  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 first
principles calculations. The obtained results show that antiferromagnetic (AFM)
order is energetically more favored than ferromagnetic (FM) order in Cr-doped
Ge and Si with $x$=0.03125 and 0.0625. In 6.25% Fe-doped Ge, FM interaction
dominates in all range of the R-R distances while for Fe-doped Ge at 3.125% and
Fe-doped Si at both concentrations of 3.125% and 6.25%, only in a short R-R
range can the FM states exist. In the Mn-doped case, the RKKY-like mechanism
seems to be suitable for the Ge host matrix, while for the Mn-doped Si, the
short-range AFM interaction competes with the long-range FM interaction. The
different origin of the magnetic orders in these diluted magnetic
semiconductors (DMSs) makes the microscopic mechanism of the ferromagnetism in
the DMSs more complex and attractive.

Materials Science