Origin of transition metal clustering tendencies in GaAs based dilute magnetic semiconductors

While isovalent doping of GaAs (e.g., by In) leads to a repulsion between the solute atoms, two Cr, Mn, or Fe atoms in GaAs are found to have lower energy than the well-separated pair, and hence attract each other. The strong bonding interaction between levels with $t2$ symmetry on the transition metal (TM) atoms results in these atoms exhibiting a strong tendency to cluster. Using first-principles calculations, we show that this attraction is maximal for Cr, Mn, and Fe while it is minimal for V. The difference is attributed to the symmetry of the highest occupied levels. While the intention is to find possible choices of spintronic materials that show a reduced tendency to cluster, one finds that the conditions that minimize clustering tendencies also minimize the stabilization of the magnetic state.