Crystal Field Analysis of Cr$\text{}^{3+}$ Energy Levels in LiGa$\text{}_{5}$O$\text{}_{8}$ Spinel

Detailed and consistent crystal field analysis of the LiGa$\text{}_{5}$O$\text{}_{8}$:Cr$\text{}^{3+}$ absorption spectrum is performed in the present paper by using the exchange charge model of crystal field. We calculate the crystal field parameters from the crystal structure date and diagonalize the crystal field Hamiltonian to obtain the energy level structure of Cr$\text{}^{3+}$ ions in LiGa$\text{}_{5}$O$\text{}_{8}$. The obtained energy levels and estimated Racah parameters B and C were compared with the experimental spectroscopic data; good agreement was demonstrated.