Field theoretical approach to spin torques: Slonczewski torques

TL;DR

This paper uses a quantum field theoretical approach to analyze spin-transfer torques in magnetic junctions, revealing quantum oscillations in the Slonczewski torque coefficient at zero temperature.

Contribution

It introduces a field theoretical method to derive the Slonczewski torque, highlighting quantum oscillations in the torque coefficient at absolute zero temperature.

Findings

Quantum oscillations in the Slonczewski torque coefficient at zero temperature.

Evaluation of a field-like torque alongside the Slonczewski torque.

Application of linear response theory with Green functions to magnetic multilayer systems.

Abstract

The quantum field theoretical approach with the Kubo formula has successfully captured spin torques, such as spin-transfer torques and spin-orbit torques, for continuum systems. We examine the field theoretical approach to current-induced spin-transfer torques in a magnetic junction system. We first give a brief overview of the field theoretical approach to spin torques. Then, we consider a five-layers system consisting of three nonmagnetic metal layers separated by two ferromagnetic metal layers and apply an electric field perpendicular to the layers. We demonstrate that the Slonczewski-type spin-transfer torque, or shortly the Slonczewski torque, on the magnetizations in ferromagnetic layers is obtained by evaluating nonequilibrium electron spin density, based on the linear response theory with the Green function method. The obtained coefficient of the Slonczewski torque has a quantum oscillation at absolute zero temperature, which has not been mentioned before. A field-like torque accompanied by the Slonczewski torque is also evaluated.