  We report neutron scattering measurements of the structural correlations
associated with the apparent relaxor transition in K$_{1-x}$Li$_x$TaO$_3$ for
$x=0.02$ (KLT(0.02)). This compound displays a broad and frequency-dependent
peak in the dielectric permittivity, which is the accepted hallmark of all
relaxors. However, no evidence of elastic diffuse scattering or any soft mode
anomaly is observed in KLT(0.02) [J. Wen et al., Phys. Rev. B 78, 144202
(2008)], a situation that diverges from that in other relaxors such as
PbMg$_{1/3}$Nb$_{2/3}$O$_3$. We resolve this dichotomy by showing that the
structural correlations associated with the transition in KLT(0.02) are purely
dynamic at all temperatures, having a timescale on the order of $\sim$THz.
These fluctuations are overdamped, non-propagating, and spatially uncorrelated.
Identical measurements made on pure KTaO$_3$ show that they are absent (within
experimental error) in the undoped parent material. They exhibit a temperature
dependence that correlates well with the dielectric response, which suggests
that they are associated with local ferroelectric regions induced by the Li$^+$
doping. The ferroelectric transition that is induced by the introduction of
Li$^+$ cations is therefore characterized by quasistatic fluctuations, which
represents a stark contrast to the soft harmonic-mode-driven transition
observed in conventional perovskite ferroelectrics like PbTiO$_3$. The dynamic,
glass-like, structural correlations in KLT(0.02) are much faster than those
measured in random-field-based lead-based relaxors, which exhibit a frequency
scale of order of $\sim$GHz and are comparatively better correlated spatially.
Our results support the view that random fields give rise to the relaxor
phenomena, and that the glass-like dynamics observed here characterize a
nascent response.
