We study the spin resonance in the superconducting state of iron-based materials within multiband models with two unequal gaps, ${\mathrm{\Delta }}_L$ and ${\mathrm{\Delta }}_S$, 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 $\tilde{\mathrm{\Delta }}$ 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 of most iron pnictides and chalcogenides, the indirect gap is either $\tilde{\mathrm{\Delta }}={\mathrm{\Delta }}_L+{\mathrm{\Delta }}_S$ or $\tilde{\mathrm{\Delta }}=2{\mathrm{\Delta }}_L$. In the $s_{++}$ state, spin excitations below $\tilde{\mathrm{\Delta }}$ are absent unless additional scattering mechanisms are assumed. The spin resonance appears in the $s_{\pm }$ superconducting state at frequency ${\omega }_R\le \tilde{\mathrm{\Delta }}$. 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.

• Received 31 July 2016
• Revised 7 September 2016

DOI:https://doi.org/10.1103/PhysRevB.94.094517