Coupling of the A1g As-phonon to magnetism in iron pnictides

Charge, spin, and lattice degrees of freedom are strongly entangled in iron superconductors. A neat consequence of this entanglement is the behavior of the A1g As-phonon resonance in the different polarization symmetries of Raman spectroscopy when undergoing the magnetostructural transition. In this work, we show that the observed behavior could be a direct consequence of the coupling of the phonons with the electronic excitations in the anisotropic magnetic state. We discuss this scenario within a five-orbital tight-binding model coupled to phonons via the dependence of the Slater-Koster parameters on the As position. We identify two qualitatively different channels of the electron-phonon interaction: a geometrical one related to the Fe-As-Fe angle α and another one associated with the modification upon As displacement of the Fe-As energy integrals pdσ and pdπ. While both mechanisms result in a finite B1g response, the behavior of the phonon intensity in the A1g and B1g Raman polarization geometries is qualitatively different when the coupling is driven by the angle or by the energy integral dependence. We discuss our results in view of the experimental reports.