We report a detailed investigation on the lower critical field $H_{c1}$ of the superconducting Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$ (FeAs-122) single crystals. A pronounced kink is observed on the $H_{c1}(T)$ curve, which is attributed to the existence of two superconducting gaps. By fitting the data $H_{c1}(T)$ to the two-gap BCS model in full temperature region, a small gap of $Delta_a(0)=2.0pm 0.3$ meV and a large gap of $Delta_b(0)=8.9pm 0.4$ meV are obtained. The in-plane penetration depth $lambda_{ab}(0)$ is estimated to be 105 nm corresponding to a rather large superfluid density, which points to the breakdown of the Uemura plot in FeAs-122 superconductors.
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