First-principles model potentials for lattice-dynamical studies: general methodology and example of application to ferroic perovskite oxides

We present a scheme to construct model potentials, with parameters computed from first principles, for large-scale lattice-dynamical simulations of materials. We mimic the traditional solid-state approach to the investigation of vibrational spectra, i.e., we start from a suitably chosen reference configuration of the compound and describe its energy as a function of arbitrary atomic distortions by means of a Taylor series. Such a form of the potential-energy surface is general, trivial to formulate for any material, and physically transparent. Further, such models involve clear-cut approximations, their precision can be improved in a systematic fashion, and their simplicity allows for convenient and practical strategies to compute/fit the potential parameters. We illustrate our scheme with two challenging cases in which the model potential is strongly anharmonic, namely, the ferroic perovskite oxides PbTiO3 and SrTiO3. Studying these compounds allows us to better describe the connection between the so-called effective-Hamiltonian method and ours (which may be seen as an extension of the former), and to show the physical insight and predictive power provided by our approach—e.g., we present new results regarding the factors controlling phase-transition temperatures, novel phase transitions under elastic constraints, an improved treatment of thermal expansion, etc.