Effect of heavy-ion irradiation on London penetration depth in overdoped Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$

Irradiation with 1.4 GeV ${}^{208}$Pb ions was used to induce artificial disorder in single crystals of iron-arsenide superconductor Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ and to study its effects on the temperature-dependent London penetration depth and transport properties. A study was undertaken on overdoped single crystals with $x=0.108$ and $x=0.127$ characterized by notable modulation of the superconducting gap. Irradiation corresponding to the matching fields of $B_{\varphi }=6$ T and 6.5 T with doses $2.22\times {10}^{11}$ $\mathit{\text{d}}$/cm${}^2$ and $2.4\times {10}^{11}$ $\mathit{\text{d}}$/cm${}^2$, respectively, suppresses the superconducting $T_c$ by approximately 0.3 to 1 K. The variation of the low-temperature penetration depth in both pristine and irradiated samples is well described by the power law $\Delta \lambda \left(T\right)=A{T}^n$. Irradiation increases the magnitude of the prefactor $A$ and decreases the exponent $n$, similar to the effect of irradiation in optimally-doped samples. This finding supports universal $s_{\pm }$ pairing in Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ compounds for the entire Co doping range.

Figure 1

Temperature-dependent electrical resistivity for the reference samples $x=0.108$ and $x=0.127$, and the irradiated sample of $x=0.127$. The irradiated sample $x=0.127$ is the same sample as used in penetration depth measurements, with contacts soldered after measurements completed. The top inset shows the same curves using a normalized resistivity scale $\rho /\rho \left(300\text{K}\right)$, showing the main difference between resistivity values comes from the error of geometric factor determination.[41, 47] The bottom inset shows a sketch of the doping phase diagram for BaCo122 with the position of the samples used in this study.

Figure 2

Comparison of the temperature-dependent electrical resistivity of reference and irradiated samples $x=0.127$, with a geometric factor correction by normalizing slopes of the $\rho \left(T\right)$ curves at 300 K. For the pristine sample, we assumed $\rho \left(300\text{K}\right)=220$ $\mu \Omega$ cm.[49] Inset zooms for the superconducting transition range. Heavy ion irradiation does not change the shape of the $\rho \left(T\right)$ curves, but increases residual resistivity, sharpens the superconducting transition, and shifts $T_c$ downward.

Figure 3

In-plane resistivity $\rho \left(T\right)$ for slightly overdoped Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$, $x=0.108$, in magnetic fields (a) parallel to the conducting plane, perpendicular to the $c$ axis, and (b) parallel to the crystallographic $c$ axis. The field values are (right to left) 0, 1, 2.5, 5, 10, 15, 20, 23, 25, 28, and 35 T. The bottom panel (c) shows $H_{c2}$(T) phase diagrams for both directions of the magnetic field.

Figure 4

In-plane resistivity $\rho \left(T\right)$ for heavily overdoped Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$, $x=0.127$ in magnetic fields (a) parallel to the conducting plane and perpendicular to the $c$ axis, field values (right to left) 0, 1, 2.5, 5, 10, 15, 20, 23, and 25 T, and (b) parallel to the crystallographic $c$ axis, field values (right to left) 0, 1, 2, 4, 6, 8, and 10 T. Bottom panel (c) shows $H_{c2}$(T) phase diagrams for both directions of magnetic field.

Figure 5

$H_{c2}\left(T\right)$ and anisotropy parameter, $\gamma \equiv H_{c2,ab}/H_{c2,c}$, for overdoped samples of BaCo122 $x=0.108$ and $x=0.127$. Top panel shows configurations with magnetic fields parallel to the conducting plane. The middle panel shows configurations with the magnetic field parallel to the crystallographic $c$ axis. For reference, we show bulk $H_{c2,c}\left(0\right)$ as determined from the thermal conductivity study in the sample $x=0.127$ (red star, Ref. 18), which suggests the data for strongly overdoped samples $x=0.127$ show very close to $T$-linear dependence. The top and middle panels show data for previously studied overdoped samples with $x=0.102$ and $x=0.114$,[41] determined using the same midpoint criterion. The bottom panel shows the temperature-dependent anisotropy parameter for samples $x=0.108$ and $x=0.127$.

Figure 6

Low temperature London penetration depth $\Delta$$\lambda$(T) for samples of Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ with $x=0.108$ (top panel) and $x=0.127$ (bottom panel). Data were taken in both a ${}^3$He-cryostat (down to $\sim$0.5 K, black curves) and a dilution refrigerator ($\sim$0.05 $\text{K}<T<3$ K, red curve), showing a good match between the data sets taken in these two systems and the robustness of the power-law dependence.

Figure 7

Low temperature London penetration depth $\Delta$$\lambda$(T) measured in single crystals of Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ with $x=0.108$ (green and blue curves) and $x=0.127$ (black and red curves) plotted vs ${(T/T_c)}^2$. Linear plot for $x=0.127$ shows the dependence is very close to $T^2$, consistent with more detailed fitting analysis using a floating fitting range, see Fig. 9. Clear deviations for sample $x=0.108$ suggest $n>2$.

Figure 8

Effect of heavy-ion irradiation on London penetration depth, $\Delta \lambda \left(T\right)$ in samples with $x=0.108$ (top) and $x=0.127$ (bottom). Black curves show pristine samples, red curves show irradiated with matching fields of 6.5 T and 6 T, respectively. Insets show the variation of the London penetration depth in the entire range to $T_c$.

Figure 9

Dependence of the fitting parameters, $n$ (top panels) and $A$ (bottom panels), of the power-law function, $\Delta \lambda =A{T}^n$, on the temperature of the high-temperature boundary of the fitting interval. Data are shown for pristine (black squares) and irradiated (yellow-brown circles) sample with $x=0.108$ (left) and $x=0.127$ (right).