Damped soft phonons and diffuse scattering in (Bi1/2Na1/2)TiO3

Abstract

Neutron-scattering studies of (Bi${}_{1/2}$Na${}_{1/2}$)TiO${}_{3}$ (BNT) have been performed to elucidate the microscopic mechanism of the broad maximum in the temperature dependence of the dielectric constant at ${T}_{\mathrm{m}}\ensuremath{\sim}600$ K and the reduction in the piezoelectric properties above the depolarization temperature, $460\ensuremath{\sim}480$ K. We observed diffuse scattering near the $\ensuremath{\Gamma}$ point below 700 K, which competes with the superlattice peak at the $M$ point of the tetragonal phase but coexists with the superlattice peak at the $R$ point of the rhombohedral phase. The diffuse scattering shows an anisotropic $Q$ shape extending along the $\ensuremath{\langle}100\ensuremath{\rangle}$ direction transverse to the scattering vector $Q$, which is explained by atomic shifts bridging the tetragonal and rhombohedral structures. We propose that the broad maximum in the dielectric constant is associated with a diffusive first-order transition between the competing tetragonal and rhombohedral phases. In addition, we found that the diffuse scattering is reduced for single crystals grown under high oxygen pressure, which suggests an analogy with the central peak in hydrogen-reduced SrTiO${}_{3}$. Inelastic neutron scattering near the $\ensuremath{\Gamma}$ point reveals a heavily overdamped soft mode similar to those reported in lead-based relaxors, the ``waterfall'' feature. Moreover, a damped soft transverse acoustic mode is observed for the $\ensuremath{\langle}100\ensuremath{\rangle}$ direction as the anisotropic diffuse scattering, indicating phase instabilities with the same origin as that of the diffuse scattering. The recovery of the soft mode is observed near the depolarization temperature, which coincides with the disappearance of the superlattice peak at the $M$ point. These results indicate that the depolarization and the waterfall feature originate in the dynamic nature of ferroelectric clusters in the coexisting tetragonal/rhombohedral phase.