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We use neutron scattering to characterize the acoustic phonons in the relaxorPMN and demonstrate the presence of an anisotropic damping mechanism directlyrelated to short-range, polar correlations. For a large range of temperaturesabove Tc ~ 210, K, where dynamic polar correlations exist, acoustic phononspropagating along [1\bar{1}0] and polarized along [110] (TA2 phonons) areoverdamped and softened across most of the Brillouin zone. By contrast,acoustic phonons propagating along [100] and polarized along [001] (TA1phonons) are overdamped and softened for only a limited range of wavevectors.The anisotropy and temperature dependence of the acoustic phonon energylinewidth are directly correlated with the elastic diffuse scattering,indicating that polar nanoregions are the cause of the anomalous behavior. Thedamping and softening vanish for q -> 0, i.e. for long-wavelength acousticphonons, which supports the notion that the anomalous damping is a result ofthe coupling between the relaxational component of the diffuse scattering andthe harmonic TA phonons. Therefore, these effects are not due to large changesin the elastic constants with temperature because the elastic constantscorrespond to the long-wavelength limit. We compare the elastic constants wemeasure to those from Brillouin scattering and to values reported for pure PT.We show that while the values of C44 are quite similar, those for C11 and C12are significantly less in PMN and result in a softening of (C11-C12) over PT.There is also an increased elastic anisotropy (2C44/(C11-C12)) versus that inPT. These results suggest an instability to TA2 acoustic fluctuations inrelaxors. We discuss our results in the context of the debate over the"waterfall" effect and show that they are inconsistent with TA-TO phononcoupling or other models that invoke the presence of a second optic mode.

Evidence for anisotropic polar nanoregions in relaxor PMN: A neutron study of the elastic constants and anomalous TA phonon damping