  The London penetration depth, $\lambda$, is directly related to the density,
$n_{s}$, of the Cooper pairs ($\lambda^{2}\propto 1/n_{s}$) and its variation
with temperature provides valuable insight into the pairing mechanism. Here we
study the evolution with doping of the temperature dependence of the in-plane
($\lambda_{ab}$) and out-of-plane ($\lambda_{c}$) penetration depths in single
crystals of electron-doped Ba(Fe$_{1-x}$Ni$_x$)$_2$As$_2$. As is the case for
other pnictides, $\lambda(T) \sim T^n$ over the whole doping range and this
behavior extends down to at least $T=T_c/100$, setting a very small upper limit
on the gap minimum. Furthermore, in the overdoped regime: 1) the exponent $n$
becomes substantially smaller than 2, which is incompatible with the models
that explain power-law behavior to be due to scattering; 2) the exponent $n$
becomes anisotropic, with $\lambda_{c}(T)$ showing a clear $T$-linear behavior
over a large temperature interval. These findings suggest that in the overdoped
regime the superconducting gap in iron-based pnictide superconductors develops
nodal structure, which unlike in the cuprates, cannot be understood within a
two-dimensional picture.
