Vibronic coupling and the near-infrared spectrum of ${\mathrm{Fe}}^{2+}$ in CdTe and ZnS

The main characteristics of the near-infrared spectrum of ${\mathrm{Fe}}^{2+}$ in both CdTe and ZnS are attributed to vibronic coupling between the 3$d^6$ configuration of ${\mathrm{Fe}}^{2+}$ and the local vibrations induced by the lattice dynamics. A strategy is devised to obtain the quantitative aspects of the coupling (coupling energy and energy of the coupling mode) from the low-energy zero-phonon absorption lines. The calculation includes the diagonalization of a Jahn-Teller Hamiltonian with respect to a number of wave functions that depends on the number N of vibrational quanta. Numerical results are obtained for the intensities of the absorbed lines and energies of the absorbed photons that are in good agreement with experiments. The values of the two free parameters also are in good agreement: the energy of the coupling phonon is the expected one in accordance with the lattice dynamics of both CdTe and ZnS; the value of the Jahn-Teller energy is in correspondence with previous estimates. The method is simple and easy to use for other similar systems. The convergence with respect to N is also studied and found to give reproducible results for N=10 in the case of CdTe; the convergence for ZnS is actually faster than that for CdTe.