Systematic study of the magnetic circular dichroism ofns2ions in KBr and KI

We report the measurement of the magnetic circular dichroism in the $A$, $B$, and $C$ bands of ${\mathrm{Ga}}^{+}$, ${\mathrm{In}}^{+}$, ${\mathrm{Tl}}^{+}$ in KI and of ${\mathrm{Ga}}^{+}$ and ${\mathrm{In}}^{+}$ in KBr. A complete analysis of the magnetic circular dichroism and absorption data is performed using the method of moments. Expressions are obtained for the coupling to the cubic vibrational modes ($A_{1g}$) and to the noncubic modes ($E_g$ and $T_{2g}$) both in terms of the zeroth and first moments of the absorption band and in terms of the third moment of the magnetic circular dichroism. Both methods are found to agree for ${\mathrm{In}}^{+}$ in KI and KBr. Results of the analysis of both the orbital $g$ factor and the second moments of the noncubic modes indicate that there are significant differences between the orbital states of the singlet ($C$ band) and triplet ($A$ band). Furthermore, the coupling to the cubic modes is found to be as important as coupling to the noncubic modes in the triplet states of ${\mathrm{Ga}}^{+}$ and ${\mathrm{In}}^{+}$ in KBr and KI. Lastly, electron-lattice coupling is found to increase for these ions in going from KI to KBr as the host crystals.