London penetration depth in $\text{Ba}{\left({\text{Fe}}_{1-x}{T}_x\right)}_2{\text{As}}_2$ $\left(T=\text{Co},\text{Ni}\right)$ superconductors irradiated with heavy ions

Irradiation with Pb ions was used to study the effect of disorder on the in-plane London penetration depth, $\lambda \left(T\right)$, in single crystals of $\text{Ba}{\left({\text{Fe}}_{1-x}{T}_x\right)}_2{\text{As}}_2$ $\left(T=\text{Co},\text{Ni}\right)$. An increase in the irradiation dose results in a monotonic decrease in the superconducting transition temperature, $T_c$, without affecting much the transition width. In both Co- and Ni-doped systems we find a power-law behavior, $\Delta \lambda \left(T\right)\propto T^n$ with the exponent $n$ systematically decreasing with the increase in disorder. This observation, at qualitative odds with the response of $s$- and $d$-wave superconductors, finds natural explanation in a nodeless $s^{\pm }$ state with pairbreaking (interband) impurity scattering. We are able to describe the effect quantitatively assuming the pairbreaking strength intermediate between Born and unitary limits.

Figure 1

(Color online) Variation in the in-plane London penetration depth, $\Delta \lambda \left(T\right)$, for irradiated FeCo122 (top panel) and FeNi122 (bottom panel). The low-temperature variations are shown in the main frame of each panel along with the best power-law fits. The curves are offset vertically for clarity. The variations in the vicinity of $T_c$ are shown in the insets of each panel.

Figure 2

(Color online) Detailed comparison of the functional form of $\Delta \lambda \left(T\right)$ for irradiated FeCo122 and FeNi122. In the main panels $\Delta \lambda \left(T\right)$ is plotted vs ${\left(t=T/T_c\right)}^{n_0}$ with the exponents $n$ taken from the best fits of unirradiated samples: $n_0=2.8$ and 2.5 for FeCo122 and FeNi122, respectively (see Fig. 1). Apparently, irradiation causes low-temperature deviations, which are better seen in the derivatives, $d\Delta \lambda \left(t\right)/d{t}^{n_0}$, plotted in the insets.

Figure 3

(Color online) Top panel: the suppression of $T_c$ with disorder relative to unirradiated $T_c^{\text{un}}$. The vertical bars denote the width of the transition corresponding the diamagnetic signal change from 90% (onset) to 20% (end), see insets in Fig. 1. Symbols are shown at the mean values between onset and end of the transition. Lower panel: exponent $n$ vs $B_{\varphi }$.

Figure 4

(Color online) (a) Superfluid density and (b) the density of states $n\left(\epsilon \right)=N\left(\epsilon \right)/N_f$, computed for the $s^{\pm }$ state with sign-changing isotropic gaps and strong interband impurity scattering, between the Born and unitary limits. The dashed line in (a) is an example of a power-law fit $\rho \left(T\right)/{\rho }_0=\rho \left(0\right)/{\rho }_0-a{\left(T/T_{c0}\right)}^n$ for $0<T<0.4T_{c0}$; best fitting parameters for a given set of $\Gamma =n_{imp}/\pi N_f$ are listed in the table. (b) As the impurity concentration $n_{imp}\sim \Gamma$ increases, the band of midgap states approaches the Fermi level and the exponent $n$ is reduced. (c) $T_c$ vs power $n$, from the theoretical model (triangles) and experiment (squares and circles).