Phonon localization drives polar nanoregions in a relaxor ferroelectric

Relaxor ferroelectrics exemplify a class of functional materials where interplay between disorder and phase instability results in inhomogeneous nanoregions. Although known for about 30 years, there is no definitive explanation for polar nanoregions (PNRs). Here we show that ferroelectric phonon localization drives PNRs in relaxor ferroelectric PMN-30%PT using neutron scattering. At the frequency of a preexisting resonance mode, nanoregions of standing ferroelectric phonons develop with a coherence length equal to one wavelength and the PNR size. Anderson localization of ferroelectric phonons by resonance modes explains our observations and, with nonlinear slowing, the PNRs and relaxor properties. Phonon localization at additional resonances near the zone edges explains competing antiferroelectric distortions known to occur at the zone edges. Our results indicate the size and shape of PNRs that are not dictated by complex structural details, as commonly assumed, but by phonon resonance wave vectors. This discovery could guide the design of next generation relaxor ferroelectrics.