Heavy-tailed interactions and concentration-driven broadening of low energy scales in dilute Au:Er alloys

Dilute Au:Er alloys provide a clean realization of long-range Ruderman-Kittel-Kasuya-Yosida (RKKY)-coupled local moments and are widely used as paramagnetic sensor materials in metallic magnetic calorimeters (MMCs). Here we investigate how the low-temperature heat capacity evolves as the Er concentration is increased from a few hundred to a few thousand ppm. We combine heat-capacity measurements on Au:Er thin films with exact diagonalization of random spin clusters including Zeeman, RKKY, and dipolar couplings. At low Er content, the residual heat capacities remain more compatible with a reference single-scale rescaling, whereas at higher concentration this reference description becomes less adequate and a pronounced high-temperature tail develops, which is empirically close to linear over the measured window. The cluster model exhibits heavy-tailed distributions of pair couplings and broad local field statistics, while the lowest-gap analysis indicates a broadening of low-energy scales within the finite-cluster framework. Taken together, these results are compatible with a crossover from a more nearly single-scale paramagnetic regime at low concentration to broader local-energy scale distributions at higher concentration.