  Using first-principles total-energy methods, we investigate Jahn-Teller
distortions in III-V dilute magnetic semiconductors, GaAs:Mn and GaN:Mn in the
cubic zinc blende structure. The results for an isolated Mn impurity on a Ga
site show that there is no appreciable effect in GaAs, whereas, in GaN there is
a Jahn-Teller effect in which the symmetry around the impurity changes from
T$_{d}$ to D$_{2d}$ or to C$_{2v}$. The large effect in GaN occurs because of
the localized d$^4$ character, which is further enhanced by the distortion. The
lower symmetry should be detectable experimentally in cubic GaN with low Mn
concentration, and should be affected by charge compensation (reductions of
holes and conversion of Mn ions to d$^5$ with no Jahn-Teller effect).
Jahn-Teller effect is greatly reduced because the symmetry at each Mn site is
lowered due to the Mn-Mn interaction. The tendency toward ferromagnetism is
found to be stronger in GaN:Mn than in GaAs:Mn and to be only slightly reduced
by charge compensation.
