with the aim of reducing 𝑐 𝑠 and alleviating the bottleneck. Rates for 5%Dy@2-Y are significantly faster than 2-Dy at low temperature (Figure ), in accord with the presence of a phonon bottleneck in 2-Dy. For AC measurements of 5%Dy@2-Y three peaks were observed; the slowest peak (A) has near-identical Orbach rates to 2-Dy and similar Raman rates above ca. 10 K (Figure ), while the other peaks may correspond to other species such as the diluted Dy analog of 6-Y. Fitting of the relaxation rates of 5%Dy@2-Y to Equation S7 gives similar parameters to 2-Dy but with observable QTM (τQTM = 10 2.12(5) s). The similarity of 3-Dy to isomorphous 2-Dy suggests 3-Dy also experiences a phonon bottleneck; however, as there is no significant downturn in rates at low temperatures it appears the bottleneck has similar parameters to the Raman relaxation in this sample, and the relaxation profile was fit with Orbach and Raman terms only (Equation S8).