We study anharmonic effects in $\mathrm{Mg}{\mathrm{B}}_2$ by comparing inelastic x-ray and Raman scattering together with ab initio calculations. Using high-statistics and high-$q$-resolution measurements we show that the $E_{2g}$-mode linewidth is independent of temperature along $\Gamma \text{−}A$. We show, contrary to previous claims, that the Raman-peak energy decreases as a function of increasing temperature, a behavior inconsistent with all the anharmonic ab initio calculations of the $E_{2g}$ mode at $\Gamma$ available in the literature. These findings and the excellent agreement between the x-ray-measured and ab initio—calculated phonon spectra suggest that anharmonicity is not the main mechanism determining the temperature behavior of the Raman-peak energy. The Raman-$E_{2g}$-peak position and linewidth can be explained by large dynamical effects in the phonon self-energy. In light of the present findings, the commonly accepted explanation of the reduced isotope effect in terms of anharmonic effects needs to be reconsidered.

• Received 16 January 2007

DOI:https://doi.org/10.1103/PhysRevB.75.174508