Lattice and ultrasonic effects of orbital ordering and fluctuation

点击翻译按钮获取中文摘要

In the present project we have investigated on orbital orderings and fluctuations by use of the coupling of the elastic strain of sound waves to the quadrupole of the orbital degrees of freedom. By the ultrasonic measurements, we have investigated the magnetic phase diagram of Ce_xLa_<1-x>B_6 with ヲ」_8 ground state. In the compound x=0.75 the ordered phase IV changes into the antiferro-magnetic phase III. In more diluted compounds x=0.70 and 0.65, however, the phase IV is stable down to absolute zero. The ultrasonic measurements show significant difference in low-temperature limit of C_<44>ofx=0.70, 0.65 and that of x=0.60, 0.50. We have deduced, therefore, that the compounds x=0.60 and 0.50 falls into a non-magnetic ground state showing no distinct phase transition. This is consistent with the previous specific heat measurements by Nakamura et al. In order to examine the order parameter of the phase IV, we have made thermal expansion measurements showing an expansion along the (001) d … More irection and a shrink along the(111) direction in phase IV. This result is a proof for a trigonal distortion in phase IV indicating a quadrupole ordering O_<yz>=O_<zx>=O_<xy>。・.We。。have。。found that tetragonal ternary compounds HoB_2C_2 and DyB_2C_2 exhibit softenings in (C_<11>-C_<12>)/2, C_<44>, C_<66>. These results indicate a pseudo-triplet model consisting of E-doublet and B or A singlet is responsible for HoB_2C_2 and a pseudo-quartet model with E_<1/2> doublet and E_<3/2> doublet is for DyB_2C_2. We have also performed ultrasonic investigation on La_<1-x>Sr_xMnO_3 and Pr_xCa_<1-x>MnO_3 to investigate their orbital orderings. We have commonly observed the softening in (C_<11>-C_<12>)/2, in para-phase, where the Jahn-Teller coupling of quadrupoles O^0_2 and O^2_2 of E_g doublet is responsible. We obtained the energy gain 10。チ100K, which is considerable smaller than that in Mills' theory. The elastic softening in C_<44> due to charge ordering in Pr_xCa_<1-x>MnO_3 with x=0.50 has been found. We have successfully applied the Landau theory to explain the charge ordering of the system associated with the softening of C_<44>. Less