Static, quasistatic, and quasidynamic Jahn-Teller effect in the EPR spectra ofAg2+in SrO, CaO, and MgO

The EPR spectra observed for ${\mathrm{Ag}}^{2+}$ in the alkaline-earth-oxide host crystals SrO, CaO, and MgO provide an exceptionally clear example of the unusual spectral features associated with the transition from a static to a dynamic Jahn-Teller effect at low temperature. The spectrum observed for ${\mathrm{Ag}}^{2+}$ in SrO exhibits the low-temperature threefold tetragonal symmetry with symmetric line shapes and averaging at higher temperatures (80 to 200 K) which characterize the static Jahn-Teller (JT) effect. A threefold tetragonally symmetric spectrum is also observed for ${\mathrm{Ag}}^{2+}$ in CaO at 1.3 K, but, in this case, the line shapes are not symmetric and resemble those observed for systems exhibiting a dynamic JT effect. Additionally, a complex line shape is observed at 1.3 K for ${\mathrm{Ag}}^{2+}$ in CaO with the orientation $\overrightarrow{\mathrm{H}}\parallel \mathrm{}\left[111\right]\mathrm{}$. These line-shape effects are due to a value of the ratio of random strain splitting $\overline{\delta }$ to "tunneling" splitting $3\Gamma$ which is intermediate to those associated with either the static or dynamic JT effect. The complex line shapes observed at 9 GHz with $\overrightarrow{\mathrm{H}}\parallel \mathrm{}\left[111\right]\mathrm{}$ have been computed by performing a numerical diagonalization of the matrix of strain and tunneling for the manifold of states consisting of the ground ${}_{}{}^2{}_{}{}^{}E$ and first-excited $A_2$ vibronic singlet levels. From this calculation a value of 1.2 has been determined for the ratio $\frac{\overline{\delta }}{3\Gamma }$. At a frequency of 23 GHz, the line shapes for ${\mathrm{Ag}}^{2+}$ in CaO exhibit additional effects due to the increased Zeeman interaction, and, by performing a simultaneous diagonalization of the strain, tunneling, and Zeeman matrices, it is possible to independently determine values of 4.7 and 3.9 ${\mathrm{cm}}^{-1\mathrm{}}$ for $\overline{\delta }$ and $3\Gamma$, respectively. For ${\mathrm{Ag}}^{2+}$ in MgO, the angular variation of the EPR spectrum at 1.3 K resembles the type of variation typical of a dynamic JT system, but with one component shifted and broadened by coupling via random strain to a nearly excited $A_2$ vibronic singlet level. A value of $\frac{\overline{\delta }}{3\Gamma }=0.13\mathrm{}$ was determined for ${\mathrm{Ag}}^{2+}$ in MgO by fitting the observed angular variation to a computed angular variation derived from a numerical diagonalization of the matrix of strain and tunneling for the ${}_{}{}^2{}_{}{}^{}E-A_2$ manifold. These observed features classify the JT effect as static, quasistatic, and quasidynamic for