Non-equilibrium spatial distribution of Rashba spin torque in ferromagnetic metal layer

TL;DR

This paper investigates the spatial distribution of Rashba spin torque in ferromagnetic metals using non-equilibrium Green's functions, revealing how Rashba strength and exchange splitting influence spin torque and magnetic switching.

Contribution

It provides a detailed mapping of Rashba spin torque distribution and uncovers the impact of Rashba strength and exchange splitting on spin torque behavior.

Findings

Rashba spin torque correlates with spatial spin current distribution.

An in-plane Spin Hall effect is observed when local magnetism is present.

Low current density can achieve magnetic switching with Rashba spin torque.

Abstract

We study the spatial distribution of spin torque induced by a strong Rashba spin-orbit coupling (RSOC) in a ferromagnetic (FM) metal layer, using the Keldysh non-equilibrium Green's function method. In the presence of the s-d interaction between the non-equilibrium conduction electrons and the local magnetic moments, the RSOC effect induces a torque on the moments, which we term as the Rashba spin torque. A correlation between the Rashba spin torque and the spatial spin current is presented in this work, clearly mapping the spatial distribution of Rashba Spin torque in a nano-sized ferromagnetic device. When local magnetism is turned on, the out-of-plane (Sz) Spin Hall effect (SHE) is disrupted, but rather unexpectedly an in-plane (Sy) SHE is detected. We also study the effect of Rashba strength (\alpha_R) and splitting exchange (\Delta) on the non-equilibrium Rashba spin torque averaged over the device. Rashba spin torque allows an efficient transfer of spin momentum such that a typical switching field of 20 mT can be attained with a low current density of less than 10^6 A/cm^2.