Thermodynamic evidence of the ferroelectric Berry phase in europium-based ferrobismuthite Eu₂Bi₂Fe₄O₁₂

Abstract

The possible low temperature biferroic feature of Eu₂Bi₂Fe₄O₁₂ complex perovskites was recently reported. The aim of this work is to present a theoretical study of the structural, magnetic, electronic and ferroelectric properties of this material. Several energy minimization processes were performed for three types of cationic distributions, different angles of rotation, octahedral inclination, and some kinds of magnetic ordering. The results reveal that the most stable crystallographic arrangement corresponds to an intercalated distribution of the Eu³⁺ and Bi³⁺ cations between the FeO₆ octahedra. Similarly, energy is minimized for rotations and octahedral inclinations corresponding to angles θₑ = 12.86° and ϕₑ = 13.32°, respectively. With respect to the distribution of magnetic moments, the results reveal that a G-type antiferromagnetic configuration is the most energetically favorable. The electronic structure is studied from ab initio calculations following the formalism of density functional theory and the pseudopotential plane wave method. In this formalism, the exchange and correlation mechanisms are described by means of the generalized gradient approach (GGA + U), considering spin polarization. The ferroelectric characteristic is analysed by determining ferroelectric polarization based on the calculation of the Berry phase. The theoretical results obtained are consistent with the experimental reports, which is why the Eu₂Bi₂Fe₄O₁₂ material is expected to exhibit biferroic behavior at low temperatures, because the Berry phase introduces hybridizations between the 3d-Fe and 2p-O states that favor the occurrence of Dzyaloshinskii-Moriya interactions, which facilitate the occurrence of ferroelectricity coexisting with weak ferromagnetism. An extensive study of the thermodynamic properties in the presence and absence of the Berry phase is undertaken by means of the Debye quasi harmonic model. The specific heat difference with and without the Berry phase reveals the occurrence of a ferroelectric transition at T = 113 K without the application of external pressure. When the applied pressure is incremented, a systematic increase in the transition temperature is observed due to the reduction of overlap between the 3d-Fe orbitals and the 2p-O orbitals in the compressed octahedra of perovskite.