Eliashberg analysis of optical spectra reveals a strong coupling of charge carriers to spin fluctuations in doped iron-pnictide ${\text{BaFe}}_2{\text{As}}_2$ superconductors

The temperature and frequency dependences of the optical conductivity of Co-doped ${\text{BaFe}}_2{\text{As}}_2$ are analyzed and the electron-boson spectral density ${\alpha }^{2}F\left(\omega \right)$ are extracted using Eliashberg’s formalism. For the normal state at $T=30\text{K}$ there is a relatively sharp and large peak around 10 meV and a secondary smaller and broader peak centered around 50 meV with the spectrum extending to high energies beyond the maximum phonon energy. The electron-boson mass enhancement parameter is 4.4, a value more consistent with spin-fluctuation scattering rather than with phonons. In addition the spectrum is found to evolve with temperature toward a less structured background at higher energies as in the spin susceptibility.

Figure 1

(Color online) Results of the inversion calculations of the electron-boson spectral function ${\alpha }^{2}F\left(\omega \right)$ for $\text{Ba}{\left({\text{Fe}}_{0.92}{\text{Co}}_{0.08}\right)}_2{\text{As}}_2$ at different temperatures in the normal state. (a) Measured real part of the optical conductivity (solid lines) compared with computational results (dashed lines). (b) Frequency-dependent optical scattering rate obtained by the extended Drude analysis of the conductivity data plotted in panel (a) (solid lines) compared with the calculated ${\tau }^{-1}\left(\omega \right)$ according to Eq. (6) (dashed lines) with a constant contribution of ${\tau }_{\text{imp}}^{-1}=304{\text{cm}}^{-1}$ due to impurities. (c) The corresponding electron-boson spectral density ${\alpha }^{2}F\left(\omega \right)$ as the result of an unbiased MEM inversion.

Figure 2

(Color online) The Eliashberg function ${\alpha }^{2}F\left(\omega \right)$ for $\text{Ba}{\left({\text{Fe}}_{0.92}{\text{Co}}_{0.08}\right)}_2{\text{As}}_2$ as a function of the boson energy $\hslash \omega$ for several temperatures as a result of a biased MEM inversion.

Figure 3

(Color online) The mass enhancement factor $\lambda \left(T\right)$ for $\text{Ba}{\left({\text{Fe}}_{0.92}{\text{Co}}_{0.08}\right)}_2{\text{As}}_2$ as a function of temperature $T$ (left-hand scale applies). The solid (black) squares indicate results of an unbiased MEM inversion and the open (black) squares refer to the biased MEM inversion. Furthermore, we show the shift of the position of the main peak with temperature (right-hand scale applies). The solid (red) triangles refer to the unbiased MEM inversion while the open (red) triangles refer to the biased MEM inversion.