# Spin-relaxation time in the impurity band of wurtzite semiconductors

## TL;DR

This paper investigates the spin-relaxation time of electrons in the impurity band of wurtzite semiconductors, combining theoretical models and calculations to match experimental data and predict effects of external tuning.

## Contribution

It introduces a detailed theoretical framework for calculating spin-relaxation times in wurtzite semiconductors, incorporating symmetry considerations and spin-orbit interactions.

## Key findings

- Theoretical spin-relaxation times agree with experiments in GaN and ZnO.
- Predicted significant increase in relaxation time for InN and AlN under external potential tuning.
- Provided estimates for key materials' spin-relaxation times.

## Abstract

The spin-relaxation time for electrons in the impurity band of semiconductors with wurtzite crystal structure is determined. The effective Dresselhaus spin-orbit interaction Hamiltonian is taken as the source of the spin relaxation at low temperature and for doping densities corresponding to the metallic side of the metal-insulator transition. The spin-flip hopping matrix elements between impurity states are calculated and used to set up a tight-binding Hamiltonian that incorporates the symmetries of wurtzite semiconductors. The spin-relaxation time is obtained from a semiclassical model of spin diffusion, as well as from a microscopic self-consistent diagrammatic theory of spin and charge diffusion in doped semiconductors. Estimates are provided for particularly important materials. The theoretical spin-relaxation times compare favorably with the corresponding low-temperature measurements in GaN and ZnO. For InN and AlN, we predict that tuning of the spin-orbit coupling constant induced by an external potential leads to a potentially dramatic increase of the spin-relaxation time related to the mechanism under study.