Theory of in-plane current induced spin torque in metal/ferromagnet bilayers

TL;DR

This paper develops a semiclassical model to analyze the combined effects of spin Hall effect, spin diffusion, quantum well states, and interface spin-orbit coupling on in-plane current induced spin torque in metal/ferromagnet bilayers, revealing the interplay of multiple mechanisms.

Contribution

It introduces a comprehensive semiclassical framework that simultaneously considers SHE, SOC, and quantum well states to explain spin torque phenomena in bilayer thin films.

Findings

The model captures the self-consistent interaction between spin voltage and spin current.

Quantum well states may explain rapid variation of spin torque with ferromagnet thickness.

Interface SOC modifies angular momentum conservation and influences spin torque.

Abstract

Using a semiclassical approach that simultaneously incorporates the spin Hall effect (SHE), spin diffusion, quantum well states, and interface spin-orbit coupling (SOC), we address the interplay of these mechanisms as the origin of the in-plane current induced spin torque observed in the normal metal/ferromagnetic metal bilayer thin films. Focusing on the bilayers with a ferromagnet much thinner than its spin diffusion length, such as Pt/Co with $\sim 10$nm thickness, our approach addresses simultaneously the two contributions to the spin torque, namely the spin-transfer torque (SHE-STT) due to SHE induced spin injection, and the spin-orbit torque (SOT) due to SOC induced spin accumulation. The SOC produces an effective magnetic field at the interface, hence it modifies the angular momentum conservation expected for the SHE-STT. The SHE induced spin voltage and the interface spin current are mutually dependent, hence are solved in a self-consistent manner. In addition, the spin transport mediated by the quantum well states may be responsible for the experimentally observed rapid variation of the spin torque with respect to the thickness of the ferromagnet.