First Principles Investigation on the Spatial Distribution and Magnetism in Cr doped GaN

Exhaustive structural and magnetic configurations have been investigated to understand the magnetism of Cr:GaN. Our results provide direct evidence that the magnetic ions have a strong tendency to get close by forming ``constrained clusters'' with short-range magnetic interactions. Substitutional clustering configurations are found much more favourable than the substitutional-interstitial complexes. Significantly, while for isolated and ``pair'' substitutional configurations the ferromagnetic state is the ground state with a magnetic moment close to 3$\mu _{B}$/Cr, for more than three Cr atoms configurations, antiferromagnetic states are found energetically more favourable where the net spin is much lower (0-1.8 $\mu _{B})$. We propose a picture that various Cr-configurations coexist and the statistical distribution and associated magnetism depend sensitively on the growth conditions. Such a view can elucidate and explain many of the hitherto puzzling experimental observations. We argue such a picture may also hold for other diluted magnetic semiconductor systems.