Magnetic degeneracy and hidden metallicity of the spin-density-wave state in ferropnictides

We analyze spin-density-wave (SDW) order in iron-based superconductors and electronic structure in the SDW phase. We consider an itinerant model for Fe pnictides with two hole bands centered at (0,0) and two electron bands centered at $\left(0,\pi \right)$ and $\left(\pi ,0\right)$ in the unfolded Brillouin zone. A SDW order in such a model is generally a combination of two components with momenta $\left(0,\pi \right)$ and $\left(\pi ,0\right)$, both yield $\left(\pi ,\pi \right)$ order in the folded zone. Neutron experiments, however, indicate that only one component is present. We show that $\left(0,\pi \right)$ or $\left(\pi ,0\right)$ order is selected if we assume that only one hole band is involved in the SDW mixing with electron bands. A SDW order in such three-band model is highly degenerate for a perfect nesting and hole-electron interaction only but we show that ellipticity of electron pockets and interactions between electron bands break the degeneracy and favor the desired $\left(0,\pi \right)$ or $\left(\pi ,0\right)$ order. We further show that stripe-ordered system remains a metal for arbitrary coupling. We analyze electronic structure for parameters relevant to the pnictides and argue that the resulting electronic structure is in good agreement with angle-resolved photoemission experiments. We discuss the differences between our model and $J_1\text{−}{J}_2$ model of localized spins.

Figure 1

(Color online) Fermi surface of ferropnictides in the unfolded BZ consisting of two hole pockets centered around the $\Gamma$ point and two electron pockets centered around $\left(\pi ,0\right)$ and $\left(0,\pi \right)$ points, respectively. The wave vectors ${\mathbf{Q}}_1$ and ${\mathbf{Q}}_2$ are two degenerate nesting wave vectors.

Figure 2

(Color online) Various SDW spin configurations described by ${\vec{\Delta }}_1{e}^{i{\mathbf{Q}}_{1}R}+{\vec{\Delta }}_2{e}^{i{\mathbf{Q}}_{2}R}$. For the model of Eq. (2), only ${\vec{\Delta }}_1^2+{\vec{\Delta }}_2^2$ is fixed. Panel (a) ${\vec{\Delta }}_1=0$, panel (b) ${\vec{\Delta }}_2=0$, panel (c) ${\vec{\Delta }}_1\perp {\vec{\Delta }}_2$, and panel (d) ${\vec{\Delta }}_1={\vec{\Delta }}_2$.

Figure 3

(Color online) Energy dispersions in the SDW state for full nesting: (a) one-electron band and one hole band and (b) one-electron band and two hole bands. Dashed lines in (a) are the dispersions without SDW order.

Figure 4

(Color online) The changes to the magnetic structure introduced by the weak SDW coupling ${\vec{\Delta }}_2$ between the second hole band and the electron bands. Panels (a) and (b) are for the FS topology of the pnictides, panels (c) and (d) are for the FS topology of $t^{\prime }\text{−}t$ model for $t⪡t^{\prime }$.

Figure 5

(Color online) The FS for the tight-binding model ${\epsilon }_{\mathbf{p}}=4t^{\prime }\text{cos}{p}_x\text{cos}{p}_y+2t\left(\text{cos}{p}_x+\text{cos}{p}_y\right)$ for $t=0$ (squares) and $t=0.5t^{\prime }$ (curves). $h$ and $e$ refer to the hole and electron states occupying the corresponding parts of the BZ. Observe that the hole bands are now centered at (0,0) and $\left(\pi ,\pi \right)$.

Figure 6

(Color online) Calculated image of the electronic structure in the folded BZ in the SDW phase. Left panel—near $\Gamma =\left(0,0\right)$ and right panel—near $M=\left(\pi ,\pi \right)$. In figures (a) and (b) we show the dispersion, in figures (c) and (d) the spectral function $\text{Im}G\left(\mathbf{k},\omega \right)={\sum }_i\text{Im}{G}_i$, and in figures (e) and (f) ARPES intensity, i.e., the product $\text{Im}G\left(\mathbf{k},\omega \right)\times n_f\left(E_{\mathbf{k}}\right)$. The direction of momenta in all figures is along $k_x=k_y$ in the folded BZ. We directed SDW order parameter along $z$ axis and set ${\Delta }_1^z\ne 0$, ${\Delta }_2={\Delta }_3={\Delta }_4=0$ [$\left(0,\pi \right)$ order]. For definiteness we set ${\Delta }_1^z=\mu /4$, ${\mu }_1=\left(3/2\right)\mu$, ${\mu }_2=\left(3/2\right)\mu$, and $m_1=m_2=m_y=2m_x=1$. For numerical purposes we added the small damping constant $\delta =0.04\mu$.

Figure 7

(Color online) Same as in Fig. 6 but for a multidomain sample with equal distribution of the domains with $\left(\pi ,0\right)$ and $\left(0,\pi \right)$ SDW orders.