We present an ab-initio and analytical study of the Jahn-Teller effect in two
diluted magnetic semiconductors (DMS) with d4 impurities, namely Mn-doped GaN
and Cr-doped ZnS. We show that only the combined treatment of Jahn-Teller
distortion and strong electron correlation in the 3d shell may lead to the
correct insulating electronic structure. Using the LSDA+U approach we obtain
the Jahn-Teller energy gain in reasonable agreement with the available
experimental data. The ab-initio results are completed by a more
phenomenological ligand field theory.Comment: 15 pages, 5 figure