Coupling of the As A1g 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 A(1g) 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 alpha and another one associated with the modification upon As displacement of the Fe-As energy integrals pd sigma and pd pi. While both mechanisms result in a finite B-1g response, the behavior of the phonon intensity in the A(1g) and B-1g 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.