We present a theoretical description of the excitonic giant Zeeman effect observed in wide gap diluted magnetic semiconductors (Zn,Co)O and (Ga,Mn)N. In these materials, A and B excitons present quite complex energy shifts and change of oscillator strengths under magnetic field. These features can be well reproduced using an excitonic Hamiltonian, taking into account ion-carrier exchange, wurtzite trigonal crystal field, spin-orbit and electron-hole exchange interactions.
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