  The temperature-dependent polarization of SrTiO_3 thin films is investigated
using confocal scanning optical microscopy. A homogeneous out-of-plane and
inhomogeneous in-plane ferroelectric phase are identified from images of the
linear electrooptic response. Both hysteretic and non-hysteretic behavior are
observed under a dc bias field. Unlike classical transitions in bulk
ferroelectrics, local ferroelectricity is observed at temperatures far above
the dielectric permittivity maximum. The results demonstrate the utility of
local probe experiments in understanding inhomogeneous ferroelectrics.
