Theory of One- and Two-Phonon Reorientation Rates of Paraelectric Defects in Ionic Crystals

Abstract

A theory of one- and two-phonon-assisted reorientation rates of substitutional O${\mathrm{H}}^{-}$ ions in alkali-halide crystals has been developed. We treat the case of reorientation of dipoles preferring $〈100〉$ directions with a large static applied electric field in a $〈100〉$ direction. We use unperturbed breathing shell-model phonons and a dipole-lattice Hamiltonian which includes both one- and two-phonon operators and which is not limited in its validity to the long-wave limit. The theory is applied primarily to O${\mathrm{H}}^{-}$ in RbBr with good qualitative agreement with experiment. In particular, we find an approximate $T^4$ dependence of relaxation rate due to two-phonon Raman-type processes in the 5-10 °K temperature range, in agreement with experiment. Our theory also agrees with experiment in its prediction that two-phonon reorientation processes will begin to dominate one-phonon processes above a temperature of about 4 °K. In the temperature range studied, those two-phonon reorientation rates produced by the one-phonon operators in the dipole-lattice interaction Hamiltonian acting twice exceed by several orders of magnitude the two-phonon reorientation rates produced by the interaction Hamiltonian two-phonon operators acting once. Similar results are found for O${\mathrm{H}}^{-}$ in KBr and KCl.