Ising and spin orders in the iron-based superconductors

Motivated by recent neutron scattering experiments, we study the ordering of spins in the iron-based superconductors $mathrm{LaFeAs}({mathrm{O}}_{1ensuremath{-}x}{mathrm{F}}_{x})$, assuming them in proximity to a Mott insulator in the phase diagram. The ground state of the parent system with $x=0$ is a spin-density wave with ordering wave vector $stackrel{Pvec}{Q}=(0,ensuremath{pi})$ or $(ensuremath{pi},0)$. Upon raising the temperature, we find that the system restores SU(2) symmetry, while an Ising symmetry remains broken, explaining the experimentally observed lattice distortion to a monoclinic crystal structure. Upon further temperature increase, the spins finally disorder at a second transition. The phase transition driven by doping with charge carriers similarly splits into an $mathrm{O}(3)$ transition and an Ising transition with $z=3$ at larger doping.