Local Measurement of the Superfluid Density in the Pnictide Superconductor $\mathrm{Ba}({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{As}}_2$ across the Superconducting Dome

We measure the penetration depth ${\lambda }_{ab}(T)$ in $\mathrm{Ba}({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{As}}_2$ using local techniques that do not average over the sample. The superfluid density ${\rho }_s(T)\equiv 1/{\lambda }_{ab}(T{)}^2$ has three main features. First, ${\rho }_s(T=0)$ falls sharply on the underdoped side of the dome. Second, ${\lambda }_{ab}(T)$ is flat at low $T$ at optimal doping, indicating fully gapped superconductivity, but varies more strongly in underdoped and overdoped samples, consistent with either a power law or a small second gap. Third, ${\rho }_s(T)$ varies steeply near $T_c$ for optimal and underdoping. These observations are consistent with an interplay between magnetic and superconducting phases.

Figure 1

The temperature dependence of ${\rho }_s(T)\equiv 1/{\lambda }_{ab}(T{)}^2$ and $\Delta {\lambda }_{ab}(T)$ shows three systematic trends. (a) ${\rho }_s(T)$ vs $T$. Solid line: a single-gap equation [Eq. (1)] fits only $x=7\%$. Dashed lines: phenomenological two-gap fits [Eq. (2)] work well at every doping (fit parameters in Table. ). At $x=8.5\%$, we did not measure ${\lambda }_{ab}(T)$, so we offset $\Delta {\lambda }_{ab}(T)$ by the mean of ${\lambda }_{ab}(0)$ at $x=7\%$ and $x=11\%$. (b) ${\rho }_s(T)/{\rho }_s(0)$ vs $T/T_c$. At $x=5.1\%$ (UD) and $x=7\%$ (OptD), ${\rho }_s(T)$ rises more sharply than for ${\mathrm{MgB}}_2$ from Ref. 37, single-band weakly coupled BCS theory, or $x=11\%$ (OD). (c) $\Delta {\lambda }_{ab}(T)$ down to 0.4 K measured by SSS at the indicated $x$. Dashed lines: power-law fits [Eq. (3)] describe the data well up to $0.3T_c$ with the power $n$ fixed at 2.5 (fit parameters in Table. ). The amplitude $A$ increases away from optimal doping, where $\Delta {\lambda }_{ab}(T)$ is so flat as to be consistent with exponential behavior. $\Delta {\lambda }_{ab}(T)$ at 5.1%, 4.9%, and 11% are offset vertically by 5, 10, 15 nm, respectively, for clarity. $\Delta {\lambda }_{ab}(T)$ at $x=4.9\%$ measured on a different sample by MFM at $T>5\mathrm{K}$ is also plotted.

Figure 2

(a) ${\lambda }_{ab}(0)$ and ${\rho }_s(0)$ as extrapolated from Fig. 1a, showing the rapid drop of ${\rho }_s(0)$ on the underdoped side. For $x=4.5\%$, ${\rho }_s(5\mathrm{K})$ is plotted because the extrapolation is unclear. Bars show the errors. (b) Temperatures of structural, magnetic, and superconducting transitions $T_{\mathrm{stru}}$, $T_{\mathrm{AFM}}$, and $T_c$ (bulk), from resistivity measurements of samples from the same growth as studied here. $T_c$ (local) is from linear extrapolation of ${\rho }_s(T)$ to zero from the MFM data presented here.

Figure 3

Inhomogeneity in $\Delta {\lambda }_{ab}(T)$ observed in an $x=11\%$ sample. (a) Photograph of the $x=11\%$ sample measured by SSS. The label of positions corresponds to the position where $\Delta {\lambda }_{ab}(T)$ was measured. (b),(c) $\Delta {\lambda }_{ab}(T)$ by SSS at positions 1–3 (b) and three different positions around position 3 each separated by $15\mu \mathrm{m}$ (c). Dashed lines in (b) plot power-law fits with parameters given in Table .