Abstract
Relaxor ferroelectrics1, which are utilized as actuators and sensors2-4, exemplify a class of poorly understood materials where interplay between disorder and phase instability results in inhomogeneous nanoregions. There is no definitive explanation for the onset of relaxor behavior (Burns temperature5, Td) or the origin of polar nanoregions (PNRs). Here we show a vibrational mode that localizes on cooling to Td, remains localized as PNRs form, and then delocalizes as PNRs grow using neutron scattering on relaxor (Pb(Mg1/3Nb2/3)O3)0.69-(PbTiO3)0.31 (PMN-31%PT). Although initially appearing like intrinsic local modes (ILMs)6-10, these modes differ below Td as they form a resonance with the ferroelectric phonon. At the resonance, nanoregions of standing ferroelectric phonons develop with a coherence length matching the PNRs. The size, shape, distribution, and temporal fluctuations of PNRs, and our observations, are explained by ferroelectric phonons trapped by disordered resonance modes via Anderson localization11-13. Our results show the size and shape of PNRs are not dictated by complex structural details, as always assumed, but by a phonon resonance wavevector. This simplification could guide the design of next generation relaxors.
