Spin Excitations in Superconducting BaFe$_{2-x}$Co$_{x}$As$_{2}$

We present neutron scattering measurements on singe crystals of superconducting BaFe$_{2-x}$Co$_{x}$As$_{2}$. For optimally doped samples (x=0.16, T$_{C}$=21 K) the spin waves are gapless above T$_{C}$, while a gap opens below T$_{C}$ with the appearance of a spin resonance at an energy of 8.6 meV. The dispersion of the spin excitations is weak along the c-axis, but the in-plane dispersion is still very steep indicating a reduction in dimensionality of the spin excitations when compared to those found in the parent compound. On the other hand, in underdoped samples (x=0.08, T$_{C}$=11 K) the spin waves display a gap above T$_{C}$ with anisotropic three-dimensional interactions. Below T$_{C}$ no additional gap is observed for energies greater than 2 meV. However, below T$_{C}$ a spin resonance at 4.5 meV appears simultaneously with a reduction in the magnetic Bragg peak intensity suggesting that the spectral weight required for the spin resonance arises due to competition between superconductivity and magnetism.