  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.
