Magnetic excitations in ferropnictide materials controlled by a quantum critical point into hidden order

Abstract

The two-orbital ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ 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 $4\ifmmode\times\else\texttimes\fi{}4$ 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 wave numbers that correspond to cSDW order. These disperse anisotropically. A fit to the magnetic excitation spectrum of ferropnictide materials obtained recently by inelastic neutron-scattering measurements notably accounts for the absence of softening at the wave number that corresponds to N\'eel order.