Kinetic equations for the hopping transport and spin relaxation in random magnetic field

TL;DR

This paper develops kinetic equations for hopping electron transport considering spin and double occupation, revealing non-exponential spin relaxation influenced by traps and hyperfine interactions.

Contribution

It introduces a generalized kinetic framework for spin-dependent hopping transport, including double occupation effects, and analyzes long-term spin relaxation behavior.

Findings

Relaxation rate is governed by hops with rates similar to spin precession frequency.

Spin relaxation is non-exponential at large times.

Traps significantly influence spin relaxation in conducting clusters.

Abstract

We derive the kinetic equations for the hopping transport that take into account electron spin and the possibility of double occupation. In the Ohmic regime the equations are reduced to the generalized Miller-Abrahams resistor network. We apply these equations to the problem of the magnetic moment relaxation due to the interaction with the random hyperfine fields. It is shown that in a wide range of parameters the relaxation rate is governed by the hops with the similar rates as spin precession frequency. It is demonstrated that at the large time scale spin relaxation is non-exponential. We argue that the non-exponential relaxation of the magnetic moment is related to the spin of electrons in the slow-relaxing traps. Interestingly the traps can significantly influence the spin relaxation in the infinite conducting cluster at large times.