Important information on the lattice dynamics can be obtained from the sound velocity v_s(T) measurement. For La_1-XSr_XMnO₃ (LSMO) and La_1-XCa_XMnO₃ (LCMO), we reported the sound velocity anomalies associated with charge ordering. For the lower hole concentrations, the distribution of the temperature T*, at which v_s anomaly occurs, was centered at X=1/8, which was consistent with the polaron-ordered phase reported by the neutron diffraction analyses. Fig.1 shows the temperature dependence of the sound velocity for the LSMO system (X=0.15). The v_s anomalies were observed at the FM transition temperature T_c=170K and at the characteristic temperature T*=140K. Fig.2 shows the phase diagram of the LSMO system. T* was centered at X=1/8 and the similar behavior was also observed in the LCMO system.

left:Fig,1:The sound velocity for the LSMO system (X=0.15) right:Fig.2: Determined phase diaagram of the LSMO system by the v_s(T) measurements

Fig. 3 shows the normalized sound velocity v_s(T)/v_s(300K) for the LCMO (X=0.30~0.80) samples. For the X=0.30 sample, v_s(T) showed an abrupt upturn below the FM transition temperature T_c. However, the v_s(T) upturn becomes moderate for X=0.40 and 0.45. For the X=0.48, 0.50, 0.55 samples, where the charge order (CO) phase is observed, the anomalous v_s(T) upturn was observable below the charge ordered temperature T_CO with a slight v_s(T) softening just above T_CO. The v_s softening becomes deeper with increasing the Ca content X (=0.60, 0.67). In this way, the v_s behavior in the CO phase shows the characteristic temperature dependence at X=0.50, 0.67 and 0.75, which may results from the charge stripe structure observed by the electron diffraction.

Fig,3:The normalized sound velocity v_s(T)/v_s(300K) for the LCMO system (X=0.30~0.95)

As recent revived studies on perovskite-based manganese have confirmed, it has been widely recognized that the local lattice distortions of the MnO₆ octahedra play an important role in determining the transport properties of the doped holes and the complex behaviors of magnetic and structural transitions. The thermal conductivity k is a valuable tool to investigate the effect of the lattice dynamics near the phase transitions of the manganite system. Fig.4(a) shows the temperature dependence of the thermal conductivity k(T) for the LCMO system (X=0~0.35). For the ferromagnetic X<0.15 sample, whose electrical resistivity r(T) behaves nonmetallic, k(T) is low and no anomaly is observed around T_c. k(T) of La_0.85Ca_0.15MnO₃ suggests the existence of very strong phonon scattering over the entire temperature range. On the other hand, for the X>0.20 samples which show the FM metallic behavior, we can see that the k(T) shows an enhancement below T_c, which increases and becomes step-like just below T_c for X=0.25 and 0.30. The k(T) enhancement should not be linked only to the ferromagnetism but rather to the electronic transition to metallic state which suppresses significantly the amplitude of Jahn-Teller (J-T) distortion.
Fig.4(b) shows the thermal conductivity k(T) for the X=0.40~0.60 samples. For the X=0.40 and 0.45 samples which are FM and metallic, k(T) shows the upturn below T_c, though the step-like jump below T_c almost disappears. Because of reduction in J-T active Mn³⁺ ion concentration with increasing X, the effect of relaxation of the local lattice distortion may be somewhat weakened in these samples. For the X=0.50 sample, in which the FM state vanishes and the CO state appears, the magnitude of k(T) drastically decreases and the k(T) reduction is observable around the CO transition temperature T_CO (=230K). Thus, the k(T) behaviors of X=0.45 and 0.50 samples show a clear contrast reflecting the difference in the ordered phase. The X=0.60 sample shows the similar k(T) behavior as X=0.50. The thermal dilatation dL(T)/L for X=0.45 decreases below T_c with decreasing temperature, while for the CO samples (X>0.50), the thermal dilatation shows quite a opposite character; dL(T)/L abruptly increases below T_CO. The increase of dL(T)/L below T_CO in contrast to the decrease below the Curie temperature T_c of the metallic samples suggests that the lattice distortion rather increases below T_CO. It should also be noticed that r(T) increases below T_CO, which may inhibit the relaxation of the J-T distortion due to mobile carriers. Therefore the k(T) reduction below T_CO may come from the increase of the lattice distortion.

Fig,4:Thermal conductivity k(T) for the LCMO system

　The phase diagram was proposed for the LSMO and LCMO systems using the temperatures at which the anomalies were observed by the electrical resistivity r(T), thermal conductivity k(T), thermal dilatation dL(T)/L and the sound velocity v_s(T).

Fig.5:Phase diagram of the LSMO system

Fig.6:Phase diagram of the LCMO system