Spin Transport at Interfaces with Spin-Orbit Coupling: Formalism

TL;DR

This paper extends magnetoelectronic circuit theory to include interfacial spin-orbit coupling, enabling a comprehensive description of spin transport and torques at ferromagnet/heavy-metal interfaces, with implications for interpreting spintronic experiments.

Contribution

It introduces a generalized circuit theory that incorporates in-plane electric fields and spin-orbit effects, advancing the understanding of spin transport phenomena at interfaces.

Findings

In-plane electric fields induce spin accumulations with arbitrary polarization.

Misaligned spin accumulations exert torques on magnetization.

The theory modifies interpretations of spin-orbit related experimental results.

Abstract

We generalize magnetoelectronic circuit theory to account for spin transfer to and from the atomic lattice via interfacial spin-orbit coupling. This enables a proper treatment of spin transport at interfaces between a ferromagnet and a heavy-metal non-magnet. This generalized approach describes spin transport in terms of drops in spin and charge accumulations across the interface (as in the standard approach), but additionally includes the responses from in-plane electric fields and offsets in spin accumulations. A key finding is that in-plane electric fields give rise to spin accumulations and spin currents that can be polarized in any direction, generalizing the Rashba-Edelstein and spin Hall effects. The spin accumulations exert torques on the magnetization at the interface when they are misaligned from the magnetization. The additional out-of-plane spin currents exert torques via the spin-transfer mechanism on the ferromagnetic layer. To account for these phenomena we also describe spin torques within the generalized circuit theory. The additional effects included in this generalized circuit theory suggest modifications in the interpretations of experiments involving spin orbit torques, spin pumping, spin memory loss, the Rashba-Edelstein effect, and the spin Hall magnetoresistance.