Effect of inelastic scattering on the nuclear magnetic relaxation rate 1/T ₁T in iron-based superconductors

We present a microscopic study of the nuclear magnetic relaxation rate 1/T ₁ based on the five-orbital model for iron-based superconductors. We mainly discuss the effect of the inelastic quasi-particle damping rate γ due to many-body interaction on the size of the coherence peak, for both s ₊₊ and s _±-wave superconducting states. We focus on Ba(Fe _1xCo _x) ₂As ₂, and systematically evaluate γ in the normal state from the experimental resistivity, from optimally to overdoped compounds. Next, γ in the superconducting state is calculated microscopically based on second-order perturbation theory. In optimally doped compounds (T _c30K), it is revealed that the coherence peak on 1/T ₁T is completely suppressed due to large γ for both s ₊₊ and s _±-wave states. On the other hand, in heavily overdoped compounds with T _c<10K, the coherence peak could appear for both pairing states, since γ at T _c is quickly suppressed in proportion to . By making careful comparison between theoretical and experimental results, we conclude that it is difficult to discriminate between s ₊₊ and s _±-wave states from the present experimental results.