We report a combined study of the spin resonances and superconducting gaps for underdoped (Tc=19 K), optimally doped (Tc=25 K), and overdoped (Tc=19 K) Ba(Fe1-xCox)2As2 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 an 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.

In complex materials various interactions have important roles in determining electronic properties. Angle-resolved photoelectron spectroscopy (ARPES) is used to study these processes by resolving the complex single-particle self-energy and quantifying how quantum interactions modify bare electronic states. However, ambiguities in the measurement of the real part of the self-energy and an intrinsic inability to disentangle various contributions to the imaginary part of the self-energy can leave the implications of such measurements open to debate. Here we employ a combined theoretical and experimental treatment of femtosecond time-resolved ARPES (tr-ARPES) show how population dynamics measured using tr-ARPES can be used to separate electron-boson interactions from electron-electron interactions. We demonstrate a quantitative analysis of a well-defined electron-boson interaction in the unoccupied spectrum of the cuprate Bi₂Sr₂CaCu₂O_8+x characterized by an excited population decay time that maps directly to a discrete component of the equilibrium self-energy not readily isolated by static ARPES experiments.