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  • Open Access

Determining spin-dependent light dark matter rates from neutron scattering

Asher Berlin1,2,*, Alexander J. Millar1,2,†, Tanner Trickle1,‡, and Kevin Zhou3,4,§

  • *Contact author: aberlin@fnal.gov
  • †Contact author: amillar@fnal.gov
  • ‡Contact author: ttrickle@fnal.gov
  • §Contact author: kzhou7@berkeley.edu
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Phys. Rev. D 112, 035021 – Published 14 August, 2025

DOI: https://doi.org/10.1103/4yxf-lkr6

Abstract

The scattering and absorption rates of light dark matter with electron spin-dependent interactions depend on the target’s spin response. We show how this response is encoded by the target’s dynamical magnetic susceptibility, which can be measured using neutron scattering. We directly use existing neutron scattering data to compute the dark matter scattering rate in a candidate target material, finding close agreement with the previous first-principles calculation at MeV dark matter masses. Complementary experiments and measurements can extend the reach of this technique to other dark matter models and masses, and identify promising target materials for future experiments.

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References (104)

  1. J. Aalbers et al. (LZ Collaboration), First dark matter search results from the LUX-ZEPLIN (LZ) experiment, Phys. Rev. Lett. 131, 041002 (2023).
  2. E. Aprile et al. (XENON Collaboration), The XENONnT dark matter experiment, Eur. Phys. J. C 84, 784 (2024).
  3. C. A. J. O’Hare, New definition of the neutrino floor for direct dark matter searches, Phys. Rev. Lett. 127, 251802 (2021).
  4. D. Antypas et al., New horizons: Scalar and vector ultralight dark matter, arXiv:2203.14915.
  5. K. M. Zurek, Dark matter candidates of a very low mass, Annu. Rev. Nucl. Part. Sci. 74, 287 (2024).
  6. Y. Kahn and T. Lin, Searches for light dark matter using condensed matter systems, Rep. Prog. Phys. 85, 066901 (2022).
  7. Y. Wang et al. (CDEX Collaboration), Improved limits on solar axions and bosonic dark matter from the CDEX-1B experiment using the profile likelihood ratio method, Phys. Rev. D 101, 052003 (2020).
  8. Z. Y. Zhang et al. (CDEX Collaboration), Constraints on sub-GeV dark matter–electron scattering from the CDEX-10 experiment, Phys. Rev. Lett. 129, 221301 (2022).
  9. I. Arnquist et al. (DAMIC-M Collaboration), First constraints from DAMIC-M on sub-GeV dark-matter particles interacting with electrons, Phys. Rev. Lett. 130, 171003 (2023).
  10. Q. Arnaud et al. (EDELWEISS Collaboration), First germanium-based constraints on sub-MeV dark matter with the EDELWEISS experiment, Phys. Rev. Lett. 125, 141301 (2020).
  11. P. Adari et al. (SENSEI Collaboration), First direct-detection results on sub-GeV dark matter using the SENSEI detector at SNOLAB, Phys. Rev. Lett. 134, 011804 (2025).
  12. T. Aralis et al. (SuperCDMS Collaboration), Constraints on dark photons and axionlike particles from the SuperCDMS Soudan experiment, Phys. Rev. D 101, 052008 (2020); 103, 039901(E) (2021).
  13. D. W. Amaral et al. (SuperCDMS Collaboration), Constraints on low-mass, relic dark matter candidates from a surface-operated SuperCDMS single-charge sensitive detector, Phys. Rev. D 102, 091101 (2020).
  14. A. Aguilar-Arevalo et al. (Oscura Collaboration), The Oscura experiment, arXiv:2202.10518.
  15. K. Aggarwal et al. (DAMIC-M Collaboration), Probing benchmark models of hidden-sector dark matter with DAMIC-M, arXiv:2503.14617.
  16. R. Essig, M. Fernandez-Serra, J. Mardon, A. Soto, T. Volansky, and T.-T. Yu, Direct detection of sub-GeV dark matter with semiconductor targets, J. High Energy Phys. 05 (2016) 046.
  17. R. Catena, T. Emken, N. A. Spaldin, and W. Tarantino, Atomic responses to general dark matter-electron interactions, Phys. Rev. Res. 2, 033195 (2020); 7, 019001(E) (2025).
  18. S. M. Griffin, K. Inzani, T. Trickle, Z. Zhang, and K. M. Zurek, Extended calculation of dark matter-electron scattering in crystal targets, Phys. Rev. D 104, 095015 (2021).
  19. T. Trickle, Extended calculation of electronic excitations for direct detection of dark matter, Phys. Rev. D 107, 035035 (2023).
  20. C. E. Dreyer, R. Essig, M. Fernandez-Serra, A. Singal, and C. Zhen, Fully ab-initio all-electron calculation of dark matter-electron scattering in crystals with evaluation of systematic uncertainties, Phys. Rev. D 109, 115008 (2024).
  21. G. Krnjaic, D. Rocha, and T. Trickle, The non-relativistic effective field theory of dark matter-electron interactions, J. High Energy Phys. 03 (2025) 165.
  22. J.-H. Liang, Y. Liao, X.-D. Ma, and H.-L. Wang, A systematic investigation on dark matter-electron scattering in effective field theories, J. High Energy Phys. 07 (2024) 279.
  23. R. Catena, D. Cole, T. Emken, M. Matas, N. Spaldin, W. Tarantino, and E. Urdshals, Dark matter-electron interactions in materials beyond the dark photon model, J. Cosmol. Astropart. Phys. 03 (2023) 052.
  24. R. Catena, T. Emken, M. Matas, N. A. Spaldin, and E. Urdshals, Crystal responses to general dark matter-electron interactions, Phys. Rev. Res. 3, 033149 (2021).
  25. Y. Hochberg, Y. Kahn, M. Lisanti, K. M. Zurek, A. G. Grushin, R. Ilan, S. M. Griffin, Z.-F. Liu, S. F. Weber, and J. B. Neaton, Detection of sub-MeV dark matter with three-dimensional Dirac materials, Phys. Rev. D 97, 015004 (2018).
  26. A. Coskuner, A. Mitridate, A. Olivares, and K. M. Zurek, Directional dark matter detection in anisotropic Dirac materials, Phys. Rev. D 103, 016006 (2021).
  27. R. M. Geilhufe, F. Kahlhoefer, and M. W. Winkler, Dirac materials for sub-MeV dark matter detection: New targets and improved formalism, Phys. Rev. D 101, 055005 (2020).
  28. K. Inzani, A. Faghaninia, and S. M. Griffin, Prediction of tunable spin-orbit gapped materials for dark matter detection, Phys. Rev. Res. 3, 013069 (2021).
  29. H.-Y. Chen, A. Mitridate, T. Trickle, Z. Zhang, M. Bernardi, and K. M. Zurek, Dark matter direct detection in materials with spin-orbit coupling, Phys. Rev. D 106, 015024 (2022).
  30. M. F. Albakry et al. (SuperCDMS Collaboration), A strategy for low-mass dark matter searches with cryogenic detectors in the SuperCDMS SNOLAB Facility, in Snowmass 2021 (2022), p. 3, arXiv:2203.08463.
  31. K. Schutz and K. M. Zurek, Detectability of light dark matter with superfluid helium, Phys. Rev. Lett. 117, 121302 (2016).
  32. S. Knapen, T. Lin, and K. M. Zurek, Light dark matter in superfluid helium: Detection with multi-excitation production, Phys. Rev. D 95, 056019 (2017).
  33. S. Knapen, T. Lin, M. Pyle, and K. M. Zurek, Detection of light dark matter with optical phonons in polar materials, Phys. Lett. B 785, 386 (2018).
  34. S. Griffin, S. Knapen, T. Lin, and K. M. Zurek, Directional detection of light dark matter with polar materials, Phys. Rev. D 98, 115034 (2018).
  35. T. Trickle, Z. Zhang, K. M. Zurek, K. Inzani, and S. M. Griffin, Multi-channel direct detection of light dark matter: Theoretical framework, J. High Energy Phys. 03 (2020) 036.
  36. B. Campbell-Deem, P. Cox, S. Knapen, T. Lin, and T. Melia, Multiphonon excitations from dark matter scattering in crystals, Phys. Rev. D 101, 036006 (2020); 102, 019904(E) (2020).
  37. P. Cox, T. Melia, and S. Rajendran, Dark matter phonon coupling, Phys. Rev. D 100, 055011 (2019).
  38. N. A. Kurinsky, T. C. Yu, Y. Hochberg, and B. Cabrera, Diamond detectors for direct detection of sub-GeV dark matter, Phys. Rev. D 99, 123005 (2019).
  39. S. M. Griffin, K. Inzani, T. Trickle, Z. Zhang, and K. M. Zurek, Multichannel direct detection of light dark matter: Target comparison, Phys. Rev. D 101, 055004 (2020).
  40. G. Baym, D. H. Beck, J. P. Filippini, C. J. Pethick, and J. Shelton, Searching for low mass dark matter via phonon creation in superfluid He4, Phys. Rev. D 102, 035014 (2020); 104, 019901(E) (2021).
  41. S. M. Griffin, Y. Hochberg, K. Inzani, N. Kurinsky, T. Lin, and T. Chin, Silicon carbide detectors for sub-GeV dark matter, Phys. Rev. D 103, 075002 (2021).
  42. A. Mitridate, T. Trickle, Z. Zhang, and K. M. Zurek, Detectability of axion dark matter with phonon polaritons and magnons, Phys. Rev. D 102, 095005 (2020).
  43. S. Knapen, J. Kozaczuk, and T. Lin, python package for dark matter scattering in dielectric targets, Phys. Rev. D 105, 015014 (2022).
  44. B. Campbell-Deem, S. Knapen, T. Lin, and E. Villarama, Dark matter direct detection from the single phonon to the nuclear recoil regime, Phys. Rev. D 106, 036019 (2022).
  45. N. Taufertshöfer, M. Garcia-Sciveres, and S. M. Griffin, Proposal for broad-range directional detection of light dark matter in cryogenic ice, Phys. Rev. D 110, 103552 (2024).
  46. T. Trickle, Z. Zhang, and K. M. Zurek, Detecting light dark matter with magnons, Phys. Rev. Lett. 124, 201801 (2020).
  47. S. Chigusa, T. Moroi, and K. Nakayama, Detecting light boson dark matter through conversion into a magnon, Phys. Rev. D 101, 096013 (2020).
  48. A. Esposito and S. Pavaskar, Optimal antiferromagnets for light dark matter detection, Phys. Rev. D 108, L011901 (2023).
  49. P. G. Catinari, A. Esposito, and S. Pavaskar, Hunting axion dark matter with anti-ferromagnets: A case study with nickel oxide, arXiv:2411.11971.
  50. G. Marocco and J. Wheater, Spin-dependent dark matter scattering in quasi-two-dimensional magnets, arXiv:2501.18120.
  51. G. B. Gelmini, V. Takhistov, and E. Vitagliano, Scalar direct detection: In-medium effects, Phys. Lett. B 809, 135779 (2020).
  52. T. Trickle, Z. Zhang, and K. M. Zurek, Effective field theory of dark matter direct detection with collective excitations, Phys. Rev. D 105, 015001 (2022).
  53. A. Mitridate, K. Pardo, T. Trickle, and K. M. Zurek, Effective field theory for dark matter absorption on single phonons, Phys. Rev. D 109, 015010 (2024).
  54. M. Pospelov, A. Ritz, and M. B. Voloshin, Bosonic super-WIMPs as keV-scale dark matter, Phys. Rev. D 78, 115012 (2008).
  55. H. An, M. Pospelov, and J. Pradler, Dark matter detectors as dark photon helioscopes, Phys. Rev. Lett. 111, 041302 (2013).
  56. H. An, M. Pospelov, J. Pradler, and A. Ritz, Direct detection constraints on dark photon dark matter, Phys. Lett. B 747, 331 (2015).
  57. Y. Hochberg, T. Lin, and K. M. Zurek, Detecting ultralight bosonic dark matter via absorption in superconductors, Phys. Rev. D 94, 015019 (2016).
  58. Y. Hochberg, T. Lin, and K. M. Zurek, Absorption of light dark matter in semiconductors, Phys. Rev. D 95, 023013 (2017).
  59. A. Mitridate, T. Trickle, Z. Zhang, and K. M. Zurek, Dark matter absorption via electronic excitations, J. High Energy Phys. 09 (2021) 123.
  60. Y. Hochberg, Y. Kahn, N. Kurinsky, B. V. Lehmann, T. C. Yu, and K. K. Berggren, Determining dark-matter–electron scattering rates from the dielectric function, Phys. Rev. Lett. 127, 151802 (2021).
  61. S. Knapen, J. Kozaczuk, and T. Lin, Dark matter-electron scattering in dielectrics, Phys. Rev. D 104, 015031 (2021).
  62. R. Catena and N. A. Spaldin, Linear response theory for light dark matter-electron scattering in materials, Phys. Rev. Res. 6, 033230 (2024).
  63. R. Essig, R. Plestid, and A. Singal, Collective excitations and low-energy ionization signatures of relativistic particles in silicon detectors, Commun. Phys. 7, 416 (2024).
  64. P. Ball, Neutron scattering reaps Nobel for physics, Nature (London) 371, 642 (1994).
  65. S. W. Lovesey, Theory of Neutron Scattering from Condensed Matter. Vol. 2. Polarization Effects and Magnetic Scattering, International Series of Monographs on Physics (Clarendon Press, New York, 1984).
  66. G. Squires, Introduction to the Theory of Thermal Neutron Scattering (Dover Publications, New York, 1996).
  67. A. Boothroyd, Principles of Neutron Scattering from Condensed Matter (OUP, Oxford, 2020).
  68. R. A. Ewings, J. R. Stewart et al., Upgrade to the MAPS neutron time-of-flight chopper spectrometer, Rev. Sci. Instrum. 90, 035110 (2019).
  69. P. Coleman, Introduction to Many-Body Physics (Cambridge University Press, Cambridge, England, 2015).
  70. A. Berlin, A. J. Millar, T. Trickle, and K. Zhou, Physical signatures of fermion-coupled axion dark matter, J. High Energy Phys. 05 (2024) 314.
  71. M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory (Addison-Wesley, Reading, USA, 1995).
  72. V. Cherepanov, I. Kolokolov, and V. L’vov, The saga of YIG: Spectra, thermodynamics, interaction and relaxation of magnons in a complex magnet, Phys. Rep. 229, 81 (1993).
  73. A. J. Princep, R. A. Ewings, S. Ward, S. Tóth, C. Dubs, D. Prabhakaran, and A. T. Boothroyd, The full magnon spectrum of yttrium iron garnet, npj Quantum Mater. 2, 63 (2017).
  74. MAPS technical information, https://www.isis.stfc.ac.uk/Pages/MAPS-technical-information.aspx (accessed: 2025-02-10).
  75. R. Ewings, A. Buts, M. Le, J. van Duijn, I. Bustinduy, and T. Perring, horace: Software for the analysis of data from single crystal spectroscopy experiments at time-of-flight neutron instruments, Nucl. Instrum. Methods Phys. Res., Sect. A 834, 132 (2016).
  76. O. Arnold, J. Bilheux et al., Mantid—Data analysis and visualization package for neutron scattering and μ SR experiments, Nucl. Instrum. Methods Phys. Res., Sect. A 764, 156 (2014).
  77. R. Ewings (private communication).
  78. ISIS Data Analysis as a Service, https://isis.analysis.stfc.ac.uk/.
  79. S. Toth and B. Lake, Linear spin wave theory for single-q incommensurate magnetic structures, J. Phys. Condens. Matter 27, 166002 (2015).
  80. J. H. Chang, R. Essig, and A. Reinert, Light(ly)-coupled dark matter in the keV range: Freeze-in and constraints, J. High Energy Phys. 03 (2021) 141.
  81. X. Chu, J.-L. Kuo, J. Pradler, and L. Semmelrock, Stellar probes of dark sector-photon interactions, Phys. Rev. D 100, 083002 (2019).
  82. J. Matthewman, P. Thompson, and P. Brown, The Cambridge crystallography subroutine library, Appl. Crystallogr. 15, 167 (1982).
  83. W. DeRocco, P. W. Graham, and S. Rajendran, Exploring the robustness of stellar cooling constraints on light particles, Phys. Rev. D 102, 075015 (2020).
  84. E. Masso and J. Redondo, Compatibility of CAST search with axion-like interpretation of PVLAS results, Phys. Rev. Lett. 97, 151802 (2006).
  85. F. Mezei, C. Pappas, and T. Gutberlet, Neutron Spin Echo Spectroscopy: Basics, Trends and Applications (Springer Science & Business Media, New York, 2002), Vol. 601.
  86. T. Keller, H. Trepka, K. Habicht, and B. Keimer, Neutron spin-echo instrumentation for magnetic scattering, Phys. Status Solidi (b) 259, 2100164 (2022).
  87. S. W. Lovesey, Magnetic photon scattering, J. Phys. C 20, 5625 (1987).
  88. L. J. P. Ament, M. van Veenendaal, T. P. Devereaux, J. P. Hill, and J. van den Brink, Resonant inelastic X-ray scattering studies of elementary excitations, Rev. Mod. Phys. 83, 705 (2011).
  89. M. W. Haverkort, Theory of resonant inelastic X-ray scattering by collective magnetic excitations, Phys. Rev. Lett. 105, 167404 (2010).
  90. R. Vollmer, M. Etzkorn, P. S. A. Kumar, H. Ibach, and J. Kirschner, Spin-polarized electron energy loss spectroscopy of high energy, large wave vector spin waves in ultrathin fcc Co films on Cu(001), Phys. Rev. Lett. 91, 147201 (2003).
  91. F. Roth, A. König, J. Fink, B. Büchner, and M. Knupfer, Electron energy-loss spectroscopy: A versatile tool for the investigations of plasmonic excitations, J. Electron Spectrosc. Relat. Phenom. 195, 85 (2014).
  92. C. Boyd, Y. Hochberg, Y. Kahn, E. D. Kramer, N. Kurinsky, B. V. Lehmann, and T. C. Yu, Directional detection of dark matter with anisotropic response functions, Phys. Rev. D 108, 015015 (2023).
  93. O. Krivanek, N. Dellby et al., Progress in ultrahigh energy resolution EELS, Ultramicroscopy 203, 60 (2019).
  94. M. Moretti Sala, K. Martel et al., A high-energy-resolution resonant inelastic x-ray scattering spectrometer at ID20 of the European Synchrotron Radiation Facility, J. Synchrotron Radiat. 25, 580 (2018).
  95. N. Brookes, F. Yakhou-Harris et al., The beamline ID32 at the ESRF for soft x-ray high energy resolution resonant inelastic x-ray scattering and polarisation dependent x-ray absorption spectroscopy, Nucl. Instrum. Methods Phys. Res., Sect. A 903, 175 (2018).
  96. K.-J. Zhou, A. Walters et al., I21: An advanced high-resolution resonant inelastic x-ray scattering beamline at Diamond Light Source, J. Synchrotron Radiat. 29, 563 (2022).
  97. A. Coskuner, T. Trickle, Z. Zhang, and K. M. Zurek, Directional detectability of dark matter with single phonon excitations: Target comparison, Phys. Rev. D 105, 015010 (2022).
  98. C. Stratman and T. Lin, Daily modulation of low-energy nuclear recoils from sub-GeV dark matter, Phys. Rev. D 111, 043030 (2025).
  99. R. Kubo, M. Toda, and N. Hashitsume, Statistical Physics II: Nonequilibrium Statistical Mechanics (Springer Science & Business Media, New York, 2012), Vol. 31.
  100. D. A. Tennant, C. Broholm, D. H. Reich, S. E. Nagler, G. E. Granroth, T. Barnes, K. Damle, G. Xu, Y. Chen, and B. C. Sales, Neutron scattering study of two-magnon states in the quantum magnet copper nitrate, Phys. Rev. B 67, 054414 (2003).
  101. T. Huberman, R. Coldea, R. A. Cowley, D. A. Tennant, R. L. Leheny, R. J. Christianson, and C. D. Frost, Two-magnon excitations observed by neutron scattering in the two-dimensional spin-52 heisenberg antiferromagnet rb2Mnf4, Phys. Rev. B 72, 014413 (2005).
  102. E. Chan, H. Lane et al., Neutron scattering sum rules, symmetric exchanges, and helicoidal magnetism in mnsb2o6, Phys. Rev. B 107, 144420 (2023).
  103. V. Sears, Electromagnetic neutron-atom interactions, Phys. Rep. 141, 281 (1986).
  104. S. F. Parker, D. Lennon, and P. W. Albers, Vibrational spectroscopy with neutrons: A review of new directions, Appl. Spectrosc. 65, 1325 (2011).

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Phys. Rev. D 112, 035021– Published 14 August, 2025
  • Received 28 April 2025
  • Accepted 17 July 2025
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