Unusual dynamics of the ferroelectric phase transition in K1−xLixTaO3 crystals

${\mathrm{K}}_{1\text{−}x}{\mathrm{Li}}_x\mathrm{Ta}{\mathrm{O}}_3$ ($x=0.043$, 0.08) crystals, characterized by pyroelectric current with calculated spontaneous polarization and zero-field second-harmonic generation, have been studied by broadband dielectric spectroscopy, including time-domain terahertz transmission and infrared (IR) reflectivity, and by polarized Raman spectroscopy in the 10–300 K temperature range. This multiexperimental approach has proven the percolative nature of the ferroelectric (FE) transition at low temperatures and demonstrated that the FE phase is inherently inhomogeneous and displays coexistence of FE and relaxor regions. Thanks to the very broad frequency range studied (from 1 Hz to 20 THz), the relevant excitations were identified and fitted in the dielectric response of both crystals: three relaxations, a central mode (CM), and a soft mode (SM) that splits into three components on cooling. Two Cole-Cole relaxations (assigned to flipping of polar nanoregions around the ${\mathrm{Li}}^{+}$ ions by $\pi /2$ and π, in agreement with the known literature), thermally activated below $\sim 150\mathrm{K}$, but staying in the gigahertz range at higher temperatures, do not show any frequency anomaly at the FE transition and are therefore related to the non-FE parts of the sample volume. A third thermally activated relaxation of unusually slow dynamics was revealed at low frequencies and preliminary assigned to an expected critical relaxation connected with the percolative nature of the FE phase transition. The IR SM, which undergoes much less softening than in the undoped ${\mathrm{KTaO}}_3$, splits into three components below the FE transition. Two higher-frequency components correspond to the FE volume part of the crystals assigned to the split $A_1$ and $E$ modes due to the cubic-tetragonal transition. The third low-frequency component is assigned to the non-FE (relaxor) volume part. Our assignment was confirmed by modeling the terahertz-IR response of the SM using the Bruggeman model within the effective medium approach. Below the SM response, an additional CM in the ${10}^{11}\mathrm{Hz}$ range in the whole temperature range is inferred from the fits.