The electrical, magnetic, and structural features of bismuth manganite (BM), e.g., BiMnO3, and bismuth ferrite (BF), e.g., BiFeO3, are reviewed. Induced multiferroicity and enhanced magnetoelectric coupling are required for various modern device applications. BM and BF were synthesized using standard high-temperature sintering and processes such as sol–gel, hydrothermal, or wet chemical methods combined with annealing. The size and morphology of the nanoscale particles were controlled, although they were usually inhomogeneous. BF exhibits structurally stable antiferromagnetic (AFM) and ferroelectric (FE) phases in wide temperature ranges. Ferromagnetic (FM) order was induced in a thick shell around the AFM core of the nanoscale BF particles, which was attributed to a size effect related to surface strains and disorder. BM exhibited both structurally stable and unstable phases. The BiMnO3, Bi12MnO20, and BiMn2O5 structures are nonferroelectric. The perovskite BiMnO3 form was synthesized under high hydrostatic pressure. FM order occurs in BM at low temperatures. Bi(MnFe)O3 solid solution samples exhibited competition between AFM and FM ordering. Doping can decrease the content of unavoidable secondary phases. Doping in the Bi ion sublattice can stabilize the crystal lattice owing to local strains caused by the difference in ionic radius between Bi and the dopant. Doping in the Fe and Mn sublattices affects the electrical features. The main achievement of substitution with tetra- and pentavalent ions is compensation of the oxygen vacancies. In turn, leakage current suppression enables switching of FE domains and polarization of the samples. A significant enhancement of magnetoelectric coupling was observed in composites formed from BF and other FE materials. The leakage currents can be diminished when an insulator polymer matrix blocks percolation. The potential applicability is related to enhanced magnetoelectric coupling. The constructed devices meet the size effect limitations for FE and FM ordering. Resistive switching suggests possible use in nonvolatile memories and gaseous sensors. The sensors can be used for hydrophones and for photovoltaic and photoluminescence applications, and they can be constructed from multiphase materials. Bulk multiferroic solid solutions, composites, and nanoheterostructures have already been tested for use in sensors, transducers, and read/write devices for technical purposes.
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