Theory of Spin-Transfer Torque in the Current-in-Plane Geometries

TL;DR

This paper theoretically investigates two current-in-plane geometries for spin-transfer torque, demonstrating efficient spin current absorption and potential for magnetization switching with realistic device dimensions and robustness to interface roughness.

Contribution

It introduces and analyzes the CPIP and CIP geometries using nonequilibrium Keldysh theory, extending understanding beyond traditional CPP configurations.

Findings

Spin current absorption in lateral geometries is comparable to CPP.

Efficient absorption occurs at lateral dimensions of about 20nm.

Strong spin current absorption persists despite interface roughness.

Abstract

Two alternative current-induced switching geometries, in which the current flows parallel to the magnet/nonmagnet interface, are investigated theoretically using the nonequilibrium Keldysh theory. In the first geometry, the current is perpendicular to the polarizing magnet/nonmagnet interface but parallel to the nonmagnet/switching magnet interface (CPIP). In the second geometry, the current is parallel to both the polarizing magnet/nonmagnet and nonmagnet/switching magnet interfaces (CIP). Calculations for a single-orbital tight binding model indicate that the spin current flowing parallel to the switching magnet/nonmagnet interface can be absorbed by a lateral switching magnet as efficiently as in the traditional current-perpendicular-to-plane (CPP) geometry. The results of the model calculations are shown to be valid also for experimentally relevant Co/Cu CPIP system described by fully realistic tight binding bands fitted to an ab initio band structure. It is shown that almost complete absorption of the incident spin current by a lateral switching magnet occurs when the lateral dimensions of the switching magnet are of the order of 50-100 interatomic distances, i.e., about 20nm and its height as small as a few atomic planes. It is also demonstratedthat strong spin current absorption in the CPIP/CIP geometry is not spoilt by the presence of a rough interface between the switching magnet and nonmagnetic spacer. Polarization achieved using a lateral magnet in the CIP geometry is found to be about 25% of that in the traditional CPP geometry. The present CPIP calculations of the spin transfer torque are also relevant to the so called pure-spin-current-induced magnetization switching that had been recently observed.