First-principles theory of polarization and electric fields in ferroelectrics

Three recently introduced approaches to the theoretical treatment of ferroelectrics and related materials in finite electric fields will be reviewed. First, the use of effective-Hamiltonian treatments that have been fitted to first-principles calculations for describing applied electric fields and even field-induced structural phase transitions at finite temperatures will be discussed. Second, a recently developed approach in which a systematic expansion of the free energy is truncated at a low order in the applied electric field, allowing for a mapping of the energy landscape as a function of polarization and of electric-field induced effects, will be reviewed. Third, a fundamental development of a direct method,for treating insulators infinite electric fields within density-functional methods will be described. For each of these approaches, an example application is given.