Two-phonon contributions to the inelastic x-ray scattering spectra of ${\mathrm{MgB}}_2$

Two-phonon contributions to meV-resolved, inelastic x-ray scattering spectra of ${\mathrm{MgB}}_2$ at $300\mathrm{K}$ are identified, in good agreement, in both intensity and energy, with a harmonic calculation using the force constant matrix from ab initio calculations. This contribution impacts the determination of the linewidth of the $E_{2g}$ phonon mode that is so important for the high $T_{\mathrm{c}}$ of this material. To the best of our knowledge, this is the first observation of peaks in measurements of phonon dispersion $(q>0)$ due to two-phonon scattering in a non-rare-gas solid.

Figure 1

(Color online) Comparison of data and calculation at 300 K, $\mathbf{Q}=(-0.0203.32)$. In (a) the ab initio results for the one- and two-phonon contributions are shown, while (b) shows a fit with the one-phonon energies allowed to shift, but with the two-phonon contribution held in fixed ratio to the one-phonon one. See text.

Figure 2

Calculated two-phonon contribution at $300\mathrm{K}$ in different symmetry directions.

Figure 3

(Color online) Spectra along $\Gamma \text{−}\mathrm{M}$. Note the two-phonon contribution (solid, black) is not negligible as compared to the $E_{2g}$ mode (thick, green). Pure calculation is shown in (a), while data with fits are shown in (b). See text for details.

Figure 4

(Color online) Calculated and measured $E_{2g}$ linewidth. Line and triangles (red) are from Ref. 6 while the filled circles (green) are the present results. See text.