Model of rotational tunneling in quasicrystals of the Cd6Yb parent compound

A microscopic theoretical model of rotational tunneling within the four-shell atomic clusters of the Cd6Yb structure, representing a 1/1 periodic approximant of the Cd-Yb and Cd-Ca quasicrystals, is presented, where the Cd4 tetrahedral core undergoes reorientations around its three-fold symmetry axes in the crystal potential due to outer icosahedral atomic shells. The form of the effective hindering potential was derived from the symmetry of the four-shell cluster and was found to exhibit 12 equivalent double-well minima. These minima appear naturally from the details of the Cd6Yb atomic structure, providing link to the phenomenological tunneling-state model, where the existence of such double-well minima is assumed on the phenomenological grounds. The shape of the potential suggests two kinds of rotational tunneling processes, the Cd4 reorientations for 120°, which involve tunneling through barriers between adjacent double wells, and the reorientations for 44°, which involve tunneling within the double wells. The low-temperature energy level scheme, representing the lowest rotational states of the Cd4 tetrahedron undergoing rotational tunneling about its four three-fold symmetry axes, is obtained by a group-theoretical calculation. As the charge distribution within the Cd6Yb clusters is not known, the rotational tunneling frequencies were estimated for some trial values of the potential parameters. The estimated frequencies are slow, in accordance with the large mass of the tunneling particle, the Cd4 tetrahedron.