Origin of longitudinal spin excitations in iron-pnictide parent compounds

We investigate longitudinal spin excitations (LSEs) as a probe of microscopic origin of magnetic ordering in parent pnictides BaFe2As2 and NaFeAs. Currently adopted interpretation of LSEs as bottom of particle-hole continuum points unambiguously toward itinerant-electron magnetism, but is difficult to reconcile with available optical measurements. We study the possibility that the LSEs originate from multi-magnon processes which are not energetically constrained by optical spectroscopy and do not sharply distinguish between local-moment and itinerant scenarios. Two mechanisms, capable of enhancing multi-magnon continuum to the level indicated by neutron scattering experiments, are proposed. The first emphasizes itinerant electrons and is based on electronic transitions between magnetically split bands, while the other relies on purely spin fluctuations close to a magnetic quantum phase transition. Electronic excitations enhance multi-magnon contribution to LSEs for small Fermi surface taking part in the SDW instability, but are insufficient to account for measured intensities. The correct order of LSEs, on the other hand, can be reproduced by the spin fluctuation mechanism for a reasonable set of parameters