Mode coupling and polar nanoregions in the relaxor ferroelectric Pb(Mg_1/3Nb_2/3)O₃

We present a quantitative analysis of the phonon line shapes obtained by neutron inelastic scattering methods in the relaxor ferroelectric Pb(Mg_1/3Nb_2/3)O₃ (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 F(q,T). 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.