Abstract: Neutron scattering has played a seminal role in elucidating fundamental concepts in ferroelectrics, such as the existence of soft modes and their relationship to the dielectric permittivity. Similarly, our current understanding of the complex physics of relaxors, in particular the titanium-doped lead-oxide perovskites that exhibit ultrahigh piezoelectricity and other remarkable properties, has benefited significantly from studies that have exploited a wide variety of neutron scattering methods. This is primarily due to the neutron’s ability to probe spatial and dynamical correlations simultaneously in condensed matter spanning several orders of magnitude in distance and time, which is arguably the most powerful aspect of the neutron scattering technique. For this reason, neutron scattering is ideally suited to studies of relaxors, as these materials not only exhibit relaxational effects over an enormous frequency range spanning mHz to GHz, but they also display competing short and long-range spatial correlations.

Nevertheless, after more than a half century of research, a unified picture of the relaxor lattice dynamics is only beginning to emerge. Disagreement about the nature of the mode coupling in relaxors has spawned divergent models of the soft mode in PbMg_1/3Nb_2/3O₃ (PMN), the most widely studied relaxor, while the strong diffuse scattering observed has been attributed either to a relaxational mode or to a local, harmonic mode. PMN also exhibits soft zone-boundary modes that track the Γ-point soft mode, suggesting that the presence of competing ferroelectric and antiferroelectric correlations may be central to the relaxor phase. I will briefly review neutron scattering studies of the excitations in relaxors and discuss recent theoretical models that have shown success in reproducing experimental results.