Fluorescence Studies of Energy Transfer between Single and Pair ${\mathrm{Cr}}^{3+}$ Systems in ${\mathrm{Al}}_2$${\mathrm{O}}_3$

The fluorescence intensities and lifetimes of various no-phonon lines in ruby samples with 2.1 and 0.94% ${\mathrm{Cr}}^{3+}$ were studied from 13 to 700°K. The temperature dependences of the intensities of numerous lines were used to determine the energy levels of two pair systems. The relative intensities of the single-ion ($R$) lines and the pair ($N$) lines are proportional to Boltzmann factors $e^{\frac{-\Delta E}{\mathrm{kT}}}$, where $\Delta E$ is the difference in energy of the metastable states, at high temperatures but not at low temperatures. The deviation from this law is greater and occurs at higher temperatures in the less concentrated sample. The fluorescence decays of the $R$ and $N$ lines are pure exponentials in the temperature region where the $N$ lines follow a Boltzmann law; at low temperatures the $N$ lines have an initial rise in fluorescence and then a decay. These results are interpreted in terms of coupled fluorescence systems consisting of single ions and pairs. A phonon-assisted cross-relaxation coupling process is suggested which allows for thermalization of the systems at high temperatures and direct pumping of the pair systems by the single-ion system at low temperatures. Energy transfer from single-ion to multi-ion systems was also observed.