Nonequivalence of chemical and hydrostatic pressures: A1gandEgfrequencies and Stokes shift ofMn2+-doped perovskites

Abstract

The frequency of ${A}_{1g}$ and ${E}_{g}$ modes of ${\mathrm{MnF}}_{6}^{4\ensuremath{-}}$ in cubic $\mathrm{AB}{\mathrm{F}}_{3}$ (A: K; B: Mg, Zn and A: Rb, Cs; B: Cd, Ca) perovskites has been derived through density functional calculations on ${\mathrm{MnF}}_{6}{A}_{8}{B}_{6}^{16+}$ clusters which reproduce the experimental impurity-ligand distance ${R}_{e}.$ Both frequencies are found to experience a drastic decrement on passing from ${\mathrm{KMgF}}_{3}:{\mathrm{Mn}}^{2+}$ $(\ensuremath{\Elzxh}{\ensuremath{\omega}}_{A}=556{\mathrm{cm}}^{\ensuremath{-}1},$ $\ensuremath{\Elzxh}{\ensuremath{\omega}}_{E}=456{\mathrm{cm}}^{\ensuremath{-}1})$ to ${\mathrm{CsCdF}}_{3}:{\mathrm{Mn}}^{2+}$ $(\ensuremath{\Elzxh}{\ensuremath{\omega}}_{A}=317{\mathrm{cm}}^{\ensuremath{-}1},$ $\ensuremath{\Elzxh}{\ensuremath{\omega}}_{E}=239{\mathrm{cm}}^{\ensuremath{-}1})$ despite the fact that ${R}_{e}$ increases only by 5%, leading to effective Gr\uneisen constants (called ${\ensuremath{\gamma}}_{A}^{c}$ and ${\ensuremath{\gamma}}_{E}^{c})$ around 3.0 along the series. This figure is 60% higher than the usual Gr\uneisen constant ${\ensuremath{\gamma}}_{A}$ calculated for a given system like ${\mathrm{KMgF}}_{3}:{\mathrm{Mn}}^{2+}$ or ${\mathrm{KZnF}}_{3}:{\mathrm{Mn}}^{2+}$ when hydrostatic pressure is applied. For supporting this relevant result the value of ${\ensuremath{\gamma}}_{A}$ for ${\mathrm{CrF}}_{6}^{3\ensuremath{-}}$ in a fluoroelpasolite has been calculated as well. The obtained value ${\ensuremath{\gamma}}_{A}=2.1$ is close to the experimental one $({\ensuremath{\gamma}}_{A}=1.9)$ derived in ${\mathrm{K}}_{2}{\mathrm{NaGaF}}_{6}:{\mathrm{Cr}}^{3+}$ by combined optical and Raman measurements. As a salient feature, the increase of the Stokes shift when ${R}_{e}$ increases observed along the $\mathrm{AB}{\mathrm{F}}_{3}:{\mathrm{Mn}}^{2+}$ series is now well explained through the bigger variations of ${A}_{1g}$ and ${E}_{g}$ frequencies induced by the chemical pressure in comparison to those coming from an hydrostatic pressure on a given system. The difference between ${\ensuremath{\gamma}}_{A}^{c}$ and ${\ensuremath{\gamma}}_{A}$ is discussed through a simple model that emphasizes the role played by the coupling of the ${\mathrm{MnF}}_{6}^{4\ensuremath{-}}$ complex to the lattice. The influence of chemical and hydrostatic pressures upon the luminescence efficiency is also briefly discussed. Attention is addressed to the method of calculating impurity-associated Gr\uneisen constants using clusters. Recent results on ${\mathrm{Cr}}^{3+}$ in several cubic chloroelpasolites that support the present conclusions are briefly discussed as well.