  We use an x-ray free-electron laser to study the ultrafast lattice dynamics
following above band-gap photoexcitation of the incipient ferroelectric
potassium-tantalate, \kto. %
  We use ultrafast near-UV (central wavelength 266\,nm and 50 fs pulse
duration) laser light to photoexcite charge carriers across the gap and probe
the ultrafast lattice dynamics by recording the x-ray diffuse intensity
throughout multiple Brillouin zones using pulses from the Linac Coherent Light
Source (LCLS) (central wavelength 1.3\,\AA\, and $< 10$~fs pulse duration). We
observe changes in the diffuse intensity that we conclude are associated with a
hardening of the soft transverse optical and transverse acoustic phonon
branches along $\Gamma$ to $X$ and $\Gamma$ to $M$. Using ground- and
excited-state interatomic force constants from density functional theory (DFT)
and assuming the phonon populations can be described by a time-dependent
temperature, we fit the quasi-equilibrium thermal diffuse intensity to the
experimental time-dependent intensity. We obtain the instantaneous lattice
temperature and density of photoexcited charge carriers as a function of time
delay. The DFT calculations demonstrate that photoexcitation transfers charge
from oxygen $2p$ derived $\pi$-bonding orbitals to Ta $5d$ derived antibonding
orbitals, further suppressing the ferroelectric instability and increasing the
stability of the cubic, paraelectric structure.
