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A number of transition-metal (TM) doped group-IV semiconductors,R$_{x}$Y$_{1-x}$ (R=Cr, Mn and Fe; Y=Si, Ge), have been studied by the firstprinciples calculations. The obtained results show that antiferromagnetic (AFM)order is energetically more favored than ferromagnetic (FM) order in Cr-dopedGe and Si with $x$=0.03125 and 0.0625. In 6.25% Fe-doped Ge, FM interactiondominates in all range of the R-R distances while for Fe-doped Ge at 3.125% andFe-doped Si at both concentrations of 3.125% and 6.25%, only in a short R-Rrange can the FM states exist. In the Mn-doped case, the RKKY-like mechanismseems to be suitable for the Ge host matrix, while for the Mn-doped Si, theshort-range AFM interaction competes with the long-range FM interaction. Thedifferent origin of the magnetic orders in these diluted magneticsemiconductors (DMSs) makes the microscopic mechanism of the ferromagnetism inthe DMSs more complex and attractive.Comment: 14 pages, 2 figures, 6 table

physical review. b, condensed matter and materials physics

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First-principles investigation of transition-metal-doped group-IV semiconductors:RxY1−x(R=