  We use inelastic neutron scattering to systematically investigate the
Ni-doping evolution of the low-energy spin excitations in BaFe2-xNixAs2
spanning from underdoped antiferromagnet to overdoped superconductor (0.03< x <
0.18). In the undoped state, the low-energy (<80 meV) spin waves of BaFe2As2
form transversely elongated ellipses in the [H, K] plane of the reciprocal
space. Upon Ni-doping, the c-axis magnetic exchange coupling is rapidly
suppressed and the momentum distribution of spin excitations in the [H, K]
plane is enlarged in both the transverse and longitudinal directions with
respect to the in-plane AF ordering wave vector of the parent compound. As a
function of increasing Ni-doping x, the spin excitation widths increase
linearly but with a larger rate along the transverse direction. These results
are in general agreement with calculations of dynamic susceptibility based on
the random phase approximation (RPA) in an itinerant electron picture. For
samples near optimal superconductivity at x= 0.1, a neutron spin resonance
appears in the superconducting state. Upon further increasing the
electron-doping to decrease the superconducting transition temperature Tc, the
intensity of the low-energy magnetic scattering decreases and vanishes
concurrently with vanishing superconductivity in the overdoped side of the
superconducting dome. Comparing with the low-energy spin excitations centered
at commensurate AF positions for underdoped and optimally doped materials
(x<0.1), spin excitations in the over-doped side (x=0.15) form transversely
incommensurate spin excitations, consistent with the RPA calculation.
Therefore, the itinerant electron approach provides a reasonable description to
the low-energy AF spin excitations in BaFe2-xNixAs2.
