Theoretical Study of the Soft Optic Mode Scattering in a Relaxor Ferroelectric: the Strong Effect of the Depolarizing Fields

TL;DR

This study investigates how depolarizing fields influence the scattering of soft optic modes by nano regions in relaxor ferroelectrics, revealing effects on phase transition temperatures and scattering behaviors relevant to waterfall phenomena.

Contribution

It provides a theoretical analysis incorporating depolarizing fields into mode scattering, highlighting their impact on local phase transitions and scattering cross sections in relaxor ferroelectrics.

Findings

Depolarizing fields lower the local QP phase transition temperature.

Vortex scattering remains unaffected by depolarizing fields.

QP scattering cross section saturates at small wave vectors, explaining waterfall phenomena.

Abstract

We analyze scattering of the transverse optic modes by spherically symmetric Polarized Nano Regions (PNR) in the paraelectric phase of relaxor ferroelectrics. Calculations have done in the frame of mean-field model early supposed by E.Iolin & J.Toulouse but depolarization field effects, DF, were taken into account. Elementary excitations of the system are found to be of two types - Vortex (V) and Quasi Polar (QP). DF decreases temperature of the local QP phase transition. The local phase transition temperature is found to be lower (higher) for Vortex than for QP excitations for the case of small (large) size PNR. Therefore both QP and Vortex condensations are possible. Depolarization field hasn't effect on the Vortex scattering. For the case of QP scattering DF effect is essential especially in the case when total angular momentum j=1. Vortex and QP (at j \geq 2) cross section of scattering {\Sigma} are nullified at the small value of momentum q of the incident wave. However QP cross section {\Sigma}(j=1) is saturated at q~0.01-0.001, and nullified only at the ultra small value of q corresponding macroscopic value of the soft mode wavelength. This scattering leads to the suppression of the TO spreading wave regime and allows qualitative understand some features of so-called waterfall phenomena observed early by the Brookhaven group in the neutron inelastic scattering in relaxors. PACS: 77.80.-e; 77.84.-s; 78.70.Nx; 77.22.Gm