Abstract

We propose a mechanism of torque generation by injection of an orbital current, which we call $\textit{orbital torque}$. In a magnetic bilayer consisting of a nonmagnet (NM) and a ferromagnet (FM), we consider a situation where the spin-orbit coupling (SOC) is present only in the FM. Although the SOC is absent in the NM, the orbital Hall effect can arise in the NM. When the resulting orbital Hall current is injected to the FM, the SOC of the FM converts the orbital angular momentum into spin, which exerts torque to the magnetization of the FM. Remarkably, even for small SOC strength comparable to that of $3d$ FMs, the orbital torque can be comparable to the spin torque induced by the spin Hall effect of the NM with strong SOC. This provides a way to experimentally probe the OHE and opens a new venue to achieving spin-torque devices based on light elements that exhibit gigantic orbital response. Experimental implications are discussed.

Highlights

  • Spin injection into a ferromagnet (FM) generates a spin torque (ST) on local magnetic moments of the FM by the angular momentum transfer from the spin of injected conduction electrons

  • We propose a mechanism of torque generation by the orbital injection, called the orbital torque (OT)

  • In a NM/FM bilayer, the orbital Hall effect (OHE) arises in the NM even without the spin-orbit coupling (SOC), by which the orbital angular momentum (OAM) can be injected to the FM

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Summary

INTRODUCTION

Spin injection into a ferromagnet (FM) generates a spin torque (ST) on local magnetic moments of the FM by the angular momentum transfer from the spin of injected conduction electrons. Considering that an orbital current carries the angular momentum just like a spin current does, it is reasonable to expect that injection of an orbital current (or orbital injection in short) into a FM may generate a torque on local magnetic moments of the FM We call such torque as orbital torque (OT), which provides an experimental way to detect the OHE. By numerical calculation on a tight-binding model, we show that the OT can be sizable in magnetic bilayers consisting of NM and FM, even in a situation when the SOC of the NM is absent This is attributed to highly efficient generation of the orbital current in the NM by the OHE.

MECHANISM
Tight-binding model
Kubo formula
Definition of the OT
What determines the sign of the OT?
Disentangling the OT from the ST
Onsager’s reciprocity
Role of the interface crystallinity
Material systems
Findings
CONCLUSION
Interface
Full Text
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