We perform theoretical analysis of polarization-sensitive Raman spectroscopy on NaFe1-xCoxAs, EuFe2As2, SrFe2As2, and Ba(Fe1-xCox)2As2, focusing on two features seen in the B1g 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 B1g 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 scenario for the resonance below Tc. One is the resonance due to development of a pole in the fully renormalized Ising-nematic susceptibility. Another is orbital excitonic scenario, in which spin fluctuations generate attractive interaction between low-energy fermions.
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