Tunneling and rattling in clathrate crystal

TL;DR

This paper investigates the tunneling and rattling behaviors of off-center guest atoms in a clathrate crystal, revealing thermally activated and quantum tunneling motions through elastic constant measurements.

Contribution

It provides the first detailed analysis of both rattling and tunneling motions of off-center atoms in La_3Pd_{20}Ge_6 using elastic constant data.

Findings

Identification of Debye-type dispersion in elastic constant C_{44} around 20 K.

Observation of low-temperature softening of C_{44} indicating tunneling motion.

Evidence for two distinct off-center motions with Gamma_5 symmetry.

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.