Transfer of optical spectral weight in magnetically ordered superconductors

We show that, in antiferromagnetic superconductors, the optical spectral weight transferred to low frequencies below the superconducting transition temperature originates from energies that can be much larger than twice the superconducting gap Δ. This contrasts to nonmagnetic superconductors, where the optical spectrum is suppressed only for frequencies below 2Δ. In particular, we demonstrate that the superfluid condensate of the magnetically ordered superconductor is not only due to states of the magnetically reconstructed Fermi surface but is enhanced by transfer of spectral weight from the mid-infrared peak generated by the spin-density wave gap. We apply our results to the iron arsenide superconductors, addressing the decrease in the zero-temperature superfluid density in the doping regime where magnetism coexists with unconventional superconductivity.