| Summary: | Here, we propose an idea to realize noncollinear ferrimagnetic orders with a considerably high magnetization M and their coupling with an improper ferroelectric (FE) order in hexagonal LuFeO_{3} type systems which exhibit interesting topological orders. These magnetic and magnetoelectric phenomena are driven by the antisymmetric Dzyaloshinskii-Moriya interactions between the magnetic ions and their coupling with the ferroelectricity. The proposed two-sublattice magnetic system, generated by a specific charge-ordered state, forms multiple energetically close, noncollinear ferrimagnetic orders. This offers a platform to manipulate the microscopic magnetic interactions and to trigger spin-reorientation (SR) transitions by various efficient means. The two-sublattice structure was realized in the hexagonal phase of LuFeO_{3} doped with electrons. The proposed electron-doped systems are expected to exhibit switchable electric polarization (P∼6–15 μC/cm^{2}), considerably high magnetization (M∼1.1–1.3μ_{B}/Fe), and magnetic transition near room temperature (∼275–290K). Based on the coupling between the magnetic interactions and the FE primary order parameter observed in this system, microscopic mechanisms to achieve electric field E induced SR transitions and 180^{∘} switching of the direction of M are discussed.
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