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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, $Δ_L$ and $Δ_S$, 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 $\tildeΔ$ 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 $\tildeΔ= Δ_L + Δ_S$ or $\tildeΔ= 2Δ_L$. In the $s_{++}$ state, spin excitations below $\tildeΔ$ are absent unless additional scattering mechanisms are assumed. The spin resonance appears in the $s_\pm$ superconducting state at frequency $ω_R \leq \tildeΔ$. 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.