Two-level tunneling states and the constant density of states in quadrupolar glasses

Starting from a microscopic Hamiltonian for interacting quadrupoles (QP’s) randomly placed in a solid, we obtain a model for the two-level tunneling states and the constant density of states in quadrupolar glasses from fundamentals. We use perturbation theory to show that in a quenched system of strongly interacting QP’s, 180° reorientational flips of single QP’s give low-energy excitations. These low-energy excitations arise from our starting Hamiltonian and are described in the form of an effective two-level state (TLS) Hamiltonian. For intermediate concentrations of ${\mathrm{CN}}^{\mathrm{-}}$ ions dissolved in KBr, we propose that it is the center of mass displacement of the ${\mathrm{CN}}^{\mathrm{-}}$ ion that leads to a constant density of states rather than the electric dipole interaction between the cyanides, as was proposed earlier by Sethna et al. The physical mechanism for the glasslike low-energy excitations proposed here thus involves 180° tunneling flips with a translation of the center of mass of the tunneling unit. We then show that it is the elastic random fields experienced by the QP’s that give a constant density of states and specific heat linear in temperature and logarithmic in time and that this result is not sensitive to the exact form of the QP-QP interaction or the presence of a weak electric dipole interaction. We suggest that the concepts developed for KCN-KBr mixed crystals may also help to explain the quasiuniversal low-temperature thermal properties of canonical and other quadrupolar glasses.