Strong Correlations and Magnetic Frustration in the High $T_c$ Iron Pnictides

We consider the iron pnictides in terms of a proximity to a Mott insulator. The superexchange interactions contain competing nearest-neighbor and next-nearest-neighbor components. In the undoped parent compound, these frustrated interactions lead to a two-sublattice collinear antiferromagnet (each sublattice forming a Néel ordering), with a reduced magnitude for the ordered moment. Electron or hole doping, together with the frustration effect, suppresses the magnetic ordering and allows a superconducting state. The exchange interactions favor a $d$-wave superconducting order parameter; in the notation appropriate for the Fe square lattice, its orbital symmetry is $d_{xy}$. A number of existing and future experiments are discussed in light of the theoretical considerations.

Figure 1

Placing LaOFeAs and LaOFeP in terms of the control parameter $U/W$, where $U$ is the on-site Coulomb interaction and $W$ the effective bandwidth.

Figure 2

(a) Spin-2 states relevant for the undoped LaOFeAs. The crystal levels are according to Ref. 12. The $x$ and $y$ we use differ from the standard notation, adopted there, by a rotation of 45°; see the main text. (b) Spin-$3/2$ states that become important when electron doping is introduced into the FeAs layer. Hole doping will lead to the analogous spin-$3/2$ states, corresponding to five electrons residing on the $3d$ orbitals.

Figure 3

(a) The dominant superexchange interactions are those between both a pair of nearest-neighbor Fe spins ($J_1$) and a pair of next-nearest-neighbor Fe spins ($J_2$). (b) The process contributing to the NNN superexchange interaction between a pair of $3d_{x^2-y^2}$ electrons. It involves the same $4p_{x-y}$ orbital, leading to an antiferromagnetic $J_2$. (c) The process contributing to the NN superexchange interaction between a pair of $3d_{x^2-y^2}$ electrons. It involves two orthogonal $4p$ orbitals, leading to a ferromagnetic $J_1$.

Figure 4

A square plaquette showing a spin arrangement of the two-sublattice collinear antiferromagnet.