Ultrasonic Study of the Stability of the Charge Ordering in (Nd_(0.75)Na_(0.25))_(1-x)(Nd_(0.5)Ca_(0.5))_xMnO_3

The electrical resistivity, magnetization, and ultrasonic velocity were investigated systematically in polycrystalline (Nd0.75Na0.25)1-x(Nd0.5Ca0.5)xMnO3(x=0, 0.25, 0.5, 0.75, 1). A charge ordering transition was observed in all samples through resistivity and magnetization measurements. With increasing Na content, the charge ordering transition temperature (TCO) shifts to lower temperature, the magnetization of the system is strengthened and charge ordering becomes more unstable and short-ranged. It is found that the longitudinal sound velocity shows a dramatic softening and stiffening around TCO.The ultrasonic anomaly near TCO indicates the existence of strong electron-phonon interaction, which originates from Jahn-Teller effect of Mn3+. By fitting the experimental longitudinal modulus above TCO with the cooperative Jahn-Teller theory, one can establish that the Jahn-Teller coupling energy EJT decreases with increasing Na content. The analysis of experimental results suggests that the charge mismatch should be the main reason for the suppression of the charge ordering and the weakening of cooperative Jahn-Teller effect.