Local structure of the superconductor K${}_{0.8}$Fe${}_{1.6+x}$Se${}_2$: Evidence of large structural disorder

The local structure of superconducting single crystals of K${}_{0.8}$Fe${}_{1.6+x}$Se${}_2$ with $Tc$ $=$ 32.6 K was studied by x-ray absorption spectroscopy. Near-edge spectra reveal that the average valence of Fe is 2+. The room temperature structure about the Fe, K, and Se sites was examined by iron, selenium, and potassium $K$-edge measurements. The structure about the Se and Fe sites shows a high degree of order in the nearest-neighbor Fe-Se bonds. On the other hand, the combined Se and K local structure measurements reveal a very high level of structural disorder in the K layers. Temperature-dependent measurements at the Fe sites show that the Fe-Se atomic correlation follows that of the Fe-As correlation in the superconductor LaFeAsO${}_{0.89}$F${}_{0.11}$, having the same effective Einstein temperature (stiffness). In K${}_{0.8}$Fe${}_{1.6+x}$Se${}_2$, the nearest-neighbor Fe-Fe bonds have a lower Einstein temperature and higher structural disorder than in LaFeAsO${}_{0.89}$F${}_{0.11}$. The moderate Fe site and high K site structural disorder is consistent with the high normal state resistivity seen in this class of materials. For higher shells, an enhancement of the second-nearest-neighbor Fe-Fe correlation is found just below $Tc$, possibly due to changes in magnetic or local structural ordering.

Figure 1

(a) Crystal structure of defect-free KFe${}_2$Se${}_2$ for the $I$/4$m$ space group. For the superconducting materials it is suggested that random defects occur on the K sites and that the Fe1 sites are unoccupied—resulting in ordered Fe vacancies. (b) View down the $c$ axis of FeSe layer showing the real structure with vacant Fe1 ($I$/4$m$ 4$d$ sites) sites for two unit cells. Atom symbols have the same meaning as in panel (a). (c) Resistivity curve for the single-crystal sample.

Figure 2

(a) $K$-edge absorption spectrum of superconducting K${}_{0.8}$Fe${}_{1.6+x}$Se${}_2$ compared to Fe systems of 2+, 3+, and 4+ valence states; (b) pre-edge region of the same spectra. The valence is seen to be strongly 2+ following the behavior of stoichiometric FeS.

Figure 3

Local structure about the Fe, Se, and K sites from the XAFS structure functions in panels (a), (b), and (c), respectively. In each panel, the data are represented by the solid curve and the dashed line represents the model ($I$4/$m$ space group) with reasonable thermal and/or structural parameters. The components of the atomic shells are labeled in each panel.

Figure 4

Temperature dependence of the second shell Fe-Fe peak shows enhancement of this second-neighbor Fe-Fe shell in the Fe layer near the transition (∼30 K). Note that the peaks in the Fourier transforms are at shorter distances than the corresponding bond distances due to the central atom phase shift and the scattering atom phase functions. Accurate distances are obtained by model fits.

Figure 5

Two consecutive XAFS scans in $k$ space, at 300 K, are given in (a) and the Fourier transform of the average data is shown with a fit to the Fe-Se and Fe-Fe (first-neighbor) peaks in (b). The solid line corresponds to the data.

Figure 6

Extracted thermal parameters, σ${}^2$($T$), for the (a) Fe-Se and (b)Fe-As first-neighbor bonds in K${}_{0.8}$Fe${}_{1.6+x}$Se${}_2$ and LaFeAsO${}_{1-x}$F${}_x$ (from Ref. 16), respectively. The solid lines are with fits to Einstein models. Note the similarity between the two systems with respect to the first shell coordination of Fe.

Figure 7

Extracted thermal parameters, σ${}^2$($T$), for the Fe-Fe second-neighbor bonds in K${}_{0.8}$Fe${}_{1.6+x}$Se${}_2$ (a) and LaFeAsO${}_{1-x}$F${}_x$ (from Ref. 16) (b), respectively. Compared to the LaFeAsO${}_{1-x}$F${}_x$ system [16], K${}_{0.8}$Fe${}_{1.6+x}$Se${}_2$ possesses significant static disorder in the Fe layer, consistent with the large normal state resistivity.

Figure 8

Extracted Fe-Se (solid circles) and Fe-Fe first-neighbor (solid squares) bond distances showing the stronger temperature dependence (smaller Einstein temperature) for the Fe-Fe bond.