The phonon-related effective Hamiltonian method for displacive ferroelectric materials

In this manuscript, we explain the theoretical principles and some technical details of a first-principles derived effective Hamiltonian method, which is used to calculate the ferroelectric (FE) and structural properties in displacive FE materials. Exploiting that the key instabilities responsible for this phase transition are governed by soft phonons, this Hamiltonian is phonon-related, i.e. using phonon modes as variables and describing their intra- and interactions. Upon retaining the predictive power of first-principles calculations, this method is computationally cheap, which enables large supercell being used so that the thermodynamic limit can be reached easily in the simulations at finite temperatures. Besides the known success in perovskites, it also qualifies for characterizing FE phase transitions in the rocksalt type group-IV monochalcogenides, and shows potential applications in more complicated systems, e.g. M-type hexaferrite.