Theory for the transition to self-trapping in spin-phonon systems

The dynamical correlations and thermodynamic functions for a single spin {} experiencing a static external field and a linear interaction with phonons in a direction perpendicular to the field are discussed as a function of the spin-phonon coupling in order to study the abrupt transition from a nearly free spin system to an almost self-trapped situation. The theory is based on a mode-coupling approximation which permits the expression of relaxation kernels for the dynamical spin susceptibilities in terms of convolution integrals over the spin-excitation spectra. The thermodynamic functions are obtained from transcendental equations expressing the consistency of the static response with the relaxation dynamics. The relevance of the theory for a description of paraelectric impurities is indicated.