Neutron Scattering Experiment on Doping Dependence of Spin Excitations in Superconducting BaFe$_{2-x}$Ni$_{x}$As$_{2}$

Understanding the interplay between spin fluctuation and superconductivity in high transition temperature (Tc) superconductors is important because spin fluctuations may mediate electron paring for superconductivity. In copper-oxide based superconductor (cuprates), resonance modes are found at antiferromagnetic (AF) ordering vector Q = (1/2, 1/2), which are dispersionless along the c-direction and directly coupled to Tc. In the FeAs-based superconductors, although the energies of the spin resonance are also proportional to Tc, our recently experiments found that the resonance has c-axis dispersion and display distinct energies at Q$_{z}$=0 and 1. In this paper, we use inelastic neutron scattering to study electron-doping dependence of the resonance energy in underdoped and overdoped superconducting BaFe$_{2-x}$Ni$_{x}$As$_{2}$ (x=0.075, 0.15). We find that there exists similar energy dispersion in both underdoped and overdoped samples, suggesting that the c-axis coupling in BaFe$_{2-x}$Ni$_{x}$As$_{2}$ is weakly doping dependent. We discuss the microscopic origin for such behavior.