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.