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We present resonant ultrasound elastic constant measurements of the clathratecompounds Eu8Ga16Ge30 and Sr8Ga16Ge30. The elastic response of the Eu clathrateprovides clear evidence for the existence of a new type of four-well tunnelingstates, described by two nearly degenerate four level systems (FLS). The FLS'sare closely linked with the fourfold split positions of Eu known from neutrondiffraction density profiles. Using a realistic potential we estimate thetunneling frequencies and show that the energy gap between the two FLS's is ofthe same order as the Einstein oscillator frequency. This explains why theobserved harmonic oscillator type specific heat is not modified by tunnelingstates. In addition the quadrupolar interaction of FLS's with elastic strainsexplains the pronounced depression observed in elastic constant measurements.In the case of the Sr clathrate, we show that the shallow dip in the elasticconstant c44 is explained using the same type of quadrupolar interaction with asoft Einstein mode instead of a FLS.Comment: 4 pages, 4 figures; accepted for publication in Physical Review  Letter

Four-Well Tunneling States and Elastic Response of Clathrates