  We derive exciton-spin interactions from a microscopic correlated model that
captures important aspects of the physics of charge-transfer (CT) insulators to
address magnetism associated with exciton creation. We present a minimal model
consisting of coupled clusters of transition metal d and ligand p orbitals that
captures the essential features of the local atomic and electronic structure.
First, we identify the lowest-energy state and optically allowed excited states
within a cluster by applying the molecular orbital picture to the ligand p
orbitals. Then, we derive the effective interactions between two clusters
mediated by intercluster hoppings, which include exciton-spin couplings. The
interplay of the correlations and the spatial structure of the CT exciton leads
to strong magnetic exchange couplings with spatial anisotropy. Finally, we
calculate an optical excitation spectrum in our effective model to obtain
insights into magnetic sidebands optically observed in magnetic materials. We
demonstrate that the spin-flip excitation due to the strongly enhanced local
spin interactions around the exciton gives rise to the magnetic sidebands.
