Raman scattering in ${\mathrm{V}}_3$Si, ${\mathrm{V}}_3$Ge, ${\mathrm{Nb}}_3$Sn, and ${\mathrm{Nb}}_3$Sb: Damping of the $E_g$ optical phonon by interband electronic excitations

We report measurements of the $E_g$ optical phonon in ${\mathrm{V}}_3$Ge, ${\mathrm{V}}_3$Si, and ${\mathrm{Nb}}_3$Sb, and of the $T_{2g}$ optical phonon in ${\mathrm{Nb}}_3$Sb measured from 9 to 400 K. The $E_g$ optical phonon in ${\mathrm{V}}_3$Ge has an anomalous width, shape, and temperature dependence, similar to that seen in ${\mathrm{V}}_3$Si and ${\mathrm{Nb}}_3$Sn. Both the $E_g$ and $T_{2g}$ optical phonons in ${\mathrm{Nb}}_3$Sb, on the other hand, show no anomalous behavior and can be understood in terms of simple anharmonic interactions. We point out the existence of a linear correlation between the magnetic susceptibility and the $E_g$ phonon linewidth for ${\mathrm{V}}_3$Si, ${\mathrm{V}}_3$Ge, and ${\mathrm{Nb}}_3$Sn. Scaling arguments show that the $E_g$ phonon linewidth of these three compounds exhibits very similar temperature dependences, with the remaining small differences yielding information concerning the distribution of the joint electronic density of states with respect to the Fermi level. These anomalies are attributed to coupling of the $E_g$ phonon to interband electronic transitions between the flat bands emanating from the ${\Gamma }_{12}$ level. A simple model of the interaction quantitatively reproduces the temperature dependence of the $E_g$ phonon linewidth.