Optimum filter-based analysis for the characterization of a high-resolution magnetic microcalorimeter towards the DELight experiment

Ultra-sensitive cryogenic calorimeters have become a favored technology with widespread application where eV-scale energy resolutions are needed. In this article, we characterize the performance of an X-ray magnetic microcalorimeter (MMC) using a Fe-55 source. Employing an optimum filter-based amplitude estimation and energy reconstruction, we demonstrate that an unprecedented FWHM resolution of $\Delta E_\mathrm{FWHM} = \left(1.25\pm0.17\mathrm{\scriptsize{(stat)}}^{+0.05}_{-0.07}\mathrm{\scriptsize{(syst)}}\right)\,\text{eV}$ can be achieved. We also derive the best possible resolution and discuss limiting factors affecting the measurement. The analysis pipeline for the MMC data developed in this paper is furthermore an important step for the realization of the proposed superfluid helium-based experiment DELight, which will search for direct interaction of dark matter with masses below 100 MeV/c$^2$.