Role of orbital filling on nonlinear ionic Raman scattering in perovskite titanates

Abstract

The linear and nonlinear phononic interactions between an optically excited infrared (IR) or hyper-Raman mode and a driven Raman mode are computed for the ${d}^{0} ({\mathrm{CaTiO}}_{3})$ and ${d}^{1} ({\mathrm{LaTiO}}_{3})$ titanates within a first-principles density functional framework. We calculate the potential energy surface expanded in terms of the ${A}_{g}$ or ${B}_{1g}$ mode amplitudes coupled to the ${A}_{u}$ or the ${B}_{3u}$ mode and determine the coupling coefficients for these multimode interactions. We find that the linear-quadratic coupling dominates the anharmonicities over the quadratic-quadratic interaction in the perovskite titanates. The IR and Raman modes both modify the electronic structure with the former being more significant but occurring on a different time scale; furthermore, the coupled-mode interactions lead to sizable perturbations to the valence bandwidth ($\ensuremath{\sim}100\phantom{\rule{0.16em}{0ex}}\text{meV}$) and band gap ($\ensuremath{\sim}50$ meV). By comparing the coupling coefficients of undoped ${\mathrm{CaTiO}}_{3}$ and ${\mathrm{LaTiO}}_{3}$ to those for electron-doped $({\mathrm{CaTiO}}_{3})$ and hole-doped $({\mathrm{LaTiO}}_{3})$ titanates, we isolate the role of orbital filling in the nonlinear coupling process. We find that with increasing occupancy of the $d$ manifold, the linear-quadratic interaction decreases by approximately 30% with minor changes induced by the cation chemistry (that mainly affect the phonon mode frequencies) or by electron correlation. We identify the importance of the Ti-O bond stiffness, which depends on the orbital filling, in governing the lattice anharmonicitiy. This microscopic understanding can be used to increase the nonlinear coupling coefficient to facilitate more facile access of nonequilibrium structures and properties through ionic Raman scattering processes.