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We report here the synthesis process of the perovskite-like complex material Bi0.5R0.5FeO3 (R=Eu, Sm, Dy) using the ceramic method, as well as its structural, optical, magnetic, and electrical characterizations. Refined X-ray diffraction data revealed that this material crystallizes in an orthorhombic structure (space group Pnma number 62). The band gap value in the optical response shown in the diffuse reflectance spectroscopy curve was typical of semiconductor materials. The magnetization exhibited a very low coercive field hysteretic behavior, which is characteristic of weak ferromagnetism, for all temperatures examined below 300 K and the various magnetic fields applied. The real and complex electric permittivity curves showed the occurrence of dielectric relaxation processes at 113 K in agreement with reports of pyroelectric and thermo-stimulated currents as a function of temperature revealing the appearance of ferroelectric polarization below 113 K with possible magnetoelectric coupling. On the other hand, we made a theoretical study of the electronic structure with and without the inclusion of a Berry distortional phase and ab-initio calculations following the density functional theory formalism and the pseudopotential plane wave method. In this formalism, the exchange and correlation mechanisms are described by the generalized gradient approach (GGA + U) considering spin polarization. The Berry phase analysis suggested the occurrence of ferroelectricity at temperatures below 113 K consistent with the experimental analysis evidencing a biferroic behavior at low temperatures given that the distortional phase introduces hybridizations between the 3d-Fe and 2p-O states favoring the appearance of Dzyaloshinskii-Moriya interactions, which, in turn, facilitate the appearance of ferroelectricity coexisting with a weak ferromagnetism. The thermodynamic properties in the presence or absence of the Berry phase by means of the Debye quasiharmonic model revealed the appearance of a ferroelectric transition at 113 K, which corroborates their magnetoelectric nature at low temperatures. The ferromagnetic semiconducting character found at room temperature enhances this material for applications in spintronics technology.
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