Electron-phonon coupling and longitudinal sound velocity of La0.5Ca0.5MnO3

In this paper, the microscopic theory of the relative change in velocity of sound with temperature of La_0.5Ca_0.5MnO₃ is reported. The phonon Green function is calculated using the Green function technique of Zubarev in the limit of zero wave vector and low temperature. The lattice model electronic Hamiltonian in the presence of the phonon interaction with hybridization between the conduction electrons and the l-electrons is used. The relative change in velocity of sound at various temperatures is studied for different model parameters, namely the position of the l-level, the effective phonon coupling strength and hybridization strength. The phonon anomalies observed experimentally at different temperatures are explained theoretically. An abrupt change in velocity at Neel temperature (T_N) is observed clearly. It is observed that different parameters influence the velocity of sound.