I. INTRODUCTION The discovery of ferro-pnictide superconductors has set a new and unforseen direction in the search for high-temperature superconductivity. 1 A common structural feature of these materials are square lattices of iron atoms that are stacked up on top of each other. 2 Density functional theory (DFT) calculations find that the iron 3d orbitals contribute most of the electronic spectral weight near the Fermi surface. 3 , 4 This implies that the iron 3 d electrons surprisingly play an active role in the superconductivity. In contrast, DFT calculations also predict that the iron moments order antiferromagnetically along the a and along the c axes of the iron lattice at low temperature in the undoped parent compounds, 5 with an ordered moment of approximately 2 Bohr magnetons ( µ$_{B}$ ). 6 Elastic neutron diffraction studies have confirmed the prediction of long-range commensurate spin-density wave (cSDW) order, but they find a much lower ordered moment that can be a small fraction of the Bohr magneton (0 . 36 µ$_{B}$ ) in some cases. 2 It was suggested early on that Heisenberg exchange between both nearest-neighbor ( J$_{1}$ ) and next-nearest neighbor ( J$_{2}$ ) spins on a square lattice of iron atoms could account for the low ordered moment that is observed because of magnetic frustration. 7 Recent calculations based on the linear spin-wave approximation 8 indicate that this effect requires fine tuning however, 9 and that it occurs only very close to the point of maximum frustration, J$_{2}$ = 0 . 5 J$_{1}$ . A possibly more viable explanation is that the low ordered cSDW moment commonly observed in ferro-pnictide parent compounds is due to proximity to hidden magnetic order among particular iron 3 d orbitals such that the magnetic moments cancel out per iron atom. The author and Rezayi have shown that such violations of Hund’s rule can occur in multi-orbital Heisenberg models with off-diagonal frustration. 10 Spin-wave excitations of the cSDW groundstate have also been detected in parent compounds to ferro-pnictide superconductors at low temperature by inelastic neutron scattering. 11 , 12 Contrary to the prediction of the conventional J$_{1}$ - J$_{2}$ model over the square lattice however, 13 the measured spin-wave spectrum fails to soften at the wave number as- sociated with N´ eel order, ( π/a, π/a ). Here a denotes the square lattice constant. It shows a local maximum there instead. 14 Fits to the measured spin-wave dispersion invoke unphysi- cally large anisotropy in the Heisenberg spin exchange across nearest-neighbor links on the square lattice of iron atoms in order to account for the dispersion at the Brillouin zone boundary. More recently, low-energy magnetic excitations centered at the cSDW wave num- 2