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Inelastic neutron scattering is used to probe the collective spin excitations of the near optimally-doped superconductor Ba(Fe1-xCox)2As2 (=0.065). Previous measurements on the antiferromagnetically ordered parents of this material show a strongly anisotropic spin-wave velocity. Here we measure the magnetic excitations up to 80 meV and show that a similar anisotropy persists for superconducting compositions. The dispersive mode measured here connects directly with the spin resonance previously observed in this compound. When placed on an absolute scale, our measurements show that the local- or wavevector- integrated susceptibility is larger in magnitude than that of the ordered parents over the energy range probed.

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