Intrinsic Spin Lifetime of Conduction Electrons in Germanium

TL;DR

This paper analyzes the intrinsic spin relaxation mechanisms of conduction electrons in germanium, deriving spin-flip matrix elements and quantifying anisotropy, with results validated by numerical methods.

Contribution

It introduces analytical derivations of spin-flip matrix elements in germanium and compares them with numerical results, advancing understanding of spin relaxation in this material.

Findings

Derived intravalley and intervalley spin-flip matrix elements.

Quantified anisotropy in spin relaxation.

Analytical results agree with numerical simulations.

Abstract

We investigate the intrinsic spin relaxation of conduction electrons in germanium due to electron-phonon scattering. We derive intravalley and intervalley spin-flip matrix elements for a general spin orientation and quantify the resulting anisotropy in spin relaxation. The form of the intravalley spin-flip matrix element is derived from the eigenstates of a compact spin-dependent $\mathbf{k}$$\cdot$$\mathbf{p}$ Hamiltonian in the vicinity of the $L$ point (where thermal electrons are populated in Ge). Spin lifetimes from analytical integrations of the intravalley and intervalley matrix elements show excellent agreement with independent results from elaborate numerical methods.