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Recent inelastic neutron scattering studies by Pan et al., NatureCommunications 8, 123 (2017), find evidence for spin excitations at energiesabove the quasi-particle gap in an iron-selenide high-Tc superconductor. Themomenta of the spin excitations form a diamond around the checkerboardwavevector, Q_AF, that is associated with the square lattice of iron atoms thatmakes up the system. It has been suggested that such a "hollowed-out"spin-excitation spectrum is due to hidden Neel order. We study such a hiddenspin-density wave (hSDW) state that results from nested Fermi surfaces at thecenter and at the corner of the unfolded Brillouin zone. It emerges within meanfield theory from an extended Hubbard model over a square lattice of iron atomsthat contain the minimal d_xz and d_yz orbitals. Opposing Neel order existsover the isotropic d+ = d_xz + i d_yz and d- = d_xz - i d_yz orbitals. Thedynamical spin susceptibility of the hSDW is computed within the random phaseapproximation, at perfect nesting. Unobservable Goldstone modes that disperseacoustically are found at Q_AF. A threshold is found in the spectrum ofobservable spin excitations that forms a "floating ring" at Q_AF also. The ringthreshold moves down in energy toward zero with increasing Hund's Rulecoupling, while it moves up in energy with increasing magnetic frustration.Comparison with the normal-state features of the spin-excitation spectrum shownby electron-doped iron selenide is made. Also, recent predictions of a Lifshitztransition from the nested Fermi surfaces to Fermi surface pockets at thecorner of the folded Brillouin zone will be discussed.

Spin Resonances in Iron-Selenide High-Tc Superconductors by Proximity to Hidden Spin Density Wave