Tunneling and rattling in clathrate crystal

We present tunneling and rattling motions of an off-center guest atom in a cage referring to a clathrate crystal La3Pd20Ge6. The elastic constant C-44 of La3Pd20Ge6 shows a Debye-type dispersion of around 20 K obeying a relaxation time tau=tau(0) exp(E/k(B)T) with an attempt time of tau(0)=2.0x10(-12) s 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 off-center motions with Gamma(5) symmetry in the 4a-site cage of La3Pd20Ge6, a thermally activated rattling motion over the potential hill, and a tunneling motion through the potential hill at low temperatures.