Compensation, interstitial defects and ferromagnetism in III-V semiconductors

In diluted magnetic semi-conductors, e.g. Ga(Mn)As, Ga(Mn)N and In(Mn)As, the observed magnetism depends strongly on methods of preparation and sample history, with correlation between the Curie temperature T$_c$ and the conductivity for the same concentration of magnetic ions. The transport measurements show that the simple picture of substitution of Mn$^{2+}$ ions for Ga sites is insufficient and effects of defects, e.g. Mn interstitials and As anti-sites, must be included. We present a quantitative theory, using magnetic exchange interactions from carrier- and impurity- concentration dependent {\it ab initio} estimates, and a recently developed semi-analytic theory$^{1,2}$. Spin fluctuations are treated in a locally self-consistent RPA approach, and disorder exactly, by sampling. Very good agreement, without ajustable parameters, is obtained for the T$_c$ of different samples. We predict T$_c$ as a function of hole concentration for Mn$_x$Ga$_{1-x}$As and In$_x$Ga$_{1-x}$As. For fixed x, T$_c$ is non-monotonic in carrier concentration for a restricted region of carrier density and vanishes outside. [1]G. Bouzerar, T. Ziman, J.Kudrnovsk\'y, cond-mat/0405322 [2]G. Bouzerar, T. Ziman, J.Kudrnovsk\'y, Appl. Phys. Lett. (scheduled Nov. 29 2004), cond-mat/0407101