Irreducible Phonon Interactions and Phonon-Strain Couplings in SrTiO₃

While strontium titanate (SrTiO₃) has undergone extensive first-principles analysis, there remains a need for a systematic study of the irreducible phonon interactions to gain a comprehensive understanding of the vibrational Hamiltonian within a given first-principles method. Here we accurately compute cubic, quartic, and selected sextic irreducible phonon interactions, employing both the lone and bundled irreducible derivative approaches. Furthermore, the leading order irreducible strain phonon couplings are computed, yielding a detailed Taylor series of the Born-Oppenheimer potential in terms of displacements and strains. Particular focus is placed on the <i>R</i>-point antiferrodistortive (AFD) soft mode and the Γ-point <i>T_1u</i> manifolds. We demonstrate that the three-fold AFD manifold has a potential that is nearly spherical, while the linear strain coupling mildly favors the experimentally observed tetragonal distortion. The full anharmonic Hamiltonian is solved within the Hartree-Fock approximation for phonons, and the resulting observables are compared to previous similar calculations and experimental data.