First-principles effective Hamiltonian for ferroelectric polarization in BaTiO₃/SrTiO₃ superlattices

Abstract

We present an effective Hamiltonian for the description of ferroelectric polarizations in perovskite oxide superlattices. To understand the ferroelectric behavior of (BaTiO₃)_n/(SrTiO₃)_m superlattices, we constrained the local distortion modes along the c direction only and set up the effective Hamiltonian based on the local modes that capture the physics of long-wavelength acoustic modes (strain) and lowest energy transverse optical phonon modes (soft modes) as prescribed by the localized Wannier functions. All the parameters in this effective Hamiltonian were predetermined from the first-principles density-functional theory calculations of each BaTiO₃ and SrTiO₃ components. As an application of the model parameters, we calculated the polarizations of (BaTiO₃)_n/(SrTiO₃)_m with n+m=5, the results of which are in good agreement with those of the previous first-principles calculations of average polarizations as well as local polarizations. This effective Hamiltonian procedure can provide guidance for developing ferroelectric model of other kinds of oxide superlattices.