Interlevel nonradiative transitions of impurities in solids

Abstract

The spin-orbit interaction in transition-metal ions induces fast nonradiative transitions among states of different spin; the transition rates can be directly measured by the homogeneous broadening of zero-phonon optical lines. The configuration-interaction formalism developed by Fano is well suited for the evaluation of the widths and shifts caused by these nonradiative processes. By taking the Jahn-Teller effect into account, we have shown that within the framework of Fano's formalism it is possible to reproduce the shape of the zero-phonon line of MgO: ${\mathrm{V}}^{2+}$ as regards both widths and splittings without making use of any fitting parameter. The model has also been applied to ${\mathrm{Al}}_2$ ${\mathrm{O}}_3$: ${\mathrm{Cr}}^{3+}$, ${\mathrm{Cs}}_2$Si${\mathrm{F}}_6$: ${\mathrm{Mn}}^{4+}$, and MgO: ${\mathrm{Cr}}^{3+}$; its limits of validity have been discussed.