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Simulation and Theory of Classical Spin Hopping on a Lattice

The behavior of spin for incoherently hopping carriers is critical to understand in a variety of systems such as organic semiconductors, amorphous semiconductors, and muon-implanted materials. This work specifically examined the spin relaxation of hopping spin/charge carriers through a cubic lattice in the presence of varying degrees of energy disorder when the carrier spin is treated classically and random spin rotations are suffered during the hopping process (to mimic spin–orbit coupling effects) instead of during the wait time period (which would be more appropriate for hyperfine coupling). The problem was studied under a variety of different assumptions regarding the hopping rates and the random local fields. In some cases, analytic solutions for the spin relaxation rate were obtained. In all the models, we found that exponentially distributed energy disorder led to a drastic reduction in spin polarization losses that fell nonexponentially.