THz electrodynamics of BaFe${}_{1.91}$Ni${}_{0.09}$As${}_2$ film analyzed in the framework of multiband Eliashberg theory

The temperature dependences of the plasma frequency, superfluid density and London penetration depth were determined from terahertz spectra of conductivity and dielectric permittivity of BaFe${}_{1.91}$Ni${}_{0.09}$As${}_2$ film with critical temperature $T_c=19.6$~K. Part of experimental data were analyzed within a simple three-band Eliashberg model where the mechanism of superconducting coupling is mediated by antiferromagnetic spin fluctuations, whose characteristic energy ${\mathrm{\Omega }}_0$ scales with $T_c$ according to the empirical law ${\mathrm{\Omega }}_0=4.65k_B{T}_c$, and with a total electron-boson coupling strength ${\lambda }_{tot}=2.17$.