Mode sequence, frequency change of nonsoft phonons, and LO-TO splitting in strained tetragonalBaTiO3

Abstract

Ultraviolet Raman spectroscopy revealed the existence of an unusual large-frequency shift occurring to a nonsoft mode of $E({\mathrm{TO}}_{4}$) when ${\mathrm{BaTiO}}_{3}$ is strained to a ${\mathrm{SrTiO}}_{3}$ substrate [D. Tenne et al., Science 313, 1614 (2006)]. It raised two interesting questions: (i) whether there are other nonsoft modes that possess similar or even larger strain-induced frequency shifts and (ii) how the mode sequence is altered by these shifts in frequency. Note that mode sequence is also pivotal in correctly indexing and assigning the spectroscopy peaks observed in all Raman experiments. By mapping out the evolutions of individual phonon modes as a function of strain using first-principles density functional perturbation calculations, we determine the mode sequence and strain-induced phonon frequency shifts in prototypical ${\mathrm{BaTiO}}_{3}$. Our study reveals that the mode sequence is drastically different when ${\mathrm{BaTiO}}_{3}$ is strained to ${\mathrm{SrTiO}}_{3}$ compared to that in the unstrained structure, caused by multiple mode crossings. Furthermore, we predict that three other nonsoft modes, ${A}_{1}$(${\mathrm{TO}}_{2}$), $E({\mathrm{LO}}_{4}$), and ${A}_{1}$(${\mathrm{TO}}_{3}$), display even larger strain-induced frequency shifts than $E({\mathrm{TO}}_{4}$). The strain responses of individual modes are found to be highly mode specific, and a mechanism that regulates the magnitude of the frequency shift is provided. As another key outcome of this study, we tackle a long-standing problem of LO-TO splitting in ferroelectrics. A rigorous definition for the LO-TO splitting is formulated, which allows this critical quantity to be calculated quantitatively. The definition immediately reveals a new finding; that is, a large LO-TO splitting not only exists for $E({\mathrm{LO}}_{4}$), which is previously known and originates from a soft mode, it also occurs for a nonsoft ${A}_{1}$(${\mathrm{LO}}_{3}$) mode. The LO-TO splitting is shown to decrease drastically with compressive strain, and this decrease cannot be explained by the Born effective charges and high-frequency dielectric constants.