Hanle effect in current induced spin orientation

TL;DR

This paper develops a theoretical framework for electrical spin orientation in magnetic 2D heterostructures, revealing a Hanle effect sensitive to scattering details and magnetization, with implications for graphene and semiconductor systems.

Contribution

It introduces a comprehensive Boltzmann equation-based theory for electrical spin orientation, including the Hanle effect, in magnetic 2D heterostructures with spin-orbit coupling.

Findings

Hanle effect depends on out-of-plane magnetization.

Sensitivity of the Hanle effect to scattering type.

Opposite Hanle effects in graphene valleys.

Abstract

Electrical spin orientation is the generation of electron spin proportional to the electric current. This phenomenon is allowed by symmetry in gyrotropic systems, e.g. in inversion-asymmetric structures with Rashba spin-orbit splitting. Here we develop a theory of electrical spin orientation for magnetic two-dimensional heterostructures. Spin-orbit coupled graphene and semiconductor heterostructures proximitized by ferromagnets are considered. The analytical theory is based on the Boltzmann kinetic equation for a spin-dependent distribution function and collision integral. We show that the induced spin demonstrates the Hanle effect: a direction of the spin depends on the out-of-plane magnetization. Importantly, the Hanle effect is extremely sensitive to the details of electron elastic scattering. In semiconductor heterostructures, the effect of magnetization is present for scattering by long-range disorder and absent for short-range scattering. In spin-orbit-coupled graphene, the Hanle effect occurs at any scattering potential, but the direction of the spin strongly changes with variation of the disorder type. The theory also describes the effect of valley-Zeeman splitting on the electrical spin orientation in graphene, where the spin experiences opposite Hanle effects in two valleys.