Optical probe of ferroelectric order in bulk and thin film perovskite titanates

We have measured the temperature dependence of the direct band gap, $E_g$, in SrTi${}^{16}$O${}_3$ and BaTiO${}_3$ and related materials with quantum-paraelectric and ferroelectric properties using optical spectroscopy. We show that $E_g$ exhibits an anomalous temperature dependence with pronounced changes in the vicinity of the ferroelectric transition that can be accounted for in terms of the Fr"ohlich electron-phonon interaction with an optical phonon mode, the so-called soft mode. We demonstrate that these characteristic changes of $E_g$ can be readily detected even in very thin films of SrTi${}^{16}$O${}_3$ with a strain-induced ferroelectric order. Optical spectroscopy thus can be used as a relatively simple but sensitive probe of ferroelectric order in very thin films of these titanates and probably also in subsequent multilayers and devices.