Anisotropic phonon coupling in the relaxor ferroelectric (Na1/2Bi1/2)TiO3 near its high-temperature phase transition

The lead free relaxor Na1/2Bi1/2TiO3 (NBT) undergoes a structural cubic-to-tetragonal transition near 800 K which is caused by the cooperative rotations of O-6 octahedra. These rotations are also accompanied by the displacements of the cations and the formation of the polar nanodomains (PNDs) that are responsible for the characteristic dielectric dispersion of relaxor ferroelectrics. Because of their intrinsic properties, spontaneous polarization, and lack of inversion symmetry, these PNDs are also piezoelectric and can mediate an interaction between polarization and strain or couple the optic and acoustic phonons. Because PNDs introduce a local tetragonal symmetry, the phonon coupling they mediate is found to be anisotropic. In this paper we present inelastic neutron scattering results on coupled transverse acoustic (TA) and transverse optic (TO) phonons in the [110] and [001] directions and across the cubic-tetragonal phase transition at T-C similar to 800 K. The phonon spectra are analyzed using a mode coupling model. In the [110] direction, as in other relaxors and some ferroelectric perovskites, a precipitous drop of the TO phonon into the TA branch or "waterfall" is observed at a certain q(wf) similar to 0.14 r.l.u. In the [001] direction, the highly overdamped line shape can be fitted with closely positioned bare mode energies which are largely overlapping along the dispersion curves. Two competing lattice coupling mechanism are proposed to explain these observations.