Crossover from spin-waves to diffusive spin excitations in underdoped   Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$
  Using inelastic neutron scattering, we show that the onset of superconductivity in underdoped Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ coincides with a crossover from well-defined spin waves to overdamped and diffusive spin excitations. This crossover occurs despite the presence of long-range stripe antiferromagnetic order for samples in a compositional range from x=0.04-0.055, and is a consequence of the shrinking spin-density wave gap and a corresponding increase in the particle-hole (Landau) damping. The latter effect is captured by a simple itinerant model relating Co doping to changes in the hot spots of the Fermi surface. We argue that the overdamped spin fluctuations provide a pairing mechanism for superconductivity in these materials. 
G. S. Tucker, R. M. Fernandes, D. K. Pratt, A. Thaler, N. Ni, K.   Marty, A. D. Christianson, M. D. Lumsden, B. C. Sales, A....
cond-mat.supr-con