Coupling of the AsA1gphonon to magnetism in iron pnictides

Abstract

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 $\ensuremath{\alpha}$ and another one associated with the modification upon As displacement of the Fe-As energy integrals $pd\ensuremath{\sigma}$ and $pd\ensuremath{\pi}$. 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.