Effects of electron irradiation on resistivity and London penetration depth of ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2 \left(x\le 0.34\right)$ iron-pnictide superconductor

Irradiation with 2.5 MeV electrons at doses up to $5.2\times {10}^{19} \mathrm{electrons}/\mathrm{cm}{}^2$ was used to introduce pointlike defects in single crystals of ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ with $x=0.19 \left(T_c=14\mathrm{K}\right),0.26 \left(T_c=32\mathrm{K}\right), 0.32 \left(T_c=37\mathrm{K}\right)$, and $0.34 \left(T_c=39\mathrm{K}\right)$ to study the superconducting gap structure by probing the effect of nonmagnetic scattering on electrical resistivity $\rho \left(T\right)$ and London penetration depth $\lambda \left(T\right)$. For all compositions, the irradiation suppressed the superconducting transition temperature $T_c$ and increased resistivity. The low-temperature behavior of $\lambda \left(T\right)$ is best described by the power-law function, $\Delta \lambda \left(T\right)=A{(T/T_c)}^n$. While substantial suppression of $T_c$ supports $s_{\pm }$ pairing, in samples close to the optimal doping, $x=0.26$, 0.32, and 0.34, the exponent $n$ remained high $\left(n\ge 3\right)$, indicating almost exponential attenuation and thus a robust full superconducting gap. For the $x=0.19$ composition, which exhibits coexistence of superconductivity and long-range magnetism, the suppression of $T_c$ was much more rapid, and the exponent $n$ decreased toward the $s_{\pm }$ dirty limit of $n=2$. In this sample, the irradiation also suppressed the temperature of structural/magnetic transition $T_{\mathrm{sm}}$ from 103 to 98 K, consistent with the itinerant nature of the long-range magnetic order. Our results suggest that underdoped compositions, especially in the coexisting regime, are most susceptible to nonmagnetic scattering and imply that in multiband ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ superconductors, the ratio of the interband to intraband pairing strength, as well as the related gap anisotropy, increases upon the departure from the optimal doping.

Figure 1

Evolution of the temperature-dependent resistivity (normalized by the value at 300K) with electron irradiation: (a) $x=0.19$-A, (b) $x=0.26$-A and 0.26-B, and (c) $x=0.34$-A and 0.34-B. Insets zoom in on the superconducting transitions.

Figure 2

Evolution of $T_c/T_{c0}$ as a function of $\Delta \rho \left(T_c\right)$ upon electron irradiation, where $\rho \left(T_c\right)$ is the resistivity right above $T_c$ and $\Delta \rho \left(T_c\right)$ is the change of the resistivity after irradiation. The inset shows $T_c/T_{c0}$ vs the dimensionless scattering rate $g^{\lambda }$. The classical Abrikosov-Gor'kov (AG) theory for an isotropic $s$-wave superconductor with magnetic impurities is also shown by a solid line [2].

Figure 3

Variation of normalized in-plane penetration depth $\Delta \lambda \left(T\right)/\Delta \lambda \left(T_c\right)$ before and after electron irradiation; see Table 1 for the details on the samples.

Figure 4

Variation of the reduced critical temperature $T_c/T_{c0}$ with the dose of electron irradiation for samples with $x=0.19$ (green squares), $x=0.26$ (blue triangles), $x=0.26$ (black diamonds), and $x=0.34$ (red circles).

Figure 5

Low-temperature part of $\Delta \lambda \left(T\right)$ before and after electron irradiation of samples with (a) $x=0.19$, (b) $x=0.26$, (c) $x=0.32$, and (d) $x=0.34$. The data were analyzed with a power-law function, $\Delta \lambda =A{(T/T_c)}^n$, over a variable temperature range from the base temperature to a temperature $T_{\mathrm{up}}$. (e)–(h) Corresponding fit exponents. The fitting errors are less than $\pm 0.1$.

Figure 6

Low-temperature part of $\Delta \lambda$ of the sample with $x=0.19$ before and after electron irradiation plotted as a function of ${(T/T_c)}^2$. The straight lines are the guides for the pure $T^2$ behavior.

Figure 7

Normalized superfluid density, ${\rho }_s={[\lambda \left(0\right)/\lambda \left(T\right)]}^2$, before and after electron irradiation for (a) $x=0.19$, (b) $x=0.26$, (c) $x=0.32$, and (d) $x=0.34$. Doping-dependent $\lambda \left(0\right)$ was estimated considering resistivity right above $T_c$ (Homes scaling) and an irradiation-induced $T_c$ decrease; see the text for details.