Strong emission bands in the visible region are observed in $\mathrm{Mg}{\mathrm{Al}}_2{\mathrm{O}}_4$ crystals doped with transition-metal ions under excitation at the band-to-band transitions. We report optical responses of Cr-, Co-, and Ni-doped $\mathrm{Mg}{\mathrm{Al}}_2{\mathrm{O}}_4$ and present optical models for $M$-doped $\mathrm{Mg}{\mathrm{Al}}_2{\mathrm{O}}_4$ ($M=\mathrm{Ti}$, V, Cr, Mn, Co, and Ni) to describe the charge-transfer transitions and the transitions between multiplet levels of $3d$ electrons, which are observed competitively or coexisting, depending on the number of $3d$ electrons. While the optical responses of Cr- and Ni-doped $\mathrm{Mg}{\mathrm{Al}}_2{\mathrm{O}}_4$ are dominated by the multiplet-multiplet transitions, those of Ti- and V-doped $\mathrm{Mg}{\mathrm{Al}}_2{\mathrm{O}}_4$ are governed by the charge-transfer transitions. The two kinds of transitions coexist in the Mn- and Co-doped $\mathrm{Mg}{\mathrm{Al}}_2{\mathrm{O}}_4$. These behaviors are well understood based on the numerical results of unrestricted Hartree-Fock approximation.

• Received 15 March 2007

DOI:https://doi.org/10.1103/PhysRevB.76.075111