Peculiarities of the electronic structure of phosphors possessing Mn²⁺ ions either in octahedral O_h or tetrahedral T_d coordination: A first-principles study

We report on first-principles calculations carrying out within density functional theory (DFT) of the electronic structure of three host materials that are very prospective for activation with Mn²⁺ ions, in fact KMgF₃, ZnS and Li₂ZnBr₄ crystallizing within crystal structures Pm 3 m (No. 221), F -43 m (No. 216), and Pnma (No. 62). When entering the crystal matrices due to the formation of the corresponding phosphors, Mn²⁺ ions substitute either Mg²⁺ ions being in the octahedral O_h coordination (KMgF₃:Mn²⁺) or Zn²⁺ ions (ZnS:Mn²⁺ and Li₂ZnBr₄:Mn²⁺) being in the tetrahedral T_d coordination. The DFT calculations reveal that the Mn–S and Mn–Br bond lengths for Mn²⁺ ions in the case of the tetrahedral T_d coordination in ZnS:Mn²⁺ and Li₂ZnBr₄:Mn²⁺ phosphors are longer compared to the Mn–F bond length for Mn²⁺ ions in the octahedral O_h coordination (KMgF₃:Mg²⁺). Inserting Mn²⁺ ions into the KMgF₃, ZnS and Li₂ZnBr₄ host matrices was found to cause the formation of new electronic states associated with Mn²⁺ 3 d -orbitals and positioned in the energy band gaps. The energy difference in splitting the Mn²⁺ 3 d e_g and Mn²⁺ 3 d t_2g states (spin-up and spin-down) in the case of the KMgF₃:Mn²⁺ phosphor for Mn²⁺ ions in the octahedral O_h coordination is rather big, whereas in the ZnS:Mn²⁺ and Li₂ZnBr₄:Mn²⁺ phosphors with tetrahedral T_d coordination of Mn²⁺ ions this difference is very small. The ⁴T₁ → ⁶A₁ optical transition energies and Stokes shifts for Mn²⁺-doped KMgF₃, ZnS and Li₂ZnBr₄ have been theoretically estimated.