Theory of spin accumulation and spin transfer torque in a magnetic domain wall

TL;DR

This paper develops an analytical theory for spin accumulation and transfer torque in magnetic domain walls, revealing oscillatory behaviors and the dominance of non-adiabatic torque in thin walls.

Contribution

It provides the first analytical expressions for spin accumulation and transfer torque in domain walls, highlighting the oscillatory nature and the conditions for non-adiabatic torque dominance.

Findings

Spin transfer torque oscillates with domain wall thickness.

Non-adiabatic torque dominates when wall thickness is less than the spin-flip length.

Analytical expressions for spin accumulation and torque are derived.

Abstract

We study spin accumulation and spin transfer torque in a domain wall by solving the Boltzmann equation with a diffusion approximation. We obtained the analytical expressions of spin accumulation and spin transfer torque. Both the adiabatic and the non-adiabatic components of the spin transfer torque oscillate with the thickness of the domain wall. We show that the oscillation plays a dominant role in the non-adiabatic torque when the domain wall thickness is less than the spin-flip length, which is defined by the product of the Fermi velocity and the spin-flip scattering time.