Magnetic properties and disorder effects in diluted magnetic semiconductors

We present calculations of the exchange interactions and critical temperatures for several diluted magnetic semiconductor systems. It is shown that the exchange interactions are dominated by short-ranged interactions that have a strong directional dependence. Using a combination of first-principles calculations of the exchange interactions together with Monte Carlo simulations of the classical Heisenberg model, in which the positional disorder and spin fluctuations are properly included, the calculated critical temperatures are in good agreement with experimantal observations. It is shown that agreement between theory and experiment, as regards ordering temperatures, is obtained only when the magnetic atoms are randomly positioned in a simulation cell which proves that disorder effects play a very important role. The effect of strong electron-electron interaction has been studied by means of the $\mathrm{LSDA}+U$ scheme. We investigate in detail the nature of the anisotropic exchange interactions by means of a Fermi surface analysis.