Directional detection is the dedicated strategy to
demonstrate that DM-like signals measured by direct detectors are
indeed produced by DM particles from the galactic halo. The
experimental challenge of measuring the direction of DM-induced
nuclear recoils with (sub-)millimeter tracks has limited, so far,
the maximal directional reach to DM masses around
100 GeV. In this paper, we expose the MIMAC detector to
three different neutron fields and we develop a method to
reconstruct the direction of the neutron-induced nuclear recoils. We
measure an angular resolution better than 16° for proton
recoils down to a kinetic energy of 4 keV and for carbon
recoils down to a kinetic energy of 5.5 keV. For the
first time, a detector achieves the directional measurement of
proton and carbon recoils with kinetic energies in the keV range
without any restriction on the direction of the incoming
particle. This work demonstrates that directional detection is
around the corner for probing DM with masses down to
𝒪(1 GeV).