Determining (All) Dark Matter-Electron Scattering Rates From Material Properties

We show that the scattering rate for any dark matter (DM) interaction with electrons in any target is proportional to several measurable material properties, encapsulated by a single master formula. This generalizes the dielectric function formalism--developed for DM interactions that couple to electron density--to any interaction, incorporating both spin-dependent and spin-independent interactions simultaneously. This formalism links the full many-body response of a target system to the DM probe in a clear and simple form, providing a reliable event rate prediction from measurable material quantities. We demonstrate the utility of our formalism by placing new limits from existing data on a class of spin-dependent light DM interactions, as their rates--contrary to common lore--are determined entirely by the dielectric function. We further highlight a promising avenue for the detection of sub-MeV DM using the rare earth metal Praseodymium, which exhibits a spin-dependent anisotropic response down to the meV scale. Our results lay the groundwork for a rapid systematic investigation of novel electron scattering targets going beyond the classic spin-independent searches, enhancing the prospects for DM detection.