The electronic properties of perovskite RMnO3 (R=Tb, Dy, Ho and Er) were studied using the density- functional theory (DFT). For each perovskite RMnO3, the ferromagnetic (FM) and antiferromagnetic (AFM) structural parameters in the spin-up and spin-down configurations are optimized. The band structures, the density of states (DOS) and the partial density of states (PDOS) of the hexagonal (h- RMO) and orthorhombic (o-RMO) are also investigated. As results, a relationship between the crystal structures and their electrical behavior has been established: the orthorhombic structure exhibits semiconducting behavior with bandgap ranging from 0.5 to 0.7 eV; the hexagonal structure in the spin-down configuration exhibits semiconducting behavior with a bandgap ranging from 2.4 to 2.7 eV; the hexagonal structure with an earth rare element having a small ionic radius (Tb and Dy in the present case) in the spin-up state exhibits semiconducting behavior with a bandgap of about 0.6 eV; the hexagonal structure with an earth rare element having a high ionic radius (Ho and Er in the present case) in the spin- up state exhibits metallic behavior.

RMnO3, manganite perovskites, electronic properties, DFT, Quantum Espresso