Incommensurate Spin Fluctuations in Hole-Overdoped Superconductor ${\mathrm{KFe}}_2{\mathrm{As}}_2$

A neutron scattering study of heavily hole-overdoped superconducting ${\mathrm{KFe}}_2{\mathrm{As}}_2$ revealed a well-defined low-energy incommensurate spin fluctuation at [$\pi (1\pm 2\delta ),0$] with $\delta =0.16$. The incommensurate structure differs from the previously observed commensurate peaks in electron-doped $A{\mathrm{Fe}}_2{\mathrm{As}}_2$ ($A=\mathrm{Ba}$, Ca, or Sr) at low energies. The direction of the peak splitting is perpendicular to that observed in $\mathrm{Fe}(\mathrm{Te},\mathrm{Se})$ or in $\mathrm{Ba}(\mathrm{Fe},\mathrm{Co}{)}_2{\mathrm{As}}_2$ at high energies. A band structure calculation suggests interband scattering between bands around the $\Gamma$ and $X$ points as an origin of this incommensurate peak. The perpendicular direction of the peak splitting can be understood within the framework of multiorbital band structure. The results suggest that spin fluctuation is more robust in hole-doped than in electron-doped samples, which can be responsible for the appearance of superconductivity in the heavily hole-doped samples.

Figure 1

(a)–(c) Constant-energy scan of ${\mathrm{KFe}}_2{\mathrm{As}}_2$ at $T=12\mathrm{K}$ along (a) $(H,H,1.3)$ at $\hslash \omega =8\mathrm{meV}$, (b) $(H,H,0)$ at $\hslash \omega =6\mathrm{meV}$, and (c) $(1\mathrm{\text{−}}K,K,0)$ at $\hslash \omega =6\mathrm{meV}$. Horizontal bars depict the instrumental $q$ resolution. Scan trajectories are indicated by arrows in (d) as scan 1 for (a),(b) and scan 2 for (c). The spectrum in (a) is obtained in the $(H,H,L)$ zone, and those in (b),(c) are obtained in the $(H,K,0)$ zone. Solid lines indicate Gaussian fits. The inset in (a) is the $\mathbf{q}$ spectrum at $\hslash \omega =3.5\mathrm{meV}$ and $T=0.72\mathrm{K}$ observed by using HER spectrometer. (d),(e) Schematic illustrations of magnetic peak positions of (d) ${\mathrm{KFe}}_2{\mathrm{As}}_2$ and (e) $\mathrm{Ba}(\mathrm{Fe},\mathrm{Co}{)}_2{\mathrm{As}}_2$.

Figure 2

$L$ dependence of the magnetic peak [$\mathbf{Q}=(0.65,0.65,L)$] and background [$\mathbf{Q}=(0.5,0.5,L)$ and $(0.8,0.8,L)$] intensities at $T=12\mathrm{K}$ for $\hslash \omega =6\mathrm{meV}$. Inset shows the scan trajectories.

Figure 3

Energy spectrum of ${\chi }^{\prime \prime }(\mathbf{q},\omega )$ at $T=12$ and 100 K. The solid and dashed lines are fits obtained using Eq. (1) at $T=12$ and 100 K, respectively.

Figure 4

Contour plots of the spin susceptibility for (a) $n=5.5$, (b) $n=5.8$, and (c) $n=6.1$. The strength of the $xy$ and $yz$ orbital character on the Fermi surface for (d),(e) $n=5.5$ and (f),(g) $n=6.1$. The arrows connect Fermi surface portions with similar orbital character. No arrow toward the inner hole Fermi surface is depicted in (e) since this Fermi surface has a strong three-dimensional nature in the orbital character and its contribution to the spin fluctuation is small.