  We report a combined study of the spin resonances and superconducting gaps
for underdoped ($T_c=19$ K), optimally doped ($T_c=25$ K), and overdoped
($T_c=19$ K) Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ single crystals with inelastic
neutron scattering and angle resolved photoemission spectroscopy. We find a
quasi two dimensional spin resonance whose energy scales with the
superconducting gap in all three compounds. In addition, anisotropic low energy
spin excitation enhancements in the superconducting state have been deduced and
characterized for the under and optimally doped compounds. Our data suggest
that the quasi two dimensional spin resonance is a spin exciton that
corresponds to the spin singlet-triplet excitations of the itinerant electrons.
However, the intensity enhancements of the anisotropic spin excitations are
dominated by the out-of-plane spin excitations of the ordered moments due to
the suppression of damping in the superconducting state. Hence we offer a new
interpretation of the double energy scales differing from previous
interpretations based on anisotropic superconducting energy gaps, and
systematically explain the doping-dependent trend across the phase diagram.
