Dependence of the absolute value of the penetration depth in $\left({\mathrm{Ba}}_{1-x}{\mathrm{K}}_x\right){\mathrm{Fe}}_2{\mathrm{As}}_2$ on doping

We report magnetic force microscopy (MFM) measurements on the iron-based superconductor ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$. By measuring locally the Meissner repulsion with the magnetic MFM tip, we determine the absolute value of the in-plane magnetic penetration depth (${\lambda }_{\mathrm{ab}}$) in underdoped, optimally doped, and overdoped samples. The results suggest an abrupt increase of ${\lambda }_{\mathrm{ab}}$ as doping is increased from $x_{\mathrm{opt}}$, which is potentially related to the presence of a quantum critical point. The response of superconducting vortices to magnetic forces exerted by the MFM tip for $x=0.19$ and 0.58 is compatible with previously observed structural symmetries at those doping levels.

Figure 1

Touchdown curves as a function of $T$ for a $x=0.32$ sample showing how the increase of ${\lambda }_{\mathrm{ab}}$ affects the repulsion of the tip from the surface. This sample was not used for extracting ${\lambda }_{\mathrm{ab}}$ because it did not cleave well. All the curves here were acquired with the same tip at the same location and are offset by 0.25 Hz for clarity. At $\mathrm{T}=32.5$ K ${\lambda }_{\mathrm{ab}}$ is too large for us to detect any Meissner response. Based on this and additional touchdown curves, $T_C=32.2\pm 0.2$ K. Inset: Schematic of an MFM tip. The truncated cone tip parameters are shown. $2\mathrm{\Theta }$ is the cone angle, $H$ is the effective magnetic coating height, and $h$ is the truncation height.

Figure 2

The dependence of ${\lambda }_{\mathrm{ab}}^{0\mathrm{K}}$ (circles) and $T_C$ (squares) on doping $x$. ${\lambda }_{\mathrm{ab}}^{0\mathrm{K}}$ is extrapolated from $T=4.5$ K using data from Cho et al. [18]. Stars are published values [16, 19] measured at $7\mathrm{K}$ and extrapolated to $T=0\mathrm{K}$. The abrupt jump in ${\lambda }_{\mathrm{ab}}^{0\mathrm{K}}$ is clearly visible in our data at $x=0.36$, as is the decrease upon approaching $x_{\mathrm{opt}}$ from the underdoped edge of the superconducting dome. For $x=0.19$ we show two values for ${\lambda }_{\mathrm{ab}}^{0\mathrm{K}}$ and $T_C$, as explained in the text. The error bars for ${\lambda }_{\mathrm{ab}}^{0\mathrm{K}}$ represent $70\%$ confidence intervals. The error bars for $T_C$ represent temperature increments. Lines are guides to the eye.

Figure 3

Touchdown curves taken at points $\approx 200$ $\mu \mathrm{m}$ apart on a $x=0.34$ sample during the same cool-down at $T=4.6\mathrm{K}$. Clearly the curves are very similar. Fitting gives ${\lambda }_{\mathrm{ab}}=200\pm 30$ nm. Vertical line represents $z={\lambda }_{\mathrm{ab}}$. For fitting we use the $z\ge 2{\lambda }_{\mathrm{ab}}$ part of the data. Inset: The same touchdowns presented with $z$ on a logarithmic scale showing the similarity for $z\ge 2{\lambda }_{\mathrm{ab}}$.

Figure 4

(a) Normalized touchdown curves measured at $T=4.5\mathrm{K}$ for $x=0.34,0.32,0.36$. $x=0.32,0.36$ were measured in the same cool-down with the same tip. $x=0.34$ was measured with a different tip in a different cool-down. Fitting to the curves gives ${\lambda }_{\mathrm{ab}}\approx 200\pm 30,260\pm 30,340\pm 50$ nm for $x=0.34,0.32,0.36$. Inset: The same curves before normalization. (b) Normalized touchdown curves for different samples ($x=0.58,0.52$) acquired with different tips. Both give ${\lambda }_{\mathrm{ab}}\approx 300\pm 35$ nm at $T=4.5\mathrm{K}$. The $x=0.52$ curve is offset by 20 nm to emphasize the similarity to the $x=0.58$ curve. Inset: The same curves before normalization.

Figure 5

Imaging and manipulating vortices at $x=0.58$ for $T=4.3\mathrm{K}$ with $B\approx 1.8$ G. The scans show vortex motion which depends on the scan direction, indicated by arrows (the fast direction, in which we move the tip back-and-forth, is shown by two parallel arrows; the slow direction, in which we increment the tip after one back-and-forth period, is shown by a single long arrow). (a) $z=670$ nm. (b) $z=340$ nm. (c) $z=960$ nm. (d) $z=260$ nm.

Figure 6

Imaging and manipulating vortices at $x=0.19$ for $T=4.34\mathrm{K}$ with $B\approx 1.5$ G. The scan directions are indicated by arrows as explained in Fig. 5. The scans are ordered chronologically. Dashed lines in (c),(e) are guides to the eye and highlight vortex motion. (a) Low resolution scan before manipulating vortices ($z=540$ nm). (b),(c) Manipulation scans with the slow scan direction pointing left $[z=340$ nm in (b), $z=230$ nm in (c)]. (d),(e) Scans with the slow scan direction pointing up $[z=600$ nm in (d), $z=220$ nm in (e)]. (f) Scan with $z=590$ nm after several scans with very low $z$ and significant vortex motion (not shown).