Fluctuating defects in the incipient relaxor K$_{1-x}$Li$_x$TaO$_3$ ($x=0.02$)

We have measured the structural correlations associated with the apparent relaxor transition near 70 K in K$_{0.98}$Li$_{0.02}$TaO$_3$ (KLT(0.02)) with neutrons. No elastic diffuse scattering or soft mode anomaly is observed, a situation that diverges from that in other relaxors like PMN. The structural correlations in KLT(0.02) are dynamic at all temperatures with timescales of $\sim$ THz. The fluctuations are overdamped, non-propagating, spatially uncorrelated, and absent in the parent material KTaO$_3$. The temperature dependence correlates with the dielectric response, implying that the fluctuations are associated with local, ferroelectric regions induced by the Li-doping. The ferroelectric transition induced by the introduction of sufficient Li cations is thus characterized by quasistatic fluctuations, which is a stark contrast to the soft-harmonic-mode-driven transition observed in perovskite ferroelectrics like PbTiO$_3$. The glass-like structural correlations in KLT(0.02) are much faster than those in random-field, lead-based relaxors, which occur on the $\sim$ GHz timescale, and they are better correlated spatially. Our results support the view that random fields give rise to the relaxor phenomena, and that the glassy dynamics observed here represent a nascent response.