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We use polarized inelastic neutron scattering to study low-energy spinexcitations and their spatial anisotropy in electron-overdoped superconductingBaFe$_{1.85}$Ni$_{0.15}$As$_{2}$ ($T_c=14$ K). In the normal state, theimaginary part of the dynamic susceptibility, $\chi^{\prime\prime}(Q,\omega)$,at the antiferromagnetic (AF) wave vector $Q=(0.5,0.5,1)$ increases linearlywith energy for $E\le 13$ meV. Upon entering the superconducting state, a spingap opens below $E\approx 3$ meV and a broad neutron spin resonance appears at$E\approx 7$ meV. Our careful neutron polarization analysis reveals that$\chi^{\prime\prime}(Q,\omega)$ is isotropic for the in-plane and out-of-planecomponents in both the normal and superconducting states. A comparison of theseresults with those of undoped BaFe$_2$As$_2$ and optimally electron-dopedBaFe$_{1.9}$Ni$_{0.1}$As$_{2}$ ($T_c=20$ K) suggests that the spin anisotropyobserved in BaFe$_{1.9}$Ni$_{0.1}$As$_{2}$ is likely due to its proximity tothe undoped BaFe$_2$As$_2$. Therefore, the neutron spin resonance is isotropicin the overdoped regime, consistent with a singlet to triplet excitation.

Polarized neutron scattering studies of magnetic excitations in electron-overdoped superconducting BaFe$_{1.85}$Ni$_{0.15}$As$_{2}$