Lattice and ultrasonic effects of orbital ordering and fluctuation

在目前的项目中，我们对轨道排序和流动进行了调查，该项目是通过使用弹性绳的声波对到Freedom的四个轨道度。根据超声波测量，我们对Ce_xLa_<1-x>B_6的磁相位图进行了调查。在化合物中x=0.75，有序阶段IV将改变到反磁阶段III。在更多的损耗化合物x=0.70和0.65的情况下，第四阶段稳定到绝对零。超声波测量显示C_<44>ofx=0.70， 0.65和x=0.60， 0.50的低温度限制的显著差异。我们被淘汰了，因此，化合物x=0.60和0.50落入了一个非磁性地面状态，显示出没有距离的阶段过渡。这与Nakamura等人的前一个特定热量测量有一定的一致性。在进行排序以测试第四阶段的顺序参数时，我们已经进行了热膨胀测量，以显示在（001） d ... More 第四阶段的电流和收缩（111）方向。这一结果是一个证明，证明四阶段四极排序O_<yz>= O_= <zx>O_<xy>。我们...。Have..。在（C_<11>-C_<12>）/2、C_<44>、C_<66>. These results indicate a pseudo-trilet model consisting of E-doublet and B or A singlet is responsible for HoB_2C_2 and a pseudo-quartet model with E_&lt;1/2&gt; doublet and E_&lt;3/2&gt; doublet is for DyB_2C_2。我们还在La_&lt;1-x&gt;Sr_xMnO_3 and Pr_xCa_&lt;1-x&gt;MnO_3 to investigate their orbital orderings上执行了超声波调查。我们通常在（C_<11>-C_<12>）/2中观察到了软化，在平行阶段，Jahn-Teller四重奏O^0_2和O^2_2中E_g doublet的O^0_2和O^2_2的地方。我们获得了能量10。100 K，在磨坊理论中，比这更容易被认为小。在<44>Pr_xCa_&lt;1-x&gt;MnO_3 with x=0.50 has been found中的elastic softening in C_due to charge ordering in Pr_xCa_&lt;1-x&gt;MnO_3 with x=0.50 has been found。We have successfully applied the Landau theory to？ain the system associated with the softening of C_<44>. Less（低）

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