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 $\mathrm{LaFeAs}\left({\mathrm{O}}_{1-x}{\mathrm{F}}_x\right)$, 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 $\vec{Q}=(0,\pi )$ or $(\pi ,0)$. 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 $\mathrm{O}\left(3\right)$ transition and an Ising transition with $z=3$ at larger doping.

Figure 1

(Color online) (a) The lattice structure at room temperature. The gray circles are Fe ions; the green (medium gray) and red (dark gray) circles are As ions above and below the Fe plane, respectively. The dashed square is the two-Fe unit cell. (b) The lattice structure between 150 and $134\mathrm{K}$ after the Ising order is developed: the thick lines represent the bonds between antiparallel aligned spins, but no uniform spin order is formed. The one-Fe unit cell is orthorhombic, but the two-Fe unit cell has a 3D monoclinic structure, as was seen in Ref. 10. (c) The $(0,\pi )$ spin order below $134\mathrm{K}$. (d) The global phase diagram as a function of temperature and doping $x$. The blue (light gray) curve represents the Ising transition, the red (dark gray) curve represents the $\mathrm{O}\left(3\right)$ transition.

Figure 2

(Color online) (a) The Brillouin zone for a one-Fe unit cell at zero doping. The thick blue (dark gray) circle denotes two almost overlaping hole pockets (Ref. 30), the red (light gray) dashed circle represents the electron pocket. The line that connects the electron and hole pockets is the $(\pi ,0)$ wave vector. (b) At finite doping, the electron pockets expand and the hole pockets shrink, so that the $(\pi ,0)$ vector can no longer connect points at the Fermi level. (c) Translation of the electron pocket by vector $(\pi ,0)$: If at zero doping there is a perfect overlap of the pockets, at infinitesimal doping there is no crossing between electron and hole Fermi level at all, i.e., an order with $(\pi ,0)$ wave vector cannot decay into a particle-hole pair.