Fluctuation-induced interaction of domain walls: Influence on the commensurate-incommensurate transition.

Abstract

Owing to macroscopic electric fields arising from thermal fluctuations of a ferroelectric domain wall, the attraction energy of two parallel walls decays at large distances between the walls (h) as ${\mathit{h}}^{\mathrm{\ensuremath{-}}2}$ with a prefactor that is proportional to T and to a ratio of dielectric constants that is equal to unity for the isotropic medium. For proper ferroelectrics, and improper ones with a quadratic dependence of the spontaneous polarization on the order parameter, this law is valid for all h greater than the domain wall thickness (which is the minimum length of the problem). For improper ferroelectrics with cubic (or higher-order) dependence of the polarization on the order parameter, there exists a region with a logarithmic dependence of the interaction energy on h. This attraction, which proves to prevail over the Van der Waals one, leads to a discontinuity of the ferroelectric-incommensurate transition. Estimation of the period of the incommensurate phase at the transition provides a reasonable order of magnitude and shows that this period does not depend much on the crystal parameters other than the width of the domain wall. The interaction of the ferromagnetic and ferroelastic domain walls is qualitatively analogous to that of the ferroelectric ones. The role of quantum fluctuations becomes important at not very low temperatures. For nonferroelectric, nonferroelastic, nonferromagnetic domain walls the power-law fluctuation-induced attraction is shown to arise as well.