  We use inelastic neutron scattering (INS) spectroscopy to study the magnetic
excitations spectra throughout the Brioullion zone in electron-doped iron
pnictide superconductors BaFe$_{2-x}$Ni$_{x}$As$_{2}$ with $x=0.096,0.15,0.18$.
While the $x=0.096$ sample is near optimal superconductivity with $T_c=20$ K
and has coexisting static incommensurate magnetic order, the $x=0.15,0.18$
samples are electron-overdoped with reduced $T_c$ of 14 K and 8 K,
respectively, and have no static antiferromagnetic (AF) order. In previous INS
work on undoped ($x=0$) and electron optimally doped ($x=0.1$) samples, the
effect of electron-doping was found to modify spin waves in the parent compound
BaFe$_2$As$_2$ below $\sim$100 meV and induce a neutron spin resonance at the
commensurate AF ordering wave vector that couples with superconductivity. While
the new data collected on the $x=0.096$ sample confirms the overall features of
the earlier work, our careful temperature dependent study of the resonance
reveals that the resonance suddenly changes its $Q$-width below $T_c$ similar
to that of the optimally hole-doped iron pnictides
Ba$_{0.67}$K$_{0.33}$Fe$_2$As$_2$. In addition, we establish the dispersion of
the resonance and find it to change from commensurate to transversely
incommensurate with increasing energy. Upon further electron-doping to
overdoped iron pnictides with $x=0.15$ and 0.18, the resonance becomes weaker
and transversely incommensurate at all energies, while spin excitations above
$\sim$100 meV are still not much affected. Our absolute spin excitation
intensity measurements throughout the Brillouin zone for $x=0.096,0.15,0.18$
confirm the notion that the low-energy spin excitation coupling with itinerant
electron is important for superconductivity in these materials, even though the
high-energy spin excitations are weakly doping dependent.
