Local measurement of the penetration depth in the pnictide superconductor $\text{Ba}{\left({\text{Fe}}_{0.95}{\text{Co}}_{0.05}\right)}_2{\text{As}}_2$

We use magnetic force microscopy (MFM) to measure the local penetration depth $\lambda$ in $\text{Ba}{\left({\text{Fe}}_{0.95}{\text{Co}}_{0.05}\right)}_2{\text{As}}_2$ single crystals and use scanning superconducting quantum interference device susceptometry to measure its temperature variation down to 0.4 K. We observe that superfluid density ${\rho }_s$ over the full temperature range is well described by a clean two-band fully gapped model. We demonstrate that MFM can measure the important and hard-to-determine absolute value of $\lambda$, as well as obtain its temperature dependence and spatial homogeneity. We find ${\rho }_s$ to be uniform on the submicron scale despite the highly disordered vortex pinning.

Figure 1

(Color) Technique to measure $\lambda$ and $\Delta \lambda$ by MFM from (a) Meissner repulsion and [(b) and (c)] vortex imaging. (a) $z$ dependence of $\partial F_z/\partial z$ (blue symbols) at $T=5$, 12, and 18 K and the fit to the truncated cone model (red dashed line). (Inset) Sketch to illustrate that the tip-superconductor interaction in the Meissner state can be approximated by the interaction between the tip and its image mirrored through a plane (dashed line) ${\lambda }_{ab}$ below the surface of the superconductor (solid line) when $z⪢{\lambda }_{ab}$. Comparing the curves provides $\Delta {\lambda }_{ab}$ independently of the tip model. Fits give ${\lambda }_{ab}\left(T\right)$ at $T=5$, 12, 18 K to be 0.33, 0.37, $1.10\mu \text{m}$. [(b) and (c)] Images of two vortices $\left(z=400\text{nm}\right)$ at (b) 5 and (c) 10 K. The similar shapes and amplitudes of the images show that both the spatial variation and the temperature-induced change in ${\lambda }_{ab}$ are small. [(d) and (e)] Scanning electron microscopy images of the tip (d) before and (e) after the measurements. An accidental crash during the measurement changes the truncation distance $h_0$ from (d) $300\pm 30\text{nm}$ to (e) $400\pm 20\text{nm}$. Despite the crash, $\partial F_z/\partial z$ curves taken before and after the crash give the same ${\lambda }_{ab}\left(5\text{K}\right)$ to within 10 nm.

Figure 2

(Color) Normalized superfluid density ${\rho }_s\left(T\right)/{\rho }_s\left(0\right)\equiv {\lambda }_{ab}{\left(0\right)}^2/{\lambda }_{ab}{\left(T\right)}^2$ vs $T$. We determine $\Delta {\lambda }_{ab}\left(T\right)$ by MFM (squares) and by SSS (diamonds) from measuring the change in the diamagnetic response at fixed height. These values are offset to match the absolute value of ${\lambda }_{ab}\left(T\right)$ obtained by fitting the MFM data to the truncated cone model (circles). The green solid line shows a fit of the two-band $s$-wave model discussed in the main text (${\Delta }_1=2.6T_c$, ${\Delta }_2=0.8T_c$, $x=0.88$, and $a=1.4$). The width of the dashed band reflects the uncertainty in ${\lambda }_{ab}\left(0\right)$. Inset: $\Delta {\lambda }_{ab}$ vs $T$ at low $T$. Black dashed line: one-gap $s$-wave model with $a=1.5$ and ${\Delta }_0=1.95T_c$. Magenta dashed line: $\Delta {\lambda }_{ab}\left(T\right)=c{T}^{2.2}$ $\left(c=0.14\text{nm}/{\text{K}}^{2.2}\right)$.

Figure 3

(Color) Spatial uniformity of ${\lambda }_{ab}$ from vortex imaging at 5 K. (a) Image of vortices at $T=5\text{K}$, $z=125\text{nm}$, and a vortex density giving 3.5 mT. (b) The normalized length scale associated with each vortex peak in (a) ${\mathcal{C}}^{-1/4}/⟨{\mathcal{C}}^{-1/4}⟩$ ($⟨⟩$ denotes the mean). We find ${\mathcal{C}}^{-1/4}=250\left(1\pm 0.08\right)\text{nm}$ (70% confidence interval).

Figure 4

(Color) Inhomogeneous vortex pinning. (a) Image of vortices at $T=5\text{K}$, $z=80\text{nm}$, and $B=9.5\text{mT}$, overlaid by the vortex positions (dots) in Fig. 3a and the boundary of that scan (black frame). The vortex configuration is highly disordered. Vortices avoid the same regions in both scans, taken days apart and many thermal cycles apart. (b) Local critical current (left ordinate) and the depinning force (right ordinate) vs $T$. The comparison of minimum and typical values implies inhomogeneous pinning. (c) Image of vortices at $T=5\text{K}$, $z=120\text{nm}$ showing that $F_{\text{min}}$ only moves the vortex at the bottom. (d) Image of moving vortices at $T=14.5\text{K}$, $z=430\text{nm}$ showing that $F_{\text{typ}}$ allows us to drag all vortices a distance of several microns.