An analysis of phonon anomalies due to d-band effects in transition metal compounds -effects of electron-phonon matrix elements

Effects of the electron-phonon matrix element (EPME) on phonon anomalies in transition metal compounds due to d-band effects are analysed in detail by using a simple model proposed by Gale and Pettifor (1977). Susceptibilities with and without the EPME and an energy change associated with a second derivative of hopping integrals, Delta E 2 , are calculated by using Haydock et al.'s (1972, 1975) recursion method. It is pointed out that the EPME is very important in producing phonon anomalies and an energy change Delta E 2 can enhance them. A discussion from a local bond point of view is also given to elucidate the basic role of the EPME. This argument suggests that the positions of phonon anomalies may be rather insensitive to the choice of parameters.