Non-exponential London penetration depth in Ba$_{1-}$K$_{x}$Fe$_{2}$As$_{2}$ single crystals
We have studied the in- and out-of-plane magnetic penetration depths in the hole- doped iron based superconductor Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$ ($T_{c}\approx$ 30K). The study was performed on single crystals grown from different fluxes and we find that the results are nearly the same. The in-plane London penetration depth $λ_{ab}$ does not show exponential saturation at low temperature, as would be expected from a fully gapped superconductor. Instead, $λ_{ab}(T)$ shows a power-law behavior, $λ\propto T^{n}$ ($n\approx 2$), down to $T\approx 0.02 T_{c}$, similar to the electron doped Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$. The penetration depth anisotropy $γ_λ=λ_{c}(T)/λ_{ab}(T)$ increases upon cooling, opposite to the trend observed in the anisotropy of the upper critical field, $γ_ξ=H_{c2}^{\perp c}(0)/H_{c2}^{\parallel c}(0)$. These are universal characteristics of both the electron and hole doped 122 systems, suggesting unconventional superconductivity. The behavior of the in-plane superfluid density $ρ_{ab}(T)$ is discussed in light of existing theoretical models proposed for the iron pnictides superconductors.