Theory of the excitonic spin-density-wave state in iron pnictides

We examine the appearance of a spin-density wave in the FeAs parent compounds due to an excitonic instability. Using a realistic four-band model, we show that the magnetic state depends very sensitively on the details of the band structure. We demonstrate that an orthorhombic distortion of the crystal enhances the stability of the antiferromagnetic order.

Figure 1

(Color online) (a) Fermi surface with nesting vector $\mathbf{Q}$ at filling $n_{\text{el}}=4$ and (b) dispersion of the electron and hole bands in the physical Brillouin zone. (c) Fermi surface in the unfolded Brillouin zone, showing orthogonal nesting vectors ${\mathbf{Q}}_1$ and ${\mathbf{Q}}_2$. The dashed square is the physical Brillouin zone. $\tilde{a}=a/\sqrt{2}$ is the nearest-neighbor Fe-Fe distance. (d) Variation of the excitonic gaps with temperature at $n_{\text{el}}=4$.

Figure 2

(Color online) (a) Electron Fermi surfaces at $\delta t=0.2$ (thick lines) compared to $\delta t=0$ (thin lines). (b) Variation of ${\Delta }_{eh}$ with $\delta t$ at $T=1\text{K}$. (c) Variation of ${\Delta }_{e,1}$ with $\delta t$ at various temperatures. In (b) and (c) shading beneath the curve indicates a single-$\mathbf{Q}$ solution.

Figure 3

(Color online) (a) Hole Fermi surfaces at $\delta h=0.05\text{eV}$ (thick lines) compared to $\delta h=0$ (thin lines) at $n_{e\text{l}}=4$. (b) Dependence of the critical temperature $T_{\text{SDW}}$ of the excitonic phases on electron filling $n_{\text{el}}$ for different values of $\delta h$. (c) Variation of the ${\Delta }_{eh}$ with $n_{e\text{l}}$ at $T=1\text{K}$ and $\delta h=0$. (d) Same as (c) but for $\delta h=0.05\text{eV}$.

Figure 4

(Color online) (a) Electron Fermi surface pockets at $\delta ϵ=0.04\text{eV}$ (thick lines) compared to $\delta ϵ=0$ (thin lines). (b) Dependence of the ${\Delta }_{eh}$ on $\delta ϵ$ at $T=1\text{K}$. (c) Same as for (b) but at $T=40\text{K}$. (d) Difference $\Delta F=F-F_0$ per site between the free energy $F$ and its value in the normal state $F_0$ at $\delta ϵ=0$.