Multiple-Valence and Visible to Near-Infrared Photoluminescence of Manganese in ZnGa₂O₄: A First-Principles Study

The transition metal manganese is attractive for magnetism and luminescence engineering due to the nontrivial interplay of charge, spin, lattice, and orbital freedom degrees. Here, we report the manganese site occupancy and valence states by taking experimental synthesis conditions into consideration and the optical features of target intra-atomic Mn²⁺, Mn³⁺, and Mn⁴⁺ in the framework of density functional theory in a prototype spinel ZnGa₂O₄ host. The formation energy results show that Mn²⁺ dominates in tetrahedral ligands at the Zn²⁺ site and Mn³⁺ and Mn⁴⁺ dominate in octahedral ligands at the Ga³⁺ site under the corresponding different chemical potential conditions, and the distortion of the local coordination environment of Mn³⁺ in octahedral ligands due to the Jahn–Teller effect is studied in detail. The excited-state equilibrium geometries and energies are obtained via spin or orbital occupancy constraints, which are further complemented by the Tanabe–Sugano diagram to predict the energy spectra and to interpret the experimental results on Mn²⁺, Mn⁴⁺, and Mn³⁺. In particular, the competition of ⁵T₂ and ¹T₂ excited states and the relaxation processes leading to near-infrared luminescence of rarely reported Mn³⁺ are analyzed. First-principles calculations complemented by the Tanabe–Sugano diagram analysis may serve as an effective and predictive tool for exploring valence states, energy structures, and luminescence of complexes containing 3dⁿ transition-metal ions.