Current-Induced Instability of a Perpendicular Ferromagnet in Spin Hall Geometry

TL;DR

This paper presents a theoretical model for spin Hall torque in systems with two ferromagnets, enabling deterministic switching of perpendicular ferromagnets at zero field by manipulating magnetization directions.

Contribution

It introduces an analytical formula for spin Hall torque in a two-ferromagnet system, allowing control over torque direction and deterministic switching without external fields.

Findings

Derived analytical formula for spin Hall torque.

Demonstrated zero-field deterministic switching of perpendicular ferromagnet.

Showed manipulation of torque direction via magnetization orientation.

Abstract

We develop a theoretical formula of spin Hall torque in the presence of two ferromagnets. While the direction of the conventional spin Hall torque always points to the in-plane direction, the present system enables to manipulate the torque direction acting on one magnetization by changing the direction of another magnetization. Based on the diffusion equation of the spin accumulation and the Landauer formula, we derive analytical formula of the spin Hall torque. The present model provides a solution to switch a perpendicular ferromagnet deterministically at zero field using the spin Hall effect.