Adiabatic Electron-Phonon Interaction at High Temperature in A15 Compounds

Inelastic neutron scattering was used to measure the phonon densities of states of the A15 compounds V$_{3}$Si, V$_{3}$Ge, and V$_{3}$Co at temperatures from 10 to 1273 K. It was found that phonons in V$_{3}$Si and V$_{3}$Ge, which are superconducting at low temperatures, exhibit an anomalous stiffening with increasing temperature, whereas phonons in V$_{3}$Co have a normal softening behavior. First-principles calculations show that this anomalous increase in phonon frequencies at high temperatures originates with an adiabatic electron-phonon coupling mechanism. The anomaly is caused by the thermally induced broadening of sharp peaks in the electronic density of states of V$_{3}$Si and V$_{3}$Ge, which tends to decrease the electronic density at the Fermi level. These results show that the adiabatic electron-phonon coupling can influence the phonon thermodynamics at temperatures exceeding 1000 K.