Spin gap and magnetic resonance in superconducting BaFe$_{1.9}$Ni$%_{0.1}$As$_{2}$

We use neutron spectroscopy to determine the nature of the magnetic excitations in superconducting BaFe$_{1.9}$Ni$_{0.1}$As$_{2}$ ($T_{c}=20$ K). Above $T_{c}$ the excitations are gapless and centered at the commensurate antiferromagnetic wave vector of the parent compound, while the intensity exhibits a sinusoidal modulation along the c-axis. As the superconducting state is entered a spin gap gradually opens, whose magnitude tracks the $T$-dependence of the superconducting gap observed by angle resolved photoemission. Both the spin gap and magnetic resonance energies are temperature \textit{and} wave vector dependent, but their ratio is the same within uncertainties. These results suggest that the spin resonance is a singlet-triplet excitation related to electron pairing and superconductivity.