Optimization of Mn doping in group-IV-based dilute magnetic semiconductors by electronic codopants

The percentage of substitutional doping of magnetic atoms (Mn) in group-IV-based dilute magnetic semiconductors can be increased by codoping with another conventional electronic dopant, as demonstrated from first-principles calculations recently [W. G. Zhu, Z. Y. Zhang, and E. Kaxiras, Phys. Rev. Lett. 100, 027205 (2008)]. Here, we report extensive theoretical investigations of the kinetic and thermodynamic characteristics of several codoped systems including bulk Si and Ge as hosts and various group-III and group-V dopants. The main findings are as follows. The $n\text{\ensuremath{-}}p$ pairing of $n$-type codopants with $p$-type substitutional Mn is energetically stable in bulk Ge and Si. Mn atoms move from interstitial sites to substitutional sites easier (with lower kinetic barriers) in the presence of a neighboring $n$-type codopant. 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 codoped 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 codoping. We find an unconventional magnetic anisotropy in the codoped system, that is, the dependence of magnetic coupling on the relative positions of the magnetic ions and their neighboring donors. We map the calculated magnetic coupling to a classical Heisenberg model and employ Monte Carlo simulations to estimate the Curie temperature $({T}_{c})$. 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 $\ensuremath{\sim}5\text{ }\text{K}$ at 5% Mn doping. For Mn/As codoped Ge, ${T}_{c}$ increases nearly linearly with the Mn concentration and reaches 264 K at 5% Mn doping.