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Domain wall fluctuations in ferroelectrics coupled to strain

Using a Ginzburg--Landau--Devonshire model that includes the coupling of polarization to strain, we calculate the fluctuation spectra of ferroelectric domain walls. The influence of the strain coupling differs between 180 degree and 90 degree walls due to the different strain profiles of the two configurations. The finite speed of acoustic phonons, $v_s$, retards the response of the strain to polarization fluctuations, and the results depend on $v_s$. For $v_s \to \infty$, the strain mediates an instantaneous electrostrictive interaction, which is long-range in the 90 degree wall case. For finite $v_s$, acoustic phonons damp the wall excitations, producing a continuum in the spectral function. As $v_s\ to 0$, a gapped mode emerges, which corresponds to the polarization oscillating in a fixed strain potential.