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

We present a detailed analysis of resonant inelastic x-ray scattering from ${\text{Fe}}_{1.087}\text{Te}$ 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 noninteracting gas of fermions. Furthermore, we find that limitations to this many-body electron-only theory are realized at high Raman shift, where an exponential line shape reveals an energy scale not present in these considerations. This regime, identified as emission, requires considerations of lattice degrees of freedom to understand the line shape. We argue that both observations are intrinsic general features of many-body physics of metals.

Figure 1

(Color online) (a) False color plot of the RIXS data, plotted versus incident and scattered photon energies, with elastic peak subtracted and linear interpolation applied between the data points. (b) RIXS spectra in detail. The solid lines show the fit to Eq. (1), the two vertical dashed lines indicate the scattered photon energies ${\omega }_{pk}^{\prime }$ (left) and ${\omega }_k^{\prime }$ (right). Triangles point to the 0.9 eV feature in the Raman-dispersing, subthreshold regime. (c) Total fluorescence yield (TFY) and total electron yield (TEY) spectra, showing the two-peak $L_3$ structure.

Figure 2

(Color online) (a) RIXS line scans $\omega =706.4$ and 708.4 eV, showing the linear and exponential behavior regimes. (b) Scaled spectra, showing the collapse at high frequencies for a single value of the decay constant $a=0.472{\text{eV}}^{-1}$. Inset: X-ray emission spectra (arb. units) from the $\text{Li}K$ (Ref. 16), $\text{Si}K$ (Ref. 14), $\text{Fe}{L}_3$ (Ref. 15), and $\text{Dy}{L}_3$ edges (Ref. 13) of $\text{Dy}{\left({\text{NO}}_3\right)}_3$, measured in energy relative to the edge, showing approximate exponential behavior over a 4–17 eV range.

Figure 3

(Color online) Parameters deduced from fitting to Eq. (1), along with the TFY spectrum. In (a), the dashed line corresponds to the expression $A{\left\{\text{arctan}\left[\left(\omega -{\omega }_0\right)/\gamma \right]+\pi /2\right\}}^2$. In (d), the dashed line corresponds to a fit to $\Delta \omega /{\left(\omega -{\omega }_{th}\right)}^{2+2\eta }$ with the threshold determined from the extrapolation of the dashed line in (b).

Figure 4

(Color online) (a) Cuts along the directions indicated in Fig. 1a versus incident (unprimed letters) or scattered (primed letters) energy. [(b) and (c)] Test of scaling relation for all measured spectra with two different threshold values. The colors are the same as in Fig. 1b with the small-signal data with $\omega <703.9\text{eV}$ in black. Dashed lines are near-threshold spectra and not necessarily expected to obey the scaling relation.