Effect of capping layer on spin-orbit torques

TL;DR

This paper presents a theoretical model analyzing how capping layer properties, especially thickness, influence spin-orbit torque in multilayer structures, aligning with experimental findings and suggesting ways to optimize SOT enhancement.

Contribution

The study introduces a spin-drift-diffusion model to predict how capping layer characteristics affect spin-orbit torque, providing insights for experimental optimization.

Findings

Capping layers with opposite spin Hall angles can significantly enhance SOT.

Optimal capping layer thickness maximizes spin Hall torque.

Long spin diffusion length and high resistivity in capping layers further boost SOT.

Abstract

In order to enhance the magnitude of spin-orbit torque (SOT), considerable experimental works have been devoted to studying the thickness dependence of the different layers in multilayers consisting of heavy metal (HM), ferromagnet (FM) and capping layers. Here we present a theoretical model based on the spin-drift-diffusion (SDD) formalism to investigate the effect of the capping layer properties such as its thickness on the SOT observed in experiments. It is found that the spin Hall-induced SOT can be significantly enhanced by incorporating a capping layer with opposite spin Hall angle to that of the HM layer. The spin Hall torque can be maximized by tuning the capping layer thickness. However, in the absence of the spin Hall effect (SHE) in the capping layer, the torque decreases monotonically with capping layer thickness. Conversely, the spin Hall torque is found to decrease monotonically with the FM layer thickness, irrespective of the presence or absence of SHE in the capping layer. All these trends are in correspondence with experimental observations. Finally, our model suggests that capping layers with long spin diffusion length and high resistivity would also enhance the spin Hall torque.