Resonance Damping of the THz-frequency Transverse Acoustic Phonon in the Relaxor Ferroelectric KTa1-xNbxO3
The damping ($\Gamma_a$) of the transverse acoustic (TA) phonon in single crystals of the relaxor $KTa_{1-x}Nb_xO_3$ with x=0.15-0.17 was studied by means of high resolution inelastic cold neutron scattering near the (200) B.Z. point where diffuse scattering is absent, although it is present near (110). In a wide range of temperatures centered on the phase transition, T=195K-108K, 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 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 Nb+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 $\omega_L$ and damping $\Gamma_L$ ($\Gamma_L < \omega_L$), itself coupled to the transverse optic (TO) mode. Maximum damping of the TA phonon occurs when its frequency $\omega_a \approx{\omega_L}$. $\omega_L$ and $\Gamma_L$ are moderately dependent on temperature but the oscillator strength, $M_2$, of the resonant damping exhibits a strong maximum in the range $T\sim{150 K-120 K}$ in which neutron diffuse scattering near the (110) B.Z. 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 $\omega_L$ is found to be similar to the estimate previously obtained by Girshberg and Yacoby. Alternatively, the TA phonon damping can be successfully fitted in the framework of an empirical Havriliak - Negami (HN) relaxation model that includes a strong resonance-like transient contribution.