Spin resonances in iron selenide high- Tc superconductors by proximity to a hidden spin density wave

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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.