Lattice dynamics and vibrational spectra of the orthorhombic, tetragonal, and cubic phases of methylammonium lead iodide

The hybrid halide perovskite ${\mathrm{CH}}_{3}{\mathrm{NH}}_{3}{\mathrm{PbI}}_{3}$ exhibits a complex structural behavior, with successive transitions between orthorhombic, tetragonal, and cubic polymorphs around 165 and 327 K. Herein we report first-principles lattice dynamics (phonon spectrum) for each phase of ${\mathrm{CH}}_{3}{\mathrm{NH}}_{3}{\mathrm{PbI}}_{3}$. The equilibrium structures compare well to solutions of temperature-dependent powder neutron diffraction. By following the normal modes, we calculate infrared and Raman intensities of the vibrations, and compare them to the measurement of a single crystal where the Raman laser is controlled to avoid degradation of the sample. Despite a clear separation in energy between low-frequency modes associated with the inorganic (${\mathrm{PbI}}_{3}{}^{\ensuremath{-}}{)}_{n}$ network and high-frequency modes of the organic ${\mathrm{CH}}_{3}{\mathrm{NH}}_{3}{}^{+}$ cation, significant coupling between them is found, which emphasizes the interplay between molecular orientation and the corner-sharing octahedral networks in the structural transformations. Soft modes are found at the boundary of the Brillouin zone of the cubic phase, consistent with displacive instabilities and anharmonicity involving tilting of the ${\mathrm{PbI}}_{6}$ octahedra around room temperature.