Nonharmonic phonons in MgB2 at elevated temperatures

MgB₂ has attracted widespread attention due to its high superconductive transition temperature of 39 K, which decreases abruptly upon doping. It has been established that superconductivity in this material has a two-band character with unusually strong, anisotropic electron-phonon coupling. Nevertheless, the importance of phonon anharmonicity is not fully understood and remains controversial, while the effect of the electron-phonon coupling at high temperatures had not been previously assessed. For the present work, inelastic neutron scattering was used to measure phonon spectra in MgB₂ and Mg_0.75Al_0.25B₂ from 7 to 750 K. The thermal expansion was measured from 300 to 900 K using x-ray diffraction. First-principles calculations of phonons with a linear response method were performed at multiple unit cell volumes, and the Helmholtz free energy was minimized to obtain the lattice parameters and phonon dynamics at elevated temperature in the quasiharmonic approximation. Most of the temperature dependence of the phonon density of states could be understood with the quasiharmonic approximation, although there was also significant thermal broadening of the phonon spectra which we attributed to phonon anharmonicity. In comparison to Mg_0.75Al_0.25B₂, in the energy range of 60 to 80 meV the experimental phonon spectra from MgB₂ showed a nonmonotonic change with temperature around 500 K. This effect may originate from a change with temperature of the adiabatic electron-phonon coupling. Neither the phonon anharmonicity nor the electron-phonon interaction makes a substantial contribution to the thermodynamic stability of MgB2.