Many-body energy-transfer processes betweenEr3+ions in yttrium aluminum garnet

The results of the luminescence-quenching measurements of the ${}_{}{}^4{}_{}{}^{}$ ${\mathit{S}}_{3/2}$ level of ${\mathrm{Er}}^{3+}$ in yttrium aluminum garnet are reported. Decay data in a large temperature (10–300 K) and concentration range (0.1–100 at.%) are analyzed. The quenching process depends strongly on concentration and temperature. At low ${\mathrm{Er}}^{3+}$ content (≤3 at.%) the quenching is dominated by two-ion dipole-dipole cross-relaxation processes. It is shown that the previous proposed mechanisms can only explain the high-temperature data, and a possible active mechanism at low temperatures is proposed. At higher concentrations the quenching process depends strongly on temperature, the migration on donors playing an essential role, especially at low temperatures, where the supermigration regime is observed. The quadratic concentration dependence of the transfer parameters at high ${\mathrm{Er}}^{3+}$ content is connected with the three-ion cross-relaxation processes. The temperature dependences of the supermigration rates are consistent with two types of three-ion processes, i.e., one phonon-assisted process at low temperatures (T<100 K) and another very efficient resonant one [${(}^4$ ${\mathit{S}}_{3/2}$ ${,}^2$ ${\mathit{H}}_{11/2}$)${\to }^4$ ${\mathit{I}}_{15/2}$ ${]}_{\mathit{D}}$+[${(}^4$ ${\mathit{I}}_{15}$ ${}_{/2\mathrm{}}{}^{}{}_{}{}^{}\to _{}^4{}_{}{}^{}$ ${\mathit{I}}_{13/2}$ ${)}_{\mathit{A}1}$+${(}^4$ ${\mathit{I}}_{15/2}$ ${\to }^4$ ${\mathit{I}}_{9/2}$ ${)}_{\mathit{A}}$ at high temperatures (T>150 K). It is shown that at 300 K for C>10 at.% ${\mathrm{Er}}^{3+}$ the transfer is of direct donor-acceptor type, due to the above cross relaxation. Thus, at 300 K, the energy from the pumping ${}_{}{}^4{}_{}{}^{}$ ${\mathit{S}}_{3/2}$ level is transferred to the 3-μm laser levels