Tunneling states of CN^- ions in RbCl crystals

Abstract

Substitutional CN- impurity ions in RbCl crystals behave as hindered rotors. The energy levels for such rotors are divided into two types by the spacing of the levels. Relatively large energy intervals, 19 cm-1, are due to exciting the CN- into torsional oscillation. These torsional oscillations sweep out small angles with respect to specific crystallographic axes. Overlaps exist between wave-functions for torsional oscillation about different axes. Overlaps introduce the second type of energy levels; these levels are best viewed as arising from a tunneling type of behavior. The overlaps remove degeneracies between the various orientations of the torsional oscillator by introducing energy splittings of ≲ l cm-1. Such splittings are presently investigated by paraelectric-resonance measurements with 0.27 to 0.34 cm-1 microwaves. (This resonance measurement is the solid-state equivalent of measuring the microwave absorption in a dipolar gas under an applied (Stark) electric field.) The objectives are to obtain detailed information about the tunneling energy levels, wavefunction overlaps, and the validity of models for the energy-level spacings. Specifically, the following conclusions are obtained: The potential-energy curve (which controls the CN- hindered rotor) has energy-level minima on the 〈110〉 axes. The energy-level spacing is best fit by a model which is derived from averaging between a tunneling model and the free-rotor model. Such an averaging is necessary because the hindering potential energy is only slightly greater than the energy levels of a freely-rotating CN-. The lowest energy interval in the tunneling states is 0.16 cm-1; a width of 0.7 cm-1 is found for the entire manifold of tunneling states. The CN- exhibits a dipole moment of 0.102 e-× Å = 0.49 Debye units. Thermal relaxation is characterized by time constants of 5 × 10-10 sec and 1.3 × 10-5 sec in the liquid-helium-temperature range. The present model also provides an interpretation to previous specific-heat, thermal-conductivity, i.r. and dielectric-constant measurements. © 1968.