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We use polarized inelastic neutron scattering to study low-energy spin excitations and their spatial anisotropy in electron-overdoped superconducting BaFe$_{1.85}$Ni$_{0.15}$As$_{2}$ ($T_c=14$ K). In the normal state, the imaginary part of the dynami c susceptibility, $chi^{primeprime}(Q,omega)$, at the antiferromagnetic (AF) wave vector $Q=(0.5,0.5,1)$ increases linearly with energy for $Ele 13$ meV. Upon entering the superconducting state, a spin gap opens below $Eapprox 3$ meV and a broad neutron spin resonance appears at $Eapprox 7$ meV. Our careful neutron polarization analysis reveals that $chi^{primeprime}(Q,omega)$ is isotropic for the in-plane and out-of-plane components in both the normal and superconducting states. A comparison of these results with those of undoped BaFe$_2$As$_2$ and optimally electron-doped BaFe$_{1.9}$Ni$_{0.1}$As$_{2}$ ($T_c=20$ K) suggests that the spin anisotropy observed in BaFe$_{1.9}$Ni$_{0.1}$As$_{2}$ is likely due to its proximity to the undoped BaFe$_2$As$_2$. Therefore, the neutron spin resonance is isotropic in the overdoped regime, consistent with a singlet to triplet excitation.
Since the discovery of the metallic antiferromagnetic (AF) ground state near superconductivity in iron-pnictide superconductors, a central question has been whether magnetism in these materials arises from weakly correlated electrons, as in the case of spin-density-wave in pure chromium, requires strong electron correlations, or can even be described in terms of localized electrons such as the AF insulating state of copper oxides. Here we use inelastic neutron scattering to determine the absolute intensity of the magnetic excitations throughout the Brillouin zone in electron-doped superconducting BaFe$_{1.9}$Ni$_{0.1}$As$_{2}$ ($T_c=20$ K), which allows us to obtain the size of the fluctuating magnetic moment $<m^2>$, and its energy distribution. We find that superconducting BaFe$_{1.9}$Ni$_{0.1}$As$_{2}$ and AF BaFe$_2$As$_2$ both have fluctuating magnetic moments $<m^2>approx3.2 mu_B^2$ per Fe(Ni), which are similar to those found in the AF insulating copper oxides. The common theme in both classes of high temperature superconductors is that magnetic excitations have partly localized character, thus showing the importance of strong correlations for high temperature superconductivity.
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