Four-Well Tunneling States and Elastic Response of Clathrates

Abstract

We present resonant ultrasound elastic constant measurements of the ${\mathrm{Eu}}_8{\mathrm{Ga}}_{16}{\mathrm{Ge}}_{30}$ and ${\mathrm{Sr}}_8{\mathrm{Ga}}_{16}{\mathrm{Ge}}_{30}$ clathrates. The elastic response of the Eu clathrate provides clear evidence for the existence of a new type of four-well tunneling states, described by two nearly degenerate four level systems (FLS). The FLS’s are closely linked with the fourfold split positions of Eu known from neutron diffraction density profiles. Using a realistic potential we estimate the tunneling frequencies and show that the energy gap between the two FLS’s explains the observed harmonic oscillator type specific heat. In addition the quadrupolar interaction of FLS’s with elastic strains explains the pronounced depression observed in elastic constant measurements. In the case of the Sr clathrate, we explain the elastic properties assuming the same type of interaction, but with Sr Einstein mode.