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

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... nced 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.