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Lattice effects in a cerium based clathrate compound Ce_3Pd_20Ge_6 with acubic Cr_23C_6-type structure have been investigated by ultrasonic and thermalexpansion measurements. Elastic softenings of (C_11-C_12)/2 and C_44proportional to the reciprocal temperature 1/T above T_Q1 = 1.25 K are welldescribed in terms of the quadrupole susceptibility for the ground stateGamma_8 quartet. A huge softening of 50 % in (C_11-C_12)/2 and a spontaneousexpansion DL/L = 1.9x10^-4 along the [001] direction in particular indicate theferroquadrupole ordering of O_2^0 below T_Q1. The elastic anomalies associatedwith the antiferromagnetic ordering at T_N2 = 0.75 K and the incommensurateantiferromagnetic ordering are also found. Notable frequency dependence of C_44around 10 K is accounted for by the Debye-type dispersion indicating a Gamma_5rattling motion of an off-center Ce ion along the [111] direction with eightfractionally occupied positions around the 4a site in a cage. The thermallyactivated Gamma_5 rattling motion obeying a relaxation time t = t_0exp(E/k_BT)with an attempt time t_0 = 3.1x10^-11 sec and an activation energy E = 70 Kdies out with decreasing temperature, and then the off-center tunneling stateof Ce ion in the 4a-site cage will appear at low temperatures.Comment: 11 pages, 15 figures, to be published on Phys. Rev.

physical review. b, condensed matter

Ferroquadrupole ordering and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>Γ</mml:mi></mml:mrow><mml:mrow><mml:mn>5</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>rattling motion in the clathrate compound<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Ce</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow…

Ferroquadrupole ordering andΓ5rattling motion in the clathrate compoundCe3