Magnetic excitations in ferro-pnictide materials controlled by a quantum critical point into hidden order J.P. Rodriguez 1 $^{1}$Department of Physics and Astronomy, California State University, Los Angeles, California 90032 (Dated: June 6, 2018) The two-orbital J $_{1}$- J 2 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 4 × 4 cluster. A quantum critical point (QCP) is identified that separates hidden magnetic order at weak Hund’s rule coupling from a commensurate spin 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 N´ eel order. Abstract arXiv:1002.0891v3 [cond-mat.supr-con] 12 Jul 2010 1