Effect of electron-doping on spin excitations of underdoped BaFe$_{1.96}$Ni$_{0.04}$As$_{2}$

We use neutron scattering to study magnetic order and spin excitations in BaFe$_{1.96}$Ni$_{0.04}$As$_{2}$. On cooling, the system first changes the lattice symmetry from tetragonal to orthoromhbic near $\sim$97 K, and then orders antiferromagnetically at $T_N=91$ K before developing weak superconductivity below $\sim$15 K. Although superconductivity appears to co-exist with static antiferromagnetic order from transport and neutron diffraction measurement, inelastic neutron scattering experiments reveal that magnetic excitations do not respond to superconductivity. Instead, the effect of electron-doping is to reduce the c-axis exchange coupling in BaFe$_2$As$_2$ and induce quasi two-dimensional spin excitations. These results suggest that transition from three-dimensional spin waves to two-dimensional spin excitations by electron-doping is important for the separated structural/magnetic phase transitions and high-temperature superconductivity in iron arsenides.