Theory of electron nematic order in LaFeAsO

We study a spin $S$ quantum Heisenberg model on the Fe lattice of the rare-earth oxypnictide superconductors. Using both large $S$ and large $N$ methods, we show that this model exhibits a sequence of two phase transitions: from a high-temperature symmetric phase to a narrow region of intermediate “nematic” phase, and then to a low-temperature spin ordered phase. Identifying phases by their broken symmetries, these phases correspond precisely to the sequence of structural (tetragonal to monoclinic) and magnetic transitions that have been recently revealed in neutron-scattering studies of LaFeAsO. The structural transition can thus be identified with the existence of incipient (“fluctuating”) magnetic order.

Figure 1

(Color online) Schematic graph for the proposed model with nearest-neighbor coupling $J_1$, next-nearest-neighbor coupling $J_2$ and interlayer coupling $J_z$. The orientation of the spins in the low-temperature phase are drawn according to Ref. 11. Note that we use coordinate system with axis $x$, $y$, and $z$ in the current study, which is $45°$ rotated along the $c=z$ direction from the realistic crystal axis $a$, $b$, and $c$.

Figure 2

(Color online) $T_{\mathcal{N}}$ and $T_{\text{SDW}}$ as the function of ${\tilde{J}}_z$ for ${\tilde{J}}_2=2{\tilde{J}}_1$, $N=3$, and $S=1$.

Figure 3

$\frac{T_{\mathcal{N}}-T_{\text{SDW}}}{T_{\text{SDW}}}$ as the function of ${\tilde{J}}_z$ for ${\tilde{J}}_2=2{\tilde{J}}_1$, $N=3$, and $S=1$.