The structural, magnetic, electronic and optical properties of Pbnm BiFeO[Formula: see text] (BFO), BiFe[Formula: see text]Mn[Formula: see text]O[Formula: see text] (BFM), Bi[Formula: see text]X[Formula: see text]Fe[Formula: see text]Mn[Formula: see text]O[Formula: see text] (XBFM) (X = Ce, Gd, Lu) have been investigated by the first principles within the PBE[Formula: see text]+[Formula: see text]U scheme. It is shown that the dopant Mn in the B sites and Ce (Gd, Lu) in the A sites improves the crystalline quality. The magnetic moments of Bi[Formula: see text]Ce[Formula: see text]Fe[Formula: see text]Mn[Formula: see text]O[Formula: see text] (CBFM) and Bi[Formula: see text]Gd[Formula: see text]Fe[Formula: see text]Mn[Formula: see text]O[Formula: see text] (GBFM) are 10 [Formula: see text] and 16 [Formula: see text] which mainly arises from the strongly localized unpaired 4f electrons of Ce and Gd, 3d electrons of Mn and Fe. While, as BFM, the magnetic moment of Bi[Formula: see text]Lu[Formula: see text]Fe[Formula: see text]Mn[Formula: see text]O[Formula: see text] (LBFM) is 9 [Formula: see text] indicating no effect on the magnetization is made by Lu for its full 4f states. The densities of states of the five systems hint that CBFM is metallic and BFM, GBFM, LBFM are still semiconductors. The metallic properties of CBFM arise from the hybridization between Ce-4f and Mn-3d states which leads the Mn [Formula: see text] states to be split into [Formula: see text] and [Formula: see text] lowering the bottom of the conduction band to cross the Fermi level. Furthermore, we also study the optical properties of Pbnm BiFeO[Formula: see text] (BFO), BiFe[Formula: see text]Mn[Formula: see text]O[Formula: see text] (BFM), Bi[Formula: see text]X[Formula: see text]Fe[Formula: see text]Mn[Formula: see text]O[Formula: see text] (XBFM) (X = Ce, Gd, Lu). In this work, the optical properties including the absorption spectrum, loss function, refractive index and reflectivity spectrum are discussed in detail.
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