Comparison of theoretical and experimental dielectric functions: Electron energy-loss spectroscopy and density-functional calculations on skutterudites

We explore the possibility of combining density functional theory (DFT) and electron energy loss spectroscopy (EELS) to determine the dielectric function of materials. As model systems we use the skutterudites ${\mathrm{CoP}}_3$, ${\mathrm{CoAs}}_3$, and ${\mathrm{CoSb}}_3$ which are prototypes for thermoelectric materials. We achieve qualitative agreement between the theoretically and experimentally obtained low energy-loss spectra and dielectric function. Some of the remaining discrepancies may be caused by the challenge of refining the experimental spectra before Kramers-Kronig analysis. However, contrary to what is the case for some crystals with less complicated electronic structure, the DFT calculated plasmon energies deviate significantly from the experimental values. The great accuracy with which the plasmon energy can be determined by EELS, suggests that this technique may provide valuable inputs in further efforts to improve DFT calculations. The use of EELS as the experimental technique may become particularly powerful in studies of small volumes of materials.

Figure 1

In the raw data obtained from the EELS experiment (before deconvolution), multiple plasmons are observed. Here is shown an unprocessed experimental spectrum from ${\mathrm{CoAs}}_3$ where we observe a plasmon energy of slightly more than $20\mathrm{eV}$.

Figure 2

Example of the zero-loss peak removal and Fourier-log deconvolution. The unprocessed raw data is shown with a fully drawn line, while the fitted zero-loss peak is the dotted line. The resulting spectrum after subtraction of the zero loss peak and deconvolution is shown with a dashed line.

Figure 3

(Color online) Total and local projected density of states for ${\mathrm{CoP}}_3$, ${\mathrm{CoAs}}_3$, and ${\mathrm{CoSb}}_3$. The total density of states for ${\mathrm{CoP}}_3$ was published in a previous study (Ref. 47).

Figure 4

(Color online) Experimental and theoretical low energy-loss spectra for the three skutterudites. (a) Experimental spectra showing a single plasmon peak. (b) Theoretical spectra. The energy loss peaks associated with the As $M_{4,5}$ transitions and the Sb $N_{4,5}$ transitions are visible in both the experimental and theoretical spectra.

Figure 5

The experimental (fully drawn line), and theoretical energy-loss spectra of (a) ${\mathrm{CoP}}_3$, (b) ${\mathrm{CoAs}}_3$, and (c) ${\mathrm{CoSb}}_3$. The theoretical spectra have been calculated with (dashed) and without (dotted) a $0.3\mathrm{eV}$ Lorentzian broadening. The relative scaling of the theoretical data with respect to the experimental data is arbitrary, no direct comparison of the absolute intensity is possible.

Figure 6

(a) The real and (b) imaginary parts of the dielectric function of ${\mathrm{CoAs}}_3$. The experimentally obtained function is shown with a fully drawn line, while the theoretical function is a dashed line.