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 $\Delta \mathcal{E}\propto {P_s}^2$ relative to the valley parallel to $P_s$, where $\Delta \mathcal{E}=2.2\mathrm{}{P_s}^2$ eV for KTN and $\Delta \mathcal{E}=1.5\mathrm{}{P_s}^2$ 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 ${10}^3$ ${\mathrm{cm}}^{-1\mathrm{}}$. 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.