Reexamination of the Elliott-Yafet spin-relaxation mechanism

TL;DR

This paper refines the understanding of the Elliott-Yafet spin-relaxation mechanism by improving calculations of spin dynamics, revealing that one contribution vanishes and providing a modified expression for relaxation time.

Contribution

The authors develop an improved calculation method for the EY mechanism, introducing a torque operator and showing the Elliott contribution vanishes, leading to a new expression for spin relaxation time.

Findings

The torque operator determines spin dynamics.

The Elliott contribution to the torque vanishes.

A modified expression for the EY spin relaxation time is derived.

Abstract

We analyze spin-dependent carrier dynamics due to incoherent electron-phonon scattering, which is commonly referred to as Elliott-Yafet (EY) spin-relaxation mechanism. For this mechanism one usually distinguishes two contributions: (1) from the electrostatic interaction together with spin-mixing in the wave functions, which is often called the Elliott contribution, and (2) the phonon-modulated spin-orbit interaction, which is often called the Yafet or Overhauser contribution. By computing the reduced electronic density matrix, we improve Yafet's original calculation, which is not valid for pronounced spin mixing as it equates the pseudo-spin polarization with the spin polarization. The important novel quantity in our calculation is a torque operator that determines the spin dynamics. The contribution (1) to this torque vanishes exactly. From this general result, we derive a modified expression for the Elliott-Yafet spin relaxation time.