Density functional study of the structural, electronic, and vibrational properties ofβ-Ba2TiO4

Motivated by the reported high dielectric response of monoclinic $\ensuremath{\beta}$-Ba${}_{2}$TiO${}_{4}$ as well as its affinity for absorbing small molecules, we investigate its structural, electronic, and vibrational properties with density functional theory (DFT). DFT-based structural optimization obtains lattice parameters and bond lengths within a few percent of experimentally observed values, with specific details depending on the choice of exchange-correlation functional. Although, for both the local density approximation (LDA) and generalized gradient approximation (GGA) functionals employed, the DFT calculations produce a wide-band-gap insulating state for $\ensuremath{\beta}$-Ba${}_{2}$TiO${}_{4}$ (with an indirect gap of 4.1 eV or greater), they do not agree on the energetic ordering of this phase with respect to its perovskite-like Ruddlesden-Popper (RP) polymorph. Simulations that utilize LDA place the $\ensuremath{\beta}$ phase 0.30 eV higher, while those using the Perdew-Burke-Ernzerhof GGA functional place it 0.22 eV lower than the RP one, leaving the question of the degree of perovskite-like phase metastability under epitaxial growth conditions unresolved. Comparison of the formula unit volumes of the ${A}_{2}$TiO${}_{4}$ and $A$TiO${}_{3}$ polymorphs ($A=\text{Sr}$, Ba) reveals that both Ba${}_{2}$TiO${}_{4}$ structures possess much more open geometries---more so for the $\ensuremath{\beta}$ than for the RP phase---than their isostoichiometric Sr-based counterparts and all of the examined $A$TiO${}_{3}$ compounds, in line with the demonstrated propensity of the Ba-based 2-1-4 oxides to capture molecules like CO${}_{2}$ and H${}_{2}$O. However, an analysis of vibrations and their contributions to the static dielectric permittivity tensor of $\ensuremath{\beta}$-Ba${}_{2}$TiO${}_{4}$ indicates that, unlike the perovskite RP phase, this structure does not exhibit strong polar lattice distortions, which results in a rather low value for its average static dielectric constant.