Fig. 3: First-principles calculations for YAG:2%Ce³⁺, 20%Mn²⁺.

Configuration coordinate diagrams for the ground state ⁶A₁ and excited states ⁴T₁ of Mn²⁺-doped YAG structure, along with the corresponding partial charge density distribution of the highest occupied orbital and the lowest unoccupied orbital, are presented. In this context, four distinct computational models are derived from the local structure of YAG. a Isolated Mn²⁺ ion occupies octahedron site (\({\rm{Mn}}^{2+}_{\rm{oct}}\)); b Isolated Mn²⁺ ion occupies dodecahedron site (\({\rm{Mn}}^{2+}_{\rm{dod}}\)); c Mn²⁺ ions occupy the adjacent octahedron and dodecahedron sites (\({\rm{Mn}}^{2+}_{\rm{oct}}{-}{\rm{Mn}}^{2+}_{\rm{dod}}\)); d Mn²⁺ ions occupy the adjacent two dodecahedron sites (\({\rm{Mn}}^{2+}_{\rm{dod}}{-}{\rm{Mn}}^{2+}_{\rm{dod}}\))