Phonon coupling to dynamic short-range polar order in a relaxor ferroelectric near the morphotropic phase boundary

We report neutron inelastic scattering experiments on single crystal PbMg$_{1/3}$Nb$_{2/3}$O$_{3}$ doped with 32\% PbTiO$_{3}$, a relaxor ferroelectric that lies close to the morphotropic phase boundary. When cooled under an electric field $\mathbf{E} \parallel$ [001] into tetragonal and monoclinic phases, the scattering cross section from transverse acoustic (TA) phonons polarized parallel to $\mathbf{E}$ weakens and shifts to higher energy relative to that under zero-field-cooled conditions. Likewise, the scattering cross section from transverse optic (TO) phonons polarized parallel to $\mathbf{E}$ weakens for energy transfers $4 \leq \hbar \omega \leq 9$ meV. However, TA and TO phonons polarized perpendicular to $\mathbf{E}$ show no change. This anisotropic field response is similar to that of the diffuse scattering cross section, which, as previously reported, is suppressed when polarized parallel to $\mathbf{E}$, but not when polarized perpendicular to $\mathbf{E}$. Our findings suggest that the lattice dynamics and dynamic short-range polar correlations that give rise to the diffuse scattering are coupled.