Theory of optical absorption by a localized carrier in an antiferromagnetic insulator

We calculate the optical absorption of a spin-1/2 carrier bound to a defect site in an insulating antiferromagnet. We show that when the defect potential is symmetric under interchange of the antiferromagnetic sublattices (as is believed to be the case in most doped high-${\mathit{T}}_{\mathit{c}}$ parent compounds) the interaction of the carrier with the antiferromagnetic background leads to a low-frequency absorption feature near the zone-boundary magnon energy. This feature, however, is not consistent in peak position or total oscillator strength with the low-frequency absorption feature observed in lightly doped high-${\mathit{T}}_{\mathit{c}}$ parent compounds. We suggest the observed feature is due to electron-phonon coupling.