Relaxation in a Jahn-Teller System. II

Abstract

The strong-coupling model of a cubic Jahn-Teller (JT) system where a single $e$-type vibrational mode interacts with an $E$-type electronic ground state is extended to include the effects of a trigonal field, quadratic coupling, breakdown of the adiabatic approximation, and small static tetragonal-type perturbations (random strain fields in a crystal). Relaxation is treated by considering how lattice vibrations perturb an octahedral JT-active complex situated in a trigonal crystal, and it is found that spin-flip relaxation in the ground state is related to the non-spin-flip relaxation (reorientation amongst equivalent distortions) by the square of the $g$-tensor anisotropy of the frozen EPR spectrum and by the spin-orbit interaction within the ground state introduced by a trigonal field. The relaxation time for temperatures above the strain splittings due to random crystal strains is expected to have the form $\frac{1}{\tau }=aT+b{T}^3+c{T}^5+d{e}^{-\frac{\Delta }{\mathrm{kT}}}$, the ratio of spin-flip to non-spin-flip rates remaining constant. The magnitudes of the relaxation rates of Paper I are quite well accounted for by the model, and from those results parameters for the model are derived. There still remains some difficulty with orientation dependence of the spin-flip relaxation and with the nature of the "JT" transition" from an anisotropic to an isotropic spin-resonance spectrum.