  Polarized inelastic neutron scattering experiments were performed to study
magnetic excitations in the normal and superconducting phases of Co-underdoped
BaFe$_2$As$_2$, which exhibits coexistence of antiferromagnetic order and
superconductivity. In the normal state the antiferromagnetic order results in
broadened spin gaps opening in all three spin directions that are reminiscent
of the magnetic response in pure antiferromagnetic BaFe$_2$As$_2$. In
particular longitudinal excitations exhibit a large gap. In the superconducting
state we find two distinct resonance excitations, which both are anisotropic in
spin-space, and which both do not appear in the longitudinal polarization
channel. This behavior contrasts to previous polarized neutron results on
samples near optimum or higher doping. The gap in the longitudinal fluctuations
arising from the antiferromagnetic order seems to be sufficiently larger than
twice the superconducting gap to suppress any interplay with the
superconducting state. This suppressed low-energy weight of longitudinal
fluctuations can explain the reduced superconducting transition temperature in
underdoped BaFe$_2$As$_2$ and indicates that the coexistence of
antiferromagnetism and superconductivity occurs locally.
