  Iodine is distinguished from other elements used in dark matter direct
detection experiments both by its large mass as well as its large magnetic
moment. Inelastic dark matter utilizes the large mass of iodine to allay
tensions between the DAMA annual modulation signature and the null results from
other experiments. We explore models of inelastic dark matter that also take
advantage of the second distinct property of iodine, namely its large magnetic
moment. In such models the couplings are augmented by magnetic, rather than
merely electric, interactions. These models provide simple examples where the
DAMA signal is compatible with all existing limits. We consider dipole moments
for the WIMP, through conventional magnetism as well as "dark" magnetism,
including both magnetic-magnetic and magnetic-electric scattering. We find
XENON100 and CRESST should generically see a signal, although suppressed
compared with electric inelastic dark matter models, while KIMS should see a
modulated signal comparable to or larger than that of DAMA. In a large portion
of parameter space, de-excitation occurs promptly, producing a ~ 100 keV photon
inside large xenon experiments alongside the nuclear recoil. This effect could
be searched for, but if not properly considered may cause nuclear recoil events
to fail standard cuts.
