  The sole static electromagnetic property of a spin-$\frac{1}{2}$ Majorana
fermion is its anapole moment. Though they cannot couple to single real
photons, these particles can interact with electric currents through virtual
photons. If a Majorana fermion is immersed in a background current, there is an
energy difference between the spin states of the fermion; the higher energy
state has its anapole moment antialigned with the current. In this paper, we
address the ability of a system of initially unpolarized Majorana fermions to
achieve some degree of polarization relative to a static background current. In
considering processes that allow the Majorana fermion's spin to flip to the
lower-energy state, we focus upon two irreversible processes: the spontaneous
emission of two real photons and the emission of a single real photon emitted
in virtual Compton scattering. Both of these processes involve coupling to
photons via the fermion's polarizaibilities. We compute the spin-flip
transition rates for these processes using a low-energy expansion of the
Hamiltonian and construct a toy model to showcase how these rates depend upon
the underlying parameters within a model. Applying these ideas to a thermal
dark matter (DM) model, we find that when the DM thermally decouples from the
Standard Model plasma in the early universe, two-photon emission is negligible
but partial polarization for the DM medium can proceed via virtual Compton
scattering if sufficient currents exist.
