Finite-temperature simulation of anharmonicity and octahedral tilting transitions in halide perovskites

Octahedral tilting transitions are observed in most inorganic halide perovskites and play an important role in determining their functional and thermodynamic properties. Despite existing near room temperature, the cubic and tetragonal forms of halide perovskites become dynamically unstable at low temperature, making it impossible to study their thermodynamic properties with commonly used quasiharmonic models. An anharmonic vibrational Hamiltonian is constructed that accurately reproduces the low-energy portion of the potential-energy surface of the halide perovskite ${\mathrm{CsPbBr}}_{3}$. The Hamiltonian is validated using a large first-principles dataset of energies calculated within density functional theory for large-amplitude deformations of the ${\mathrm{CsPbBr}}_{3}$ crystal. Monte Carlo simulations performed on the Hamiltonian reproduce the orthorhombic-tetragonal-cubic phase transitions observed in ${\mathrm{CsPbBr}}_{3}$ and many other halide perovskites, demonstrating the importance of anharmonic vibrational excitations in stabilizing the tetragonal and cubic phases in these materials. Measures of local structure and octahedral tilting in the cubic and tetragonal phases, obtained from Monte Carlo simulations, confirm the connection between large anisotropic displacement factors and octahedral tilting, as observed experimentally.