Cooper pairing in the iron-based high-Tc superconductors is often conjectured to involve bosonic fluctuations. Among the candidates are antiferromagnetic spin-fluctuations and d-orbital fluctuations amplified by phonons. Any such electron-boson interaction should alter the electrons `self-energy, and then become detectable through consequent modifications in the energy dependence of the electrons momentum and lifetime. Here we introduce a theoretical/experimental approach aimed at identifying the relevant fluctuations of iron-based superconductors by measuring effects of their self-energy. We use quasiparticle interference (QPI) imaging techniques in LiFeAs to reveal strongly momentum-space anisotropic self-energy signatures that are focused along the Fe-Fe (interband scattering) direction, where the spin fluctuations of LiFeAs are concentrated. These effects coincide in energy with perturbations to the density-of-states N(omega) usually associated with the Cooper pairing interaction. We show that all the measured phenomena comprise the predicted QPI `fingerprint of a self-energy due to antiferromagnetic spin-fluctuations, thereby distinguishing them as the predominant electron-boson interaction.
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