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A neutral dark matter (DM) particle with a magnetic dipole moment has a verydifferent direct detection phenomenology with respect to standard candidates.This is due to the peculiar functional form of the differential cross sectionfor scattering with nuclei. Such a candidate could be a bound state of chargedparticles, as the neutron or an atom, or a fundamental particle coupled toheavier charged states, much like a Dirac neutrino. We analyze here the directdetection signals of DM with magnetic dipole moment, both the recoil rate andits modulation, and show that they are very different from those expected instandard scenarios. For this candidate, contrary to the common lore, the timeof maximum signal depends on the recoil energy as well as on the targetmaterial. The observation of different modulations by experiments employingdifferent targets would be a strong indication in favor of this type of DMparticles.

Direct detection signals of dark matter with magnetic dipole moment