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

TL;DR

This work provides a universal master equation that connects DM–electron scattering rates in any material to three measurable response functions: the dielectric-like charge response $\chi_{00}$, the electronic spin susceptibility $\chi_{ij}$, and the spin-charge response $\chi_{0i}$, all derived through linear response theory. The rate factorizes into a DM-dependent form factor $|V(\mathbf{q}, \mathbf{v}_\perp)|^2$ and a material-response piece, unifying spin-independent and spin-dependent interactions within a single formalism and enabling rapid, material-agnostic rate predictions. Using this framework, the authors recast existing spin-independent bounds to constrain spin-dependent operators such as electric-dipole $\mathcal{O}_{11}$ and anapole $\mathcal{O}_8$, and they demonstrate novel sensitivity from the spin dynamics of Praseodymium, including anisotropic meV-scale excitations that extend reach into the keV–MeV DM mass range. The results advocate a broad, high-throughput search for DM targets beyond magnons, including paramagnets and spintronics-enabled materials, and establish a practical bridge between material science data and DM detection capabilities.

Abstract

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.

Figures (4)

• Figure 1: Spin-dependent results using the dielectric function. Our 95% C.L. new bounds and projections on electric dipole DM ${\cal O} = {\cal O}_{11}$ with a light mediator ( left) and anapole DM ${\cal O} = {\cal O}_8$ with a heavy mediator ( right). The blue shaded regions (labeled 'this work') correspond to the new bounds we place using data from the QROCODILE Baudis:2025zyn and DAMIC-M DAMIC-M:2025luv collaborations. The solid curves correspond to future projections for several materials assuming three orders of magnitude sensitivity and no background events. The solid pink curve corresponds to $1$ yr exposure of $10^7$ WSi pixels, each of similar configuration to the current QROCODILE pixel Baudis:2025zyn, with a threshold of $42.8 \, {\rm meV}$. The green (orange) solid curves delineate projections for a kg-yr exposure of Si (superconducting Al) with a threshold of $1.12 \, {\rm eV}$ ($10 \, {\rm meV}$).
• Figure 2: Pr spin response.Left. The trace of the spin response of Pr for momenta in the $\Gamma \to M$ crystal direction. The black lines indicate the dispersion relations of the different modes. Right. The trace of the spin response of Pr at momenta $q=10 \, {\rm eV},\, 500 \, {\rm eV},\, 1 \, {\rm keV}$ along the $\Gamma \to M, K, A$ crystal directions. A constant excitation width of $\Gamma=0.45$ meV has been used to calculate the response. We find the response depends on both the magnitude and direction of the momenta.
• Figure 3: Spin-dependent results using spin response. Projected reach for DM-electron interactions mediated by a heavy axial vector ${\cal O} = 4 {\cal O}_4$ ( left) and light pseudoscalar ${\cal O} = {\cal O}_6$ ( right) for Pr, where the shaded region indicates variation with the width $\Gamma$, the anti-ferromagnet La$_2$CuO$_4$ (orange, using the model of Ref. Marocco:2025eqw), and a gapped ferromagnet (pink, see text for details). Curves are computed at 95% C.L. for a kg-year exposure and energy acceptance $\omega \in [1\, {\rm meV}, 1 \, {\rm eV}]$. Solid curves delineate the isotropic reach, whereas dashed curves delineate the directional reach. In the left panel, we also show for comparison the projected reach of YIG (green) with a $25\,{\rm meV}$ threshold Trickle:2020oki.
• Figure 4: The spin response function for Pr computed using the MF-RPA susceptibility Eq. \ref{['eq:Pr response']} with the two-ion couplings extracted from a fit of the dispersion relations Eq. \ref{['eq:Pr dispersion relation']} in neutron scattering experiments Bak:1975Houmann:1975Houmann:1979 with a width $\Gamma=0.45$ meV. The upper left and upper right panels show the trace of the spin response, ${\rm Im}(\chi_{ii})$, for momentum deposits along the $\Gamma \to K$ and $\Gamma \to M$ directions, respectively. The lower left and lower right panels present the individual components, ${\rm Im}(-\chi_{11})$ and ${\rm Im}(-\chi_{22})$, for momentum deposits along the $\Gamma \to M$ direction. The difference between the upper panels highlights the dependence of the spin susceptibility $\chi_{ij}$ on momentum direction, while the variation between the lower panels illustrates differences between its components. Black curves indicate the dispersion relations of the different modes.