We use neutron scattering to investigate spin excitations in Sr(Co$_{1-x}$Ni$_{x})_2$As$_2$, which has a $c$-axis incommensurate helical structure of the two-dimensional (2D) in-plane ferromagnetic (FM) ordered layers for $0.013leq x leq 0.25$. By comparing the wave vector and energy dependent spin excitations in helical ordered Sr(Co$_{0.9}$Ni$_{0.1}$)$_2$As$_2$ and paramagnetic SrCo$_2$As$_2$, we find that Ni-doping, while increasing lattice disorder in Sr(Co$_{1-x}$Ni$_{x})_2$As$_2$, enhances quasi-2D FM spin fluctuations. However, our band structure calculations within the combined density functional theory and dynamic mean field theory (DFT+DMFT) failed to generate a correct incommensurate wave vector for the observed helical order from nested Fermi surfaces. Since transport measurements reveal increased in-plane and $c$-axis electrical resistivity with increasing Ni-doping and associated lattice disorder, we conclude that the helical magnetic order in Sr(Co$_{1-x}$Ni$_{x})_2$As$_2$ may arise from a quantum order-by-disorder mechanism through the itinerant electron mediated Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions.
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