Resonance damping of the terahertz-frequency transverse acoustic phonon in the relaxor ferroelectricKTa1−xNbxO3

The damping $(\mathrm{\ensuremath{\Gamma}}a)$ of the transverse acoustic (TA) phonon in single crystals of the relaxor $\mathrm{KT}{\mathrm{a}}_{1\ensuremath{-}x}\mathrm{N}{\mathrm{b}}_x{\mathrm{O}}₃$ with $x=0.15--0.17$ was studied by means of high resolution inelastic cold neutron scattering near the (200) Brillouin Zone (BZ) point where diffuse scattering is absent, although it is present near (110). In a wide range of temperatures centered on the phase transition, $T=195\phantom{\rule{0.16em}{0ex}}\mathrm{K}\textdiv{}108\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, the TA phonon width (damping) exhibits a step increase around momentum $q=0.07$, goes through a shallow maximum at $q=0.09--0.12$, and remains high above and up to the highest momentum studied of $q=0.16$. These experimental results are explained in terms of a resonant interaction between the TA phonon and the collective or correlated reorientation through tunneling of the off-center $\mathrm{N}{\mathrm{b}}⁺⁵$ ions. The observed TA damping is successfully reproduced in a simple model that includes an interaction between the TA phonon and a dispersionless localized mode (LM) with frequency ${\ensuremath{\omega}}_L$ and damping ${\mathrm{\ensuremath{\Gamma}}}_L({\mathrm{\ensuremath{\Gamma}}}_L<{\ensuremath{\omega}}_L)$, itself coupled to the transverse optic (TO) mode. Maximum damping of the TA phonon occurs when its frequency is ${\ensuremath{\omega}}_a\ensuremath{\approx}{\ensuremath{\omega}}_L$. The values of ${\ensuremath{\omega}}_L$ and ${\mathrm{\ensuremath{\Gamma}}}_L$ are moderately dependent on temperature, but the oscillator strength, ${M}²$, of the resonant damping exhibits a strong maximum in the range $T\ensuremath{\sim}120\phantom{\rule{0.16em}{0ex}}\mathrm{K}\textdiv{}150\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ in which neutron diffuse scattering near the (110) BZ point is also maximum and the dielectric susceptibility exhibits the relaxor behavior. The maximum value of $M$ appears to be due to the increasing number of polar nanodomains. In support of the proposed model, the observed value of ${\ensuremath{\omega}}_L\ensuremath{\approx}0.7\phantom{\rule{0.16em}{0ex}}\mathrm{THz}$ is found to be similar to the estimate previously obtained by Girshberg and Yacoby [J. Phys.: Condens. Matter 24, 015901 (2012)]. Alternatively, the TA phonon damping can be successfully fitted in the framework of an empirical Havriliak-Negami (HN) relaxation model that includes a strong resonancelike transient contribution.