Correspondence: Phantom phonon localization in relaxors
Manley et al. report the observation of an unexpected, weak, phonon mode located in energy between that of the transverse acoustic (TA) and soft transverse optic (TO) modes in the relaxor ferroelectric Pb[(Mg 1/3 Nb 2/3 ) 1-x Ti x ]O 3 (PMN-xPT) with Ti content x = 0.30. Referred to as the local mode (LM), the energy of this extra mode varies little with wave vector in the cubic (paraelectric) phase, and this was interpreted as evidence of phonon localization. Any excitation that is localized in space must be extended in reciprocal space Q. To confirm this property, we performed a standard test on a PMN-xPT single crystal of nominally identical composition. This was done by comparing the rates at which the Bragg, TA phonon, and LM neutron scattering cross-sections decrease as the cubic crystallographic [100] axis is tilted out of the horizontal scattering plane by rotating about the orthogonal [010] axis. We find that the LM cross section varies with tilt in a manner identical to that of the Bragg peak. A local mode with short-range spatial correlations that decay exponentially will exhibit a broad Lorentzian peak as a function of tilt. Instead, we observe a narrow Gaussian peak. We conclude that the LM is not a real mode.