Abstract
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.
Highlights
Spin relaxation of carriers has garnered much interest in the past few decades due to the prospect of spin electronic or spintronic devices that use spin functionality in addition to charge functionality
Noncrystalline, organic semiconductors have recently seen a surge in interest [6,7,8,9,10,11,12] as spintronic candidates due to their small spin–orbit coupling and expected long spin lifetimes of 10−5 –10−7 s [13]
Simulations of MT and Multiple Hopping (MH) using each of the previously described models are demonstrated in Figures 6 and 7
Summary
Spin relaxation of carriers has garnered much interest in the past few decades due to the prospect of spin electronic or spintronic devices that use spin functionality in addition to charge functionality. Less effort has been expended on the spin relaxation of localized electron spins where charge transport occurs via incoherent hopping motion. Within the field of spin chemistry, spin relaxation plays a role in radical pair reactions [14], which has applications varying from organic electronic devices [15] to avian navigation [16]. Localized spin relaxation plays a role in transport through disordered crystalline semiconductors [17,18]
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