  Recent inelastic neutron scattering studies by Pan et al., Nature
Communications 8, 123 (2017), find evidence for spin excitations at energies
above the quasi-particle gap in an iron-selenide high-Tc superconductor. The
momenta of the spin excitations form a diamond around the checkerboard
wavevector, Q_AF, that is associated with the square lattice of iron atoms that
makes 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 hidden
spin-density wave (hSDW) state that results from nested Fermi surfaces at the
center and at the corner of the unfolded Brillouin zone. It emerges within mean
field theory from an extended Hubbard model over a square lattice of iron atoms
that contain the minimal d_xz and d_yz orbitals. Opposing Neel order exists
over the isotropic d+ = d_xz + i d_yz and d- = d_xz - i d_yz orbitals. The
dynamical spin susceptibility of the hSDW is computed within the random phase
approximation, at perfect nesting. Unobservable Goldstone modes that disperse
acoustically are found at Q_AF. A threshold is found in the spectrum of
observable spin excitations that forms a "floating ring" at Q_AF also. The ring
threshold moves down in energy toward zero with increasing Hund's Rule
coupling, while it moves up in energy with increasing magnetic frustration.
Comparison with the normal-state features of the spin-excitation spectrum shown
by electron-doped iron selenide is made. Also, recent predictions of a Lifshitz
transition from the nested Fermi surfaces to Fermi surface pockets at the
corner of the folded Brillouin zone will be discussed.
