Structural and dielectric properties of Sr$_{2}$TiO$_{4}$ from first principles

We have investigated the structural and dielectric properties of Sr$_{2}$TiO$_{4}$,the first member of the Sr$_{n+1}$Ti$_{n}$O$_{3n+1}$ Ruddlesden-Popper series, within density functional theory. Motivated by recent work in which thin films of Sr$_{2}$TiO$_{4}$ were grown by molecular beam epitaxy (MBE) on SrTiO$_{3}$ substrates, the in-plane lattice parameter was fixed to the theoretically optimized lattice constant of cubic SrTiO$_{3}$ (n=$\infty$), while the out-of-plane lattice parameter and the internal structural parameters were relaxed. The fully relaxed structure was also investigated. Density functional perturbation theory was used to calculate the zone-center phonon frequencies, Born effective charges, and the electronic dielectric permittivity tensor. A detailed study of the contribution of individual infrared-active modes to the static dielectric permittivity tensor was performed. The calculated Raman and infrared phonon frequencies were found to be in agreement with experiment where available. Comparisons of the calculated static dielectric permittivity with experiments on both ceramic powders and epitaxial thin films are discussed.