Re-examination of the Elliott–Yafet spin-relaxation mechanism

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 spin–diagonal 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 neglects the spin-mixing in the single-particle states for the determination of the ensemble spin. The important novel quantity in our calculation is a torque operator that determines the spin dynamics due to incoherent scattering. The contribution (1) to this torque vanishes exactly. From this general result, we derive a modified expression for the EY spin relaxation time for Kramers degenerate bands.

Keywords

• magnetization dynamics
• spin relaxation
• Elliott–Yafet mechanism