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The low-energy part of the vibration spectrum in PbMg$_{1/3}$Nb$_{2/3}$O$_3$(PMN) relaxor ferroelectric has been studied by neutron scattering above andbelow the Burns temperature, T$_d$. The transverse acoustic and the lowesttransverse optic phonons are strongly coupled and we have obtained a model forthis coupling. We observe that the lowest optic branch is always underdamped. Aresolution-limited central peak and quasi-elastic scattering appear in thevicinity of the Burns temperature. It is shown that it is unlikely that thequasi-elastic scattering originates from the combined effects of couplingbetween TA and TO phonons with an increase of the damping of the TO phononbelow T$_d$. The quasi-elastic scattering has a peak as a function oftemperature close to the peak in the dielectric constant while the intensity ofthe central peak scattering increases strongly below this temperature. Theseresults are discussed in terms of a random field model for relaxors

Quasi-elastic scattering, random fields and phonon-coupling effects in PbMg1/3Nb2/3O3

Quasi-elastic scattering, random fields and phonon-coupling effects in PbMg_1/3Nb_2/3O₃