Itinerant spin excitations and superconductivity in BaFe$_{\mathrm{2-x}}$Ni$_{\mathrm{x}}$As$_{\mathrm{2}}$

High-temperature superconductivity in iron pnictides emerges from electron or hole doped parent compounds with antiferromagnetic order, which is argued to be associated with both the presence of high-energy spin excitations and a coupling between low-energy spin excitations and itinerant electrons. Recently, we have used time-of-flight neutron spectroscopy to carefully map out the spin excitations in the electron overdoped BaFe$_{\mathrm{2-x}}$Ni$_{\mathrm{x}}$As$_{\mathrm{2}}$ especially around the zone boundary of superconductivity. We have found a spin gap actually emerges after the vanishing of zero resistivity and directly responses to the disappearance of superconductivity. Further polarized neutron analysis indicate that the spin gap actually is anisotropic, and the longitudinal mode of spin fluctuations, as a hallmark of the itinerant magnetism from Fermi surface nesting, is totally eliminated together with the hole pockets near the electron-overdoped zone boundary of superconductivity. Our results suggest that the itinerant spin excitations originated from Fermi surface nesting are crucial to the superconductivity in iron pnictides.