Effect of nodes, ellipticity, and impurities on the spin resonance in iron-based superconductors

We analyze doping dependence of the spin resonance of an s ^± superconductor and its sensitivity to the ellipticity of electron pockets, to magnetic and nonmagnetic impurities, and to the angle dependence of the superconducting gap along electron Fermi surfaces. We show that the maximum intensity of the resonance shifts from commensurate to incommensurate momentum above some critical doping which decreases with increasing ellipticity. Angle dependence of the gap and particularly the presence of accidental nodes lowers the overall intensity of the resonance peak and shifts its position toward the onset of the particle-hole continuum. Still, however, the resonance remains a true δ function in the clean limit. When nonmagnetic or magnetic impurities are present, the resonance broadens and its position shifts. The shift depends on the type of impurities and on the ratio of intraband and interband scattering components. The ratio Ω_res/ T_c increases almost linearly with the strength of the interband impurity scattering, in agreement with the experimental data. We also compare spin response of s^± and s⁺⁺ superconductors. We show that there is no resonance for s^{+ +} gap, even when there is a finite mismatch between electron and hole Fermi surfaces shifted by the antiferromagnetic momentum.