Evidence for Anisotropic Polar Nanoregions in Relaxor Pb(Mg1/3}Nb2/3})O3: A Neutron Study of the Elastic Constants and Anomalous TA Phonon Damping in PMN

Published

September 18, 2012

Author(s)

Christopher K. Stock, Peter M. Gehring, H. Hiraka, I. Swainson, Guangyong Xu, Z.-G. Ye, J.-F. Li, D. Viehland

Abstract

We use neutron inelastic scattering methods to characterize the acoustic phonons in the relaxor Pb(Mg_1/3}Nb_2/3})O₃ (PMN) and demonstrate the presence of a highly anisotropic damping mechanism that is directly related to short-range, polar correlations. For a large range of temperatures above T_c=210 K, where dynamic, short-range, polar correlations are present, acoustic phonons propagating along [110] and polarized along [110] (TA_{2 phonons) are overdamped and softened across most of the Brillouin zone. By contrast, acoustic phonons propagating along [100] and polarized along [001] (TA}d1^ phonons) are overdamped and softened for only a limited range of wavevectors q. The anisotropy and temperature dependence of the acoustic phonon energy linewidths are directly correlated with the neutron elastic diffuse scattering cross section; this indicates that polar nanoregions are the cause of the anomalous behavior. The damping and softening vanish for q -> 0, i. e. for long-wavelength acoustic phonons near the zone center; this supports the notion that the anomalous damping is the result of a coupling between the relaxational component of the diffuse scattering and the harmonic TA phonons. Therefore these effects are not due to large changes in the elastic constants with temperature because the elastic constants correspond to the long-wavelength limit. We compare the elastic constants we measure to those from Brillouin scattering experiments and to values reported for pure PbTiO₃. We show that while the values of C₄₄ are quite similar, those for C₁₁ and C₁₂ are significantly less in PMN and result in a softening of (C₁₁-C_{12) over PbTiO}d3^. The elastic constants also show an increased elastic anisotropy (2C₄₄/(C_11-CD12)) in PMN versus that in PbTiO₃. These results are suggestive of an instability to TA₂ acoustic fluctuations in PMN and other relaxor ferroelectrics. We discuss our results in the context of the current debate over the "waterfall" effect and show that they are inconsistent with acoustic-optic phonon coupling or other models that invoke the presence of a second, low-energy, optic mode.

Citation

Physical Review B

Volume

86

Issue

10

Pub Type

Journals

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Keywords

Relaxors, PMN, lattice dynamics, acoustic phonons, phonon damping, diffuse scattering, polar nanoregions, neutron scattering

Citation

Stock, C. , Gehring, P. , Hiraka, H. , Swainson, I. , Xu, G. , Ye, Z. , Li, J. and Viehland, D. (2012), Evidence for Anisotropic Polar Nanoregions in Relaxor Pb(Mg_{1/3}Nb_{2/3})O₃: A Neutron Study of the Elastic Constants and Anomalous TA Phonon Damping in PMN, Physical Review B, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=911094 (Accessed October 9, 2025)