that of correlation length in phase transition in bulk system.