Brillouin scattering study of the elastic properties of incommensurate barium sodium niobate

The elastic properties of incommensurate barium sodium niobate (BSN) are investigated with Brillouin scattering. The velocities, linewidths, and related elastic constants of the main acoustic modes propagating in the (001) plane are measured between 20 and 500 °C across the normal-incommensurate transition and the lock-in transition. The main anomalies are observed for the elastic constants $C_{11}$ and $C_{22}$. They exhibit a complex temperature dependence dominated by a large thermal hysteresis of a specific type and a high sensitiveness to the experimental procedure. A memory effect similar to the one observed by optical birefringence is described. From a theoretical point of view, the elastic behavior of BSN is derived in the framework of the standard Landau theory. This theory does not provide a good description of the experimental data. Instead, one obtains a good quantitative agreement in the normal phase and semiquantitative agreement in the incommensurate phase by considering three types of corrections: a coupling between the strains and the fluctuations of the order-parameter modulus, a dispersive coupling between the strains and the amplitude mode, and the influence of the defects. In particular, we show that the elastic anomalies induced by the defects are correlated to the anomalies observed with optical birefringence.