  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 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 $10^{-22} \, \textrm{eV} - 10^{-16}$ eV.
