Four-well tunneling states and elastic response of clathrates

We present resonant ultrasound elastic constant measurements of the clathrate compounds Eu8Ga16Ge30 and Sr8Ga16Ge30. 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 is of the same order as the Einstein oscillator frequency. This explains why the observed harmonic oscillator type specific heat is not modified by tunneling states. 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 show that the shallow dip in the elastic constant c44 is explained using the same type of quadrupolar interaction with a soft Einstein mode instead of a FLS.