Optical Properties of Perovskite Oxides in Their Paraelectric and Ferroelectric Phases

Abstract

The optical-absorption characteristics of the perovskite oxides BaTi${\mathrm{O}}_{3}$, KTa${\mathrm{O}}_{3}$, and K${\mathrm{Ta}}_{0.65}$${\mathrm{Nb}}_{0.35}$${\mathrm{O}}_{3}$ (KTN) are reported in the vicinity of the interband absorption edge, and, in the case of semiconducting KTN, in the near infrared where donor photo-ionization absorption dominates. The large optical-absorption anisotropies observed in the ferroelectric phases of BaTi${\mathrm{O}}_{3}$ and KTN are shown to be related to shifts in conduction-band valleys by using a many-valley model with three valley minima at the zone boundary along the $〈100〉$ directions. The two valleys lying along axes perpendicular to the direction of the spontaneous polarization ${P}_{s}$ are raised in energy by an amount $\ensuremath{\Delta}\mathcal{E}\ensuremath{\propto}{{P}_{s}}^{2}$ relative to the valley parallel to ${P}_{s}$, where $\ensuremath{\Delta}\mathcal{E}=2.2{{P}_{s}}^{2}$ eV for KTN and $\ensuremath{\Delta}\mathcal{E}=1.5{{P}_{s}}^{2}$ eV for BaTi${\mathrm{O}}_{3}$ (${P}_{s}$ is in C/${\mathrm{m}}^{2}$). In the case of KTN the valley energy shifts are found to be consistent with electrical-conductivity anisotropy data. The interband-absorption-edge data are found to show an exponential Urbach tail in all three materials up to absorption coefficients of at least ${10}^{3}$ ${\mathrm{cm}}^{\ensuremath{-}1}$. The band-edge results for BaTi${\mathrm{O}}_{3}$ are in disagreement with existing published data. The donor photo-ionization data in semiconducting KTN and the attendant large dichroism are shown to be governed by a simple $f$ sum rule.