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We propose a theory which allow to calculate the magnetic excitation spectrumin diluted ferromagnetic systems. The approach is rather general and based onthe Self-Consistent local Random Phase Approximation in which disorder(dilution) and thermal fluctuations are properly treated. To illustrate itsreliability and accuracy we calculate the magnetic excitation in the dilutedIII-V magnetic semiconductor $Ga_{1-x}Mn_{x}As$. It is shown that dilution hasa drastic effect on the excitation spectrum, indeed well defined magnonexcitations exist only in a small region of the Brillouin zone centered aroundthe $\Gamma$ point. We also calculate the spin stiffness in optimally annealedsample as a function of $Mn^{2+}$ concentration. A comparison to availablemeasurements is done. We find a very good agreement for both the Curietemperature and the spin stiffness measured in well annealed samples andprovide a plausible explanation for the very small values measured in as grownsamples.Comment: The manuscript has been modified, 4 figures are included. Accepted  for publication in Eur. Phys. Let

Magnetic spin excitations in diluted ferromagnetic systems: The case of Ga 1−x Mn x As

Magnetic spin excitations in diluted ferromagnetic systems: The case of Ga _1−x Mn _x As