Raman resonance in iron-based superconductors: The magnetic scenario

We perform theoretical analysis of polarization-sensitive Raman spectroscopy on NaFe$_{1-x}$Co$_x$As, EuFe$2$As$_2$, SrFe$_2$As$_2$, and Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$, focusing on two features seen in the $B_{1g}$ symmetry channel (in one Fe unit cell notation): the strong temperature dependence of the static, uniform Raman response in the normal state and the existence of a collective mode in the superconducting state. We show that both features can be explained by the coupling of fermions to pairs of magnetic fluctuations via the Aslamazov-Larkin process. We first analyze magnetically-mediated Raman intensity at the leading two-loop order and then include interactions between pairs of magnetic fluctuations. We show that the full Raman intensity in the $B_{1g}$ channel can be viewed as the result of the coupling of light to Ising-nematic susceptibility via Aslamazov-Larkin process. We argue that the singular temperature dependence in the normal state is the combination of the temperature dependencies of the Aslamazov-Larkin vertex and of Ising-nematic susceptibility. We discuss two scenarios for the resonance below $T_c$. In one, the resonance is due to the development of a pole in the fully renormalized Ising-nematic susceptibility. The other is the orbital excitonic scenario, in which spin fluctuations generate an attractive interaction between low-energy fermions.