Magnetic excitations in ferro-pnictide materials controlled by a quantum critical point into hidden order

The two-orbital J1-J2 model that describes a square lattice of frustrated spin-1 iron atoms is analyzed within the linear spin-wave approximation and by exact diagonalization over a 4x4 cluster. A quantum critical point (QCP) is identified that separates hidden magnetic order at weak Hund's rule coupling from a commensurate spins density wave (cSDW) at strong Hund's rule coupling. Although the moment for cSDW order is small at the QCP, the critical linear spin-wave spectrum shows strong low-energy excitations centered at the wavenumbers that correspond to cSDW order. These disperse anisotropically. A fit to the magnetic excitation spectrum of ferro-pnictide materials obtained recently by inelastic neutron scattering measurements notably accounts for the absence of softening at the wavenumber that corresponds to Neel order.