Macroscopic phase segregation in superconducting K${}_{0.73}$Fe${}_{1.67}$Se${}_2$ as seen by muon spin rotation and infrared spectroscopy

Using muon spin rotation and infrared spectroscopy, we investigated the recently discovered superconductor K${}_{0.73}$Fe${}_{1.67}$Se${}_2$ with $T_{\mathrm{c}}\approx 32$ K. We show that the combined data can be consistently described in terms of a macroscopically phase-segregated state with a matrix of ∼88$\%$ volume fraction that is insulating and strongly magnetic and inclusions with an ∼12$\%$ volume fraction, which are metallic, superconducting, and nonmagnetic. The electronic properties of the latter, in terms of the normal state plasma frequency and the superconducting condensate density, appear to be similar as in other iron selenide or arsenide superconductors.

Figure 1

Temperature dependence of the in-plane resistivity of a KFS_SC single crystal from the same growth batch as the samples used for the μSR and infrared measurements.

Figure 2

Representative TF-μSR data (symbols) of (a) and (b) KFS_SC just above and below $T_{\mathrm{c}}\approx 32$ K, respectively, and (c) of KFS_I. Solid lines show the fits obtained with the function in Eq. (1). (d) Temperature dependence of the local field $B_{\mu }$ and the relaxation rate ${\sigma }_{\mathrm{s}}$ of the slowly relaxing signal of sample KFS_SC.

Figure 3

TF-μSR line shapes showing the distribution of local magnetic fields during a so-called pinning experiment as described in the text.

Figure 4

Temperature dependence of the far-infrared spectra of KFS_SC in terms of (a) the in-plane polarized reflectivity $R_{ab}$, (b) the real part of the optical conductivity ${\sigma }_{1,ab}$, and (c) the dielectric function ${\varepsilon }_{1,ab}$. Shown by the circles in (b) is the dc conductivity ${\sigma }_{\mathrm{dc}}$, deduced from the resistivity data in Fig. 1. (d)–(f) Corresponding spectra for KFS_I. Since the crystal was insulating and, thus, transparent, the spectra were corrected for the interference effects that arise from multiple reflections as shown in the inset of (d).

Figure 5

Comparison of the experimental data in the normal state of KFS_SC with the fits based on the EMA model as described in the text.

Figure 6

Temperature dependence of the scattering rate of the narrow Drude peak ${\Gamma }_{\mathrm{Dn}}=1/T_{\mathrm{Dn}}$ as obtained from the fitting the with EMA model that is described in the text. Also shown for comparison is the dc conductivity ${\sigma }_{\mathrm{dc}}$, obtained from the resistivity data in Fig. 1 and the extrapolated value of ${\sigma }_1(\omega \to 0)$ obtained with the EMA model.

Figure 7

(a) Sketch of the two Drude and the Lorentzian components that were used to fit the data at 35 K just above $T_{\mathrm{c}}$. (b) and (c) sketch of the changes due to the onset of superconductivity that were assumed in the context of Model A and Model B, respectively. The shaded area indicates the missing spectral weight that is redistributed toward the origin where it accounts for the response of the superconducting condensate.

Figure 8

Comparison of the experimental data at $6\mathrm{K}\ll T_{\mathrm{c}}\approx 32\mathrm{K}$ of KFS_SC with the EMA fits using Model A and Model B, respectively. The two models are outlined in the text and are sketched in Figs. 7b and 7c.