Evidence for core-hole-mediated inelastic x-ray scattering from metallic Fe$_{1.087}$Te

We present a detailed analysis of resonant inelastic scattering (RIXS) from Fe$_{1.087}$Te with unprecedented energy resolution. In contrast to the sharp peaks typically seen in insulating systems at the transition metal $L_3$ edge, we observe spectra which show different characteristic features. For low energy transfer, we experimentally observe theoretically predicted many-body effects of resonant Raman scattering from a non-interacting gas of fermions. Furthermore, we find that limitations to this many-body electron-only theory are realized at high Raman shift, where an exponential lineshape reveals an energy scale not present in these considerations. This regime, identified as emission, requires considerations of lattice degrees of freedom to understand the lineshape. We argue that both observations are intrinsic general features of many-body physics of metals.