Study of multiplet structures of Mn⁴⁺ activated in fluoride crystals

We investigated the optical properties of Mn⁴⁺ in some fluoride crystals such as Cs₂MnF₆, Cs₂GeF₆, Rb₂GeF₆, Cs₂SiF₆, K₂SiF₆, Rb₂MnF₆, Rb₂SiF₆, K₂GeF₆, K₂TiF₆, Li₂MnF₆, Na₂GeF₆, Na₂SiF₆, and Na₂TiF₆ based on the first-principle calculation using the discrete-variational multi-electron method. In order to estimate the lattice relaxation, we performed EXAFS measurement of Mn⁴⁺ doped in K₂SiF₆, K₂TiF₆, and K₂GeF₆. The relaxation rates of A₂BF₆:Mn⁴⁺ were fixed to be the above estimated values, 102.24%, 107.37% or 96.80% for crystal having Si, Ge, or Ti at the B cation site, respectively. In this work, we also considered some corrections such as configuration dependent correction and correlation correction to improve the theoretical energies. It has been shown that to reproduce multiplet energy levels quantitatively, the lattice relaxation is very important. On the other hand, for a qualitative prediction of the tendencies of the multiplet energies, the combination of lattice relaxation effect, configuration dependent correction, and correlation correction is effective. - Highlights: • Multiplet structures of A₂BF₆:Mn⁴⁺ were calculated from first-principles. • Lattice relaxation was estimated based on EXAFS experiment. • Lattice relaxation is important to reproduce multiplet energies quantitatively. • CDC and CC are important to reproduce tendencies of multiplet energies.