Current induced torques and interfacial spin-orbit coupling: Semiclassical Modeling

TL;DR

This paper develops a semiclassical Boltzmann model to unify the understanding of current-induced torques in ferromagnetic/non-magnetic bilayer nanowires, highlighting its strengths and limitations in matching experimental data.

Contribution

It introduces a unified Boltzmann equation approach to model damping-like and field-like torques, bridging bulk and interfacial spin-orbit effects.

Findings

Boltzmann model can match sample-specific torques with reasonable parameters.

Drift-diffusion approximation qualitatively reproduces behavior but lacks quantitative accuracy.

Model struggles to capture some experimental thickness dependence trends.

Abstract

In bilayer nanowires consisting of a ferromagnetic layer and a non-magnetic layer with strong spin-orbit coupling, currents create torques on the magnetization beyond those found in simple ferromagnetic nanowires. The resulting magnetic dynamics appear to require torques that can be separated into two terms, damping-like and field-like. The damping-like torque is typically derived from models describing the bulk spin Hall effect and the spin transfer torque, and the field-like torque is typically derived from a Rashba model describing interfacial spin-orbit coupling. We derive a model based on the Boltzmann equation that unifies these approaches. We also consider an approximation to the Boltzmann equation, the drift-diffusion model, that qualitatively reproduces the behavior, but quantitatively fails to reproduce the results. We show that the Boltzmann equation with physically reasonable parameters can match the torques for any particular sample, but in some cases, it fails to describe the experimentally observed thickness dependences.