RKKY interaction in the spin-density-wave phase of iron-based superconductors

Using the multiband model we analyze the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between the magnetic impurities in layered ferropnictide superconductors. In the normal state the interaction is spin isotropic and is dominated by the nesting features of the electron and hole bands separated by the antiferromagnetic (AF) momentum, ${\mathbf{Q}}_{AF}$. In the AF state the RKKY interaction maps into an effective anisotropic XXZ-type Heisenberg exchange model. The anisotropy originates from the breaking of the spin-rotational symmetry induced by the AF order and its strength depends on the size of the AF gap and the structure of the folded Fermi surface. We discuss our results in connection with recent experiments.

Figure 1

Schematic Fermi surface topology of iron-based superconductors in the unfolded Brillouin zone (BZ) with 1 Fe per unit cell containing circular hole pocket centered around the $\Gamma$ point and two electron pockets centered around the $(\pi ,0)$ and $(0,\pi )$ points, respectively.

Figure 2

The contour mesh of the RKKY interaction for the normal (a) and the SDW state for $J_x$ (b), and $J_z$ interaction (c). In the SDW state we employ $W=40$ meV, $\epsilon =0.5$, and $5\%$ of the electron doping.

Figure 3

The intraband [upper panel, (a) ${\mathcal{J}}_n^{11}$, (b) ${\mathcal{J}}_n^{22}$, (c) ${\mathcal{J}}_n^{33}$] and interband [lower panel (d) ${\mathcal{J}}_n^{12}$, (e) ${\mathcal{J}}_n^{13}$, and (f) ${\mathcal{J}}_n^{23}$] contributions to the RKKY interaction in the normal state for $\epsilon =0.5$ and $5\%$ of the electron doping.

Figure 4

The intraband [upper panel (a) ${\mathcal{J}}_x^{11}$, (b) ${\mathcal{J}}_x^{22}$, (c) ${\mathcal{J}}_x^{33}$] and interband [lower panel (d) ${\mathcal{J}}_x^{12}$, (e) ${\mathcal{J}}_x^{13}$, and (f) ${\mathcal{J}}_x^{23}$] contributions to the RKKY interaction, $J^x$ in SDW state, $x$ direction for $W=40$ meV, $\epsilon =0.5$, and $5\%$ of the electron doping.

Figure 5

Oscillatory behavior of the RKKY interaction along the $x$ direction in the normal ($J_n$) and SDW ($J_x$ and $J_z$) states.

Figure 6

$J_x$ and $J_z$ components of the XXZ RKKY interaction in the SDW state along two crystallographic directions. As per the previous figures, we employ $W=40$ meV, $\epsilon =0.5$, and $5\%$ electron doping.

Figure 7

The effect of the ellipticity on the modified XXZ Heisenberg-type RKKY interaction in the SDW state $J_x$ along the $\left(100\right)$ (a) and $\left(010\right)$ (b) crystallographic directions, respectively.

Figure 8

Influence of the SDW gap magnitude on the RKKY interaction parameter $J_z$ for $\left(100\right)$ direction (a) and for $\left(010\right)$ direction (b).