  The percentage of substitutional doping of magnetic atoms (Mn) in
group-IV-based dilute magnetic semiconductors (DMS) can be increased by
co-doping with another conventional electronic dopant (e-dopant) [Zhu et al.,
Phys. Rev. Lett. 100, 027205 (2008)]. Here, we report extensive theoretical
investigations of the kinetic and thermodynamic characteristics of several
co-doped systems including bulk Si and Ge as hosts and various group-III and
group-V e-dopants. The main findings are as follows: The n-p pairing of n-type
e-dopants with p-type substitutional Mn is energetically stable in bulk Ge and
Si. Mn atoms move from interstitial sites to substitutional sites easier in the
presence of a neighboring n-type e-dopant. Magnetic coupling between two Mn
atoms in bulk Ge oscillates between positive (ferromagnetic) and negative
(antiferromagnetic) values with increasing Mn-Mn distance, but in Mn/As
co-doped Ge the coupling parameter remains positive at all distances beyond
nearest-neighbors and this qualitative difference does not change with the
doping level. For Mn doped Si, all coupling values except for the nearest
neighbor one are positive and do not change much upon co-doping. We find an
unconventional magnetic anisotropy in the co-doped system, that is, the
dependence of magnetic coupling on the relative positions of the magnetic ions
and their neighboring e-dopants. We employ Monte Carlo simulations to estimate
the Curie temperature (Tc). We find that in Mn doped Ge no ferromagnetic order
exists for Mn concentrations ranging from 3.13% to 6%. Instead, a spin-glass
phase transition occurs at ~5K at 5% Mn doping. For Mn/As co-doped Ge, Tc
increases nearly linearly with the Mn concentration and reaches 264K at 5% Mn
doping.
