Spectral theory of spin relaxation

Abstract

A dynamical theory of spin relaxation previously formulated in terms of stochastic differential equations is extended beyond the extreme narrowed approximation to incorporate temporal correlation in the driving random magnetic fields. An analysis of spin–spin relaxation in this case is provided, which is non-perturbative in the random field and yields an exact solution to the spin dynamical equations for axial (longitudinal) field fluctuations. We provide a real-time dynamical derivation that leads to a generalized class of spin spectra that are essentially non-Lorentzian for all finite field parameters. A spectral-moment analysis and novel parameter-extraction scheme lead to distinct notions of observable relaxation timescales compared with the standard characteristic exponential. The Lorentzian case is recovered as the extreme narrowed limit.