Spin resonance peak in Fe-based superconductors with unequal gaps

We study the spin resonance in superconducting state of iron-based materials within multiband models with two unequal gaps, $Delta_L$ and $Delta_S$, on different Fermi surface pockets. We show that due to the indirect nature of the gap entering the spin susceptibility at the nesting wave vector $mathbf{Q}$ the total gap $tildeDelta$ in the bare susceptibility is determined by the sum of gaps on two different Fermi surface sheets connected by $mathbf{Q}$. For the Fermi surface geometry characteristic to the most of iron pnictides and chalcogenides, the indirect gap is either $tildeDelta = Delta_L + Delta_S$ or $tildeDelta = 2Delta_L$. In the $s_{++}$ state, spin excitations below $tildeDelta$ are absent unless additional scattering mechanisms are assumed. The spin resonance appears in the $s_pm$ superconducting state at frequency $omega_R leq tildeDelta$. Comparison with available inelastic neutron scattering data confirms that what is seen is the true spin resonance and not a peak inherent to the $s_{++}$ state.