Two Energy Scales in the Magnetic Resonance Spectrum of Electron and Hole Doped Pnictide Superconductors

We argue that a multiband superconductor with sign-changing gaps may have multiple spin resonances. We calculate the RPA-based spin resonance spectra of a pnictide superconductor by using the five-band tight-binding model or angle-resolved photoemission spectroscopy Fermi surface (FS) and experimental values of superconducting gaps. The resonance spectra split in both energy and momenta due to the effects of multiband and multiple gaps in s(+/-) pairing; the higher energy peak appears around the commensurate momenta due to scattering between alpha-FS to gamma/delta-FS pockets. The second resonance is incommensurate, coming from beta-FS to gamma/delta-FS scatterings, and its q vector is doping-dependent and, hence, on the FS topology. Energies of both resonances omega(1,2)(res) are strongly doping-dependent and are proportional to the gap amplitudes at the contributing FSs.