Correlation radius in thin ferroelectric films

TL;DR

This paper analytically investigates the correlation radius and susceptibility in thin ferroelectric films, considering various factors like surface energy, polarization gradient, and depolarization fields, revealing size effects and phase transition behaviors.

Contribution

It provides a comprehensive analytical framework for understanding size effects and divergence phenomena in polarization fluctuations of thin ferroelectric films, accounting for multiple physical factors.

Findings

Correlation radius diverges at critical thickness for second order ferroelectrics.

Size effects depend on film orientation and depolarization field presence.

Multiple factors influence the correlation radius and susceptibility, tunable by material parameters.

Abstract

In the paper we present analytical calculations of the profiles and average values correlation radius of polarization fluctuations and generalized susceptibility in thin ferroelectric films of thickness L with in-plane (a-films) and out-of-plane (c-films) polarization orientation. The contribution of polarization gradient, surface energy and depolarization field (if any) were taken into account. For the second order ferroelectrics the correlation radius and generalized susceptibility diverge at the film critical thickness Lcr as anticipated. In the case of a-films where depolarization field is absent, the surface energy and polarization gradient govern the size effects such as thickness-induced phase transition, corresponding correlation radius and generalize susceptibility divergence in the phase transition point. In the case of c-films with strong depolarization field, the surface energy, polarization gradient, intrinsic depolarization effect related with polarization inhomogeneous distribution and incomplete screening in the electrodes determine the correlation radius and generalized susceptibility size effect. At that contribution of all the factors are comparable at reasonable material parameters, but could be easily tuned by varying of surface energy coefficients, polarization gradient contribution and screening conditions.