Longitudinal (Higgs) Modes of Spin Fluctuations in Iron-based Superconductors

Iron-based superconductors can exhibit different magnetic orders and are in a critical magnetic region where frustrated magnetic interactions strongly compete with each other. The order parameters can fluctuate transversely as gapless Goldstone modes and longitudinally as gapped Higgs modes. Here we investigate the Higgs modes of spin fluctuations in the unified effective J₁-J₂-J₃-K model for iron-based superconductors. In this work, the Higgs modes are viewed as two-magnon resonance from the linear spin wave approach for the local spin exchange model. We focus on the collinear antiferromagnetic order and calculate the longitudinal modes when different phase boundaries are approached. We compare it with the observed longitudinal gap in CaFe₂As₂, which was looked as the support for the itinerant picture. This is a systematic method to explore the longitudinal excitations in the local spin exchange model and we can easily extend it in three dimensions.