High-intensity neutron beams, such as those available at the European Spallation Source (ESS), provide new opportunities for fundamental discoveries. Here, we discuss a novel Ramsey neutron-beam experiment to search for ultralight axion dark matter through its coupling to neutron spins, which would cause the neutron spins to rotate about the velocity of the neutrons relative to the dark matter halo. We estimate that experiments at the HIBEAM beamline with a 50m free flight path at the ESS can improve the sensitivity to the axion-neutron coupling compared to the current best laboratory limits by up to 2-3 orders of magnitude over the axion mass range 10^{-22} eV-10^{-16} eV.
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