  The optical properties of the layered magnet CrSBr are dominated by
intralayer excitons: the antiferromagnetic order between the layers makes
layer-to-layer charge hopping, and therefore interlayer excitons,
spin-forbidden. An external magnetic field, however, continuously drives the
magnetic order towards layer-to-layer ferromagnetic, which opens spin-allowed
charge-transfer channels between the layers. Here we elaborate how their
admixture changes the composition and nature of the excitons, leading to an
extension over many layers, and causes a quadratic red-shift with respect to
the external magnetic field. We address these effects by ab-initio $GW$-BSE
calculations as a function of magnetic field and cast the data into a minimal
four-band model to elucidate the interplay between the various interaction and
coupling mechanisms. Our findings should be generally valid for
antiferromagnetic layered magnets with and without external magnetic fields,
and moreover for any couple of layers with different spin directions. Our
insights help to systematically address excitons and predict their optical
signatures in such systems.
