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The temperature dependence of the in-plane magnetic penetration depth$\lambda_{ab}$ of Ba(Fe$_{1-x}$Ni$_x$)$_2$As$_2$ single crystals is determineddirectly from the shielding magnetic susceptibility, measured in the Meissnerregion with the field parallel to the ab layers. The doping levels studiedcover the underdoped, optimally-doped and overdoped regimes. At temperaturesbelow 0.5Tc a well-defined power-law behavior$\lambda_{ab}(T)-\lambda_{ab}(0)=AT^n$ (with n approximately 2.5) is observed.At lower temperatures (T<0.3Tc) the data are still consistent with n=2 and$A\propto T_c^{-3}$, as predicted by the strong pair-breaking scenario proposedby Gordon et al., Phys. Rev. B 81, 180501(R) (2010). The temperature dependenceof the superfluid density $\rho_s\propto\lambda_{ab}^{-2}$ presents a markedpositive curvature just below Tc which is a sign of two-gap superconductivity.The analysis of $\rho_s(T)$ in terms of a two-gap model allowed to estimateparameters like the in-band and inter-band couplings, the relative weight ofeach band, and their dependence with the doping level. A comparison with$\rho_s(T)$ data obtained by using other techniques in compounds with a similarcomposition is also presented.

Direct measurement of the temperature dependence of the magnetic penetration depth in Ba(Fe$_{1-x}$Ni$_x$)$_2$As$_2$ superconductors