Three-mode coupling interference patterns in the dynamic structure factor of a relaxor ferroelectric

Abstract

A longstanding controversy for relaxor ferroelectrics has been the origin of the ``waterfall'' effect in the phonon dispersion curves, in which low-energy transverse phonons cascade into vertical columns. Originally interpreted as phonons interacting with polar nanoregions (PNRs), it was later explained as an interference effect of coupling damped optic and acoustic phonons. In light of a recently discovered PNR vibrational mode near the ``waterfall'' wave vector [M. E. Manley, J. W. Lynn, D. L. Abernathy, E. D. Specht, O. Delaire, A. R. Bishop, R. Sahul, and J. D. Budai, Nat. Commun. 5, 3683 (2014)], we have reexamined this feature using neutron scattering on [100]-poled PMN-30%PT $[0.6\mathrm{Pb}(\mathrm{M}{\mathrm{g}}_{1/3}\mathrm{N}{\mathrm{b}}_{2/3}){\mathrm{O}}_{3}\phantom{\rule{0.16em}{0ex}}\ensuremath{-}0.3\mathrm{PbTi}{\mathrm{O}}_{3}]$. We find that the PNR mode couples to both optic and acoustic phonons and that this results in complex patterns in the dynamic structure factor, including intensity pockets and peaks localized in momentum-energy space. These features are fully explained by extending the mode-coupling model to include three coupled damped harmonic oscillators representing the transverse optic, acoustic, and PNR modes.