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

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