Calculation of Optical and Spin-Hamiltonian Parameters for $Mn^{4+}$ Doped in $LiGa_{5}O_{8}$

The aim of this paper is to investigate, from theoretical point of view, the optical spectra and EPR (g-factors) parameters for $Mn^{4+}:LiGa_{5}O_{8}$. The optical energy levels scheme has been obtained by the diagonalization of the Hamiltonian of the system, using all 50 wave functions of the LS terms of $3d^{3}$ electron configuration. The crystal field parameters have been obtained in the exchange charge model of crystal field, taking into account the structure of the host matrix and effects of the covalent bond formation between the $Mn^{4+}$ with $O^{2-}$. The satisfactory agreement with experimental data is obtained.