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Se reporta el proceso de síntesis del material complejo de tipo perovskita Bi0.5R0.5FeO3 (R=Eu, Sm, Dy) mediante el método cerámico, así como su caracterización estructural, óptica, magnética y eléctrica. Los datos refinados de difracción de rayos X revelaron que este material cristaliza en una estructura ortorrómbica (grupo espacial Pnma número 62). La respuesta óptica en la curva de espectroscopia de reflectancia difusa proporcionó un valor de brecha energética típico de los materiales semiconductores. La magnetización presentó un comportamiento histerético de campo coercitivo muy bajo característico del ferromagnetismo débil, para todas las temperaturas examinadas por debajo de 300 K y la aplicación de varios campos magnéticos. Las curvas de permitividad eléctrica real y compleja evidenciaron la presencia de procesos de relajación dieléctrica a 113 K, lo que concuerda con los reportes sobre corrientes piroeléctricas y termoestimuladas en función de la temperatura y revela la aparición de polarización ferroeléctrica por debajo de los 113 K, con un posible acoplamiento magnetoeléctrico. Por otro lado, se hizo un estudio teórico de la estructura electrónica con y sin la fase distorsiva de Berry. Se hicieron cálculos ab initio siguiendo el formalismo de la teoría funcional de la densidad y el método de ondas planas pseudopotenciales, formalismo en el cual los mecanismos de intercambio y correlación se describen mediante el enfoque de gradiente generalizado (GGA + U) considerando la polarización de espín. El análisis con la fase de Berry sugirió la presencia de ferroelectricidad a menos de 113 K, lo que concuerda con el análisis experimental que sugiere un comportamiento biferroico a bajas temperaturas debido a que la fase distorsiva introduce hibridaciones entre los estados 3d-Fe y 2p-O que favorecen la aparición de interacciones Dzyaloshinskii-Moriya, las cuales, a su vez, facilitan la aparición de ferroelectricidad en condiciones de ferromagnetismo débil. Las propiedades termodinámicas en presencia y ausencia de la fase de Berry en el modelo cuasi-armónico de Debyerevelaron la aparición de una transición ferroeléctrica a los 113 K, lo que corrobora la naturaleza magnetoeléctrica a bajas temperaturas. El carácter ferromagnético semiconductor a temperatura ambiente potencia este material para aplicaciones en tecnología espintrónica.
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