Theory of spin relaxation in the limit of slow motion. Nuclear and electron spin relaxation in paramagnetic transition-metal complexes

Abstract

A theory of spin relaxation is developed which can be applied to cases where the Redfield limit (T₂ » t_t) does not hold. A simplification over the conventional approach is achieved by working entirely in a reference frame in which the initial density matrix is diagonal. This allows the general relaxation equations to be written in a simple analytic form without the need for perturbation theory. In the short correlation time limit this general form reduces to the usual Redfield equations for the relaxation times. In the long correlation time limit a corresponding result can be obtained, but is dependent on the assumed ensemble distribution. Electron spin relaxation by modulation of the quadratic zero-field splitting for S = 3/2 is treated explicitly. The theory is used to analyse proton spin relaxation in some halogenobis(N,N-diethyl-dithiocarbamato)iron(111) complexes.