# Spin-torque generation by dc or ac voltages in magnetic layered structures

## TL;DR

This paper derives a general expression for current-induced spin torque in magnetic layered structures under dc or ac voltages, analyzing ballistic trilayers and proposing spin torque generation via adiabatic ac modulation.

## Contribution

It introduces a comprehensive scattering matrix framework for spin torque calculation and explores quantum pumping as a novel method for spin torque generation.

## Key findings

- Derived a general expression for spin torque with dc/ac voltages
- Analyzed spin torque in ballistic magnetic trilayers
- Proposed spin torque via adiabatic ac modulation (quantum pumping)

## Abstract

A general expression of the current induced spin torque in a magnetic layered structure in the presence of external dc or ac voltages is derived in the framework of the scattering matrix approach. A detailed analysis is performed for a magnetic-nonmagnetic-magnetic trilayer connected to external leads in the presence of dc voltage bias in the ballistic regime. Alternatively, the possibility of producing spin torque by means of the adiabatic ac modulation of external gate voltages (quantum pumping) is proposed and discussed.