  Motivated by recent experiments on Mott insulators, in both iridates and
ultracold atoms, we theoretically study the effects of magnetic order on the
Mott-Hubbard excitons. In particular, we focus on spin-mediated doublon-holon
pairing in Hubbard materials. We use several complementary theoretical
techniques: mean-field theory to describe the spin degrees of freedom, the
self-consistent Born approximation to characterize individual charge
excitations across the Hubbard gap, and the Bethe-Salpeter equation to identify
bound states of doublons and holons. The binding energy of the Hubbard exciton
is found to increase with increasing the N{\'e}el order parameter, while the
exciton mass decreases. We observe that these trends rely significantly on the
retardation of the effective interaction, and require consideration of multiple
effects from changing the magnetic order. Our results are consistent with the
key qualitative trends observed in recent experiments on iridates. Moreover,
the findings could have direct implications on ultracold atom Mott insulators,
where the Hubbard model is the exact description of the system and the
microscopic degrees of freedom can be directly accessed.
