  A substantial energy gap of charge excitations induced by strong correlations
is the characteristic feature of Mott insulators. We study how the Mott gap is
affected by long-range antiferromagnetic order. Our key finding is that the
Mott gap is increased by the magnetic ordering: a magnetic blue-shift (MBS)
occurs. Thus, the effect is proportional to the exchange coupling in the
leading order in the Hubbard model. In systems with additional localized spins
the double-exchange mechanism induces an additional contribution to the MBS
which is proportional to the hopping in the leading order. The coupling between
spin and charge degrees of freedom bears the potential to enable spin-to-charge
conversion in Mott systems on extreme time scales determined by hopping and
exchange only, since a spin-orbit mediated transfer of angular momentum is not
involved in the process. In view of spintronic and magnonic applications, it is
highly promising to observe that several entire classes of compounds show
exchange and double-exchange effects. Exemplarily, we show that the magnetic
contribution to the band-gap blue-shift observed in the optical conductivity of
$\alpha$-MnTe is correctly interpreted as the MBS of a Mott gap.
