A self-consistent treatment of non-equilibrium spin torques in magnetic multilayers

TL;DR

This paper develops a self-consistent method based on spin diffusion equations to accurately evaluate non-equilibrium spin torques in magnetic multilayers, highlighting the importance of considering extended spin transport effects beyond interfaces.

Contribution

It introduces a comprehensive approach that accounts for coupled longitudinal and transverse spin accumulations across layers, improving the estimation of spin transfer in magnetic multilayer structures.

Findings

Spin torque can be significantly amplified due to extended spin diffusion.

Longitudinal and transverse spin components are interdependent across layers.

Bare spin currents underestimate the actual spin transfer at interfaces.

Abstract

It is known that the transfer of spin angular momenta between current carriers and local moments occurs near the interface of magnetic layers when their moments are non-collinear. However, to determine the magnitude of the transfer, one should calculate the spin transport properties far beyond the interface regions. Based on the spin diffusion equation, we present a self-consistent approach to evaluate the spin torque for a number of layered structures. One of the salient features is that the longitudinal and transverse components of spin accumulations are inter-twined from one layer to the next, and thus, the spin torque could be significantly amplified with respect to treatments which concentrate solely on the transport at the interface due to the presence of the much longer longitudinal spin diffusion length. We conclude that bare spin currents do not properly estimate the spin angular momentum transferred between to the magnetic background; the spin transfer that occurs at interfaces should be self-consistently determined by embedding it in our globally diffuse transport calculations.