Brillouin spectroscopy of the incommensurate—commensurate phase transition in barium sodium niobate

Abstract
Small angle and large-angle Brillouin scattering have been used to measure the sound velocity and damping of longitudinal waves propagating along (C11 and perpendicular to (C22) the incommensurate axis in Ba2NaNb5O15. For each mode strong dispersion is observed, with relaxation time 2πτ of order 1.3 × 1011s near T 1. For C11τ(T) satisfies with 2πτ0 = (1.08 ± 0.13) × 10−12s; 2πτ1 = (8.5 ± 0.7) × 10−11 s; and thediffusivity D = 1.3 cm2/s. This approximately 65 times larger than the thermal diffusivity of entropy fluctuations and implies a dynamic “central mode” for right-angle geometry light scattering of ≃60GHz. This mode is ten times the width observed for phason (soliton) diffusion by Lyons et al. in BaMnF4; it is not directly observed in the present work. For LA sound waves perpendicular to the incommensurate axis that is, τ1 and D are the same as for C11 but τ0 −1 is neligible. τ0 is interpreted as due to amplitude mode-acoustic mode interaction; τ1, and D are interpreted as interaction of acoustic modes with mobile defects, presumably soliton-like kinks in the incommensurate structure.