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 $\tilde\Delta$ 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 $\tilde\Delta = \Delta_L + \Delta_S$ or $\tilde\Delta = 2\Delta_L$. In the $s_{++}$ state, spin excitations below $\tilde\Delta$ are absent unless additional scattering mechanisms are assumed. The spin resonance appears in the $s_\pm$ superconducting state at frequency $\omega_R \leq \tilde\Delta$. 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.