Spin Relaxation in Materials Lacking Coherent Charge Transport

We describe a broadly-applicable theory of spin relaxation in materials with incoherent charge transport; examples include amorphous inorganic semiconductors, organic semiconductors, quantum dot arrays, and systems displaying trap-controlled transport or transport within an impurity band. The theory can incorporate many different relaxation mechanisms, so long as electron-electron correlations can be neglected. We focus primarily on spin relaxation caused by spin-orbit effects, which manifest through inhomogeneities in the $g$-factor and non-spin-conserving carrier hops, scattering, trapping, or detrapping. Analytic and numerical results from the theory are compared in various regimes with Monte Carlo simulations. Our results should assist in evaluating the suitability of various disordered materials for spintronic devices.