Mode coupling and polar nanoregions in the relaxor ferroelectric (formula presented)

We present a quantitative analysis of the phonon line shapes obtained by neutron inelastic scattering methods in the relaxor ferroelectric (formula presented) (PMN). Differences in the shapes and apparent positions of the transverse acoustic- (TA) and transverse optic- (TO) phonon peaks measured in the (300) and (200) Brillouin zones at 690 K are well described by a simple model that couples the TA and soft TO modes in which the primary parameter is the wave vector and temperature-dependent TO linewidth (formula presented) This mode-coupling picture provides a natural explanation for the uniform displacements of the polar nanoregions (PNR’s), discovered by Hirota et al. as the PNR result from the condensation of a soft TO mode that also contains a large acoustic component.