Spin dynamics in the regime of hopping conductivity

TL;DR

This paper investigates how electron spins relax in a disordered semiconductor's impurity band, revealing that inhomogeneity and hopping dynamics lead to complex, non-exponential spin decay behaviors largely independent of spin-orbit coupling.

Contribution

It introduces a model for spin relaxation considering inhomogeneous hopping and distinguishes regimes with different relaxation dynamics, including a novel non-exponential decay regime.

Findings

Spin relaxation rate can be averaged in weak coupling regimes.

System divides into fast and slow relaxation subsystems at larger couplings.

Spin decay is non-exponential and insensitive to spin-orbit coupling.

Abstract

We consider spin dynamics in the impurity band of a semiconductor with spin-split spectrum. Due to the splitting, phonon-assisted hops from one impurity to another are accompanied by rotation of the electron spin, which leads to spin relaxation. The system is strongly inhomogeneous because of exponential variation of hopping times. However, at very small couplings an electron diffuses over a distance exceeding the characteristic scale of the inhomogeneity during the time of spin relaxation, so one can introduce an averaged spin relaxation rate. At larger values of coupling the system is effectively divided into two subsystems: the one where relaxation is very fast and another one where relaxation is rather slow. In this case, spin decays due to escape of the electrons from one subsystem to another. As a result, the spin dynamics is non-exponential and hardly depends on spin-orbit coupling.