Zeeman effect of the energy levels of ${\mathrm{Fe}}^{2+}$ in diluted magnetic semiconductors

We present a study of the magnetic-field dependence of the energy levels of ${\mathrm{Fe}}^{2+}$ in a wurtzite diluted magnetic semiconductor. We limit our considerations to transitions in the infrared region of the electromagnetic spectrum. The Hamiltonian of the ion has been diagonalized to fourth power in the parameter ‖λ‖/Δ, the ratio of the strength of the spin-orbit interaction λ to the splitting Δ arising from the tetrahedral component of the crystal potential. We make no a priori assumption concerning the relative strengths of λ and the parameters describing the effect on the crystal field of the trigonal distortion. The parameters describing the ${\mathrm{Fe}}^{2+}$ ion in CdSe are obtained from near-infrared absorption data at zero magnetic field by Udo et al. [Phys. Rev. B 46, 7459 (1992)]. With these values we make a comparison with the electronic Raman-effect data obtained by Mauger et al. [Phys. Rev. B 43, 7102 (1991)] as functions of the intensity and direction of an applied magnetic field.