Comparison of the Jahn-Teller effect in four triply degenerate states of ${\mathrm{Mn}}^{++}$ in RbMn${\mathrm{F}}_3$

The Jahn-Teller energies and distortions for four excited states of ${\mathrm{Mn}}^{++}$ in RbMn${\mathrm{F}}_3$ have been obtained. The states are ${}_{}{}^4{}_{}{}^{}T_1^{}{}_{}{}^{}\left(\mathrm{I}\right)$, ${}_{}{}^4{}_{}{}^{}T_1^{}{}_{}{}^{}\left(\mathrm{II}\right)$, ${}_{}{}^4{}_{}{}^{}T_2^{}{}_{}{}^{}\left(\mathrm{I}\right)$, and ${}_{}{}^4{}_{}{}^{}T_2^{}{}_{}{}^{}\left(\mathrm{II}\right)$. An effective force constant and cluster frequency were derived from the data for ${}_{}{}^4{}_{}{}^{}T_1^{}{}_{}{}^{}\left(\mathrm{I}\right)$ and used to find the Jahn-Teller energies for all the states. A semiquantitative treatment of the lattice dynamics of RbMn${\mathrm{F}}_3$ has enabled us to analyze the phonon sidebands and to describe the coupling of the cluster modes to the lattice. The experimental methods primarily involve the use of uniaxial stress, and the theoretical interpretation involves the calculation of the multiplet splitting, including the reorientation of the exchange field. Both $E$ and $T_2$ distortions were observed and the Jahn-Teller energies found vary from 58 to 458 ${\mathrm{cm}}^{-1\mathrm{}}$. Even when small, the Jahn-Teller effect has significant spectral consequences. Although we did not use the crystal-field model to analyze the data, we found that it gave a good rationalization of the results.