Tunneling and rattling in clathrate crystal

Abstract

We present tunneling and rattling motions of an off-center guest atom in cage referring to a clathrate crystal La_3Pd_{20}Ge_6. The elastic constant C_{44} of La_3Pd_{20}Ge_6 shows a Debye-type dispersion around 20 K obeying a relaxation time tau = tau_0exp(E/k_{B}T) with an attempt time tau_0 = 2.0*10^{-12} sec and an activation energy E = 197 K. At low temperatures below 3 K down to 20 mK, the C_{44} shows a softening of C_{44} = C_{44}^0(T-T_C^0)/(T-Theta) with T_C^0 = -337.970 mK and Theta = -338.044 mK. These facts are attributed to two different types of the off-center motions with Gamma_5 symmetry in 4a-site cage of La_3Pd_{20}Ge_6, a thermally activated rattling motion over the potential hill and a tunneling motion through the potential hill at low temperatures.Comment: 5 pages, 4 figures, to be published Phys. Rev.

Rattling in Clathrate Compounds of ROs4Sb12and R3Pd20Ge6

“…9,10 Remarkable frequency dependences of the elastic constants, namely ultrasonic dispersion (UD), appear around 10 -50 K in the range of frequencies of ultrasonic sound waves 10 -500 MHz. With decreasing temperature, thermally activated rattling over an anharmonic potential barrier diminishes rapidly.…”

“…One of Relaxation time 0 (s) the most striking anomaly in 1/T 2 of La 3 Pd 20 Ge 6 suggests a development of intersite coherency at low temperatures down to 50 mK, 25 which seems to coincide with the continuing elastic softening of C 44 even at 20 mK with antiferro-type intercage interaction. 10 Other measurements concerning rattling are extended over, for instance, Sb-site NQR on SmOs 4 Sb 12 indicative that charge fluctuation plays an important role in its HF state. 26 Raman scattering measurements also report second-order phonon process associated with anomalous rare-earth vibration in ROs 4 Sb 12 .…”

Green's Function of Fully Anharmonic Lattice Vibration

“…The spectrum of the anharmonic lattice vibration is naturally reflected in other experiments. The present work will provide a basis of analysis of ultrasonic measurements [19][20][21] and Raman scattering experiments [22][23][24] on -pyrochlore, skutterudite, and clathrate compounds.…”

Simultaneous Measurements of Elastic Constant and Resistivity near the Tc of Non-BCS-Type Superconductor PrOs4Sb12

“…By means of ultrasonic measurements, rattling can also be observed as a frequency dependent elastic anomaly and an increase in ultrasonic attenuation, which are collectively called ultrasonic dispersion (UD) [14,15]. UD has been found even in non-4f systems such as LaOs 4 Sb 12 and La 3 Pd 20 Ge 6 [16,17]. It is expected that the motion of the guest ion between potential minima changes from thermally activated motion into a quantum tunneling state at low temperatures.…”