Ewald summation for ferroelectric perovksites with charges and dipoles

Abstract

Ewald summation is an important technique used to deal with long-range Coulomb interaction. While it is widely used in simulations of molecules and solid state materials, many important results are dispersed in literature and their implementations are often buried deep in large software packages. Since reliable and systematic calculation of Coulomb interaction is critical for the investigation of perovskites, here we start from the fundamentals of Ewald summation and derive clear expressions for long-range charge-charge, dipole-dipole, and charge-dipole interactions, which can be readily used for numerical computations. We also provide the interaction matrix for efficient Monte Carlo simulations involving charges and dipoles, implementing them in a Python software package. A new type of interaction matrix, which accounts for the electrostatic energy change when ions are displaced, is also derived and implemented. These results are the foundations for the investigation of ferroelectric perovskites.

Enhancement of Interfacial Polarization in BaTiO3 Thin Films via Oxygen Inhomogeneity

“…To further verify the mechanism of polarization enhancement near the interface due to oxygen inhomogeneity, we performed first-principles-based Monte-Carlo (MC) simulation. [26][27][28][29][30][31] For such simulation, the essential charge-dipole interaction has been added to the effective Hamiltonian and the MC simulation. Two separate charge layers in BTO lattices are used in our simulation to mimic the experimental situation.…”

“…The charge-dipole energy was treated with the Ewald method and the details can be found. [31] Based on the above effective Hamiltonian, MC simulations were performed with a pseudo-cubic supercell of size 12 × 12 × 12 (i.e., 1728 unit cells) with periodic boundary conditions. The charges were randomly distributed on their fixed layer.…”

Understanding the morphotropic phase boundary of perovskite solid solutions as a frustrated state

“…Note that the dipole-dipole term is conditionally convergent. So, we adopt Ewald summation [21][22][23] to separate it into a short-range contribution that converges rapidly in real space, a long-range contribution that converges rapidly in Fourier space, a self energy, and a surface term that depends on the boundary condition. Further, notice that for any flip, W e ≈ −E i • p i where E i = −∇ p i W e is the electric field.…”

Charge effects in donor doped perovskite ferroelectrics

“…In previous investigations, charge effects have been incorporated to understand heterovalent relaxors such as PbMg 1/3 Nb 2/3 O 3 24 . Here, for doped BaTiO 3 , we consider the long-range dipole-dipole and charge-dipole interactions, which can be conveniently computed using the Coulomb interaction matrix obtained using the Ewald method 25 .…”

“…Instead of using defect dipoles, we can deal with oxygen vacancies and impurity ions directly using the Ewald method 25 . For each unit cell with defects, we set a positive charge +q on the oxygen vacancy (V •• O ) in a certain direction (e.g.…”