Line shape of theCr3+luminescence in garnet crystals

The line shapes of ${\mathrm{Cr}}^{3+}$ photoluminescence in garnet crystals, in which the ${}_{}{}^2{}_{}{}^{}$E and ${}_{}{}^4{}_{}{}^{}$ ${\mathit{T}}_2$ excited states are close in energy, have been calculated with use of the vibronic tunneling model developed previously by the present authors. At low temperatures, the experimental luminescence spectrum from ${\mathrm{Cr}}^{3+}$ in ${\mathrm{Y}}_3$ ${\mathrm{Ga}}_5$ ${\mathrm{O}}_{12}$, ${\mathrm{Gd}}_3$ ${\mathrm{Sc}}_2$ ${\mathrm{Al}}_3$ ${\mathrm{O}}_{12}$, and ${\mathrm{Gd}}_3$ ${\mathrm{Sc}}_2$ ${\mathrm{Ga}}_3$ ${\mathrm{O}}_{12}$ is always an admixture of ${}_{}{}^2{}_{}{}^{}$E${\to }^4$ ${\mathit{A}}_2$ and ${}_{}{}^4{}_{}{}^{}$ ${\mathit{T}}_2$ ${\to }^4$ ${\mathit{A}}_2$, the relative amounts being determined by the energy difference ΔE=E${(}^4$ ${\mathit{T}}_2$)-E${(}^2$E). The line shapes, calculated in terms of mixing of ${}_{}{}^2{}_{}{}^{}$E and ${}_{}{}^4{}_{}{}^{}$ ${\mathit{T}}_2$ adiabatic vibronic wave functions via spin-orbit and nuclear kinetic-energy operators, reproduce the experimental low-temperature spectra rather well. Our calculation of the temperature dependence of the