Spin-circuit representation of spin-torque ferromagnetic resonance

TL;DR

This paper introduces a spin-circuit model for spin-torque ferromagnetic resonance, enabling easier translation of physical phenomena into circuit representations for device design and analysis.

Contribution

It presents a novel spin-circuit framework that separates different effects in ST-FMR and can be extended to multilayer structures using circuit theory.

Findings

The model reproduces standard ST-FMR results.

It allows for circuit-based analysis of multilayer spintronic devices.

The approach simplifies the design of complex spintronic circuits.

Abstract

Spin-torque ferromagnetic resonance (ST-FMR) particularly using magnetic insulators and heavy metals possessing a giant spin Hall effect (SHE) has gotten a lot of attention for the development of spintronic devices. To devise complex functional devices, it is necessary to construct the equivalent spin-circuit representations of different phenomena. Such representation is useful to translate physical equations into circuit elements, benchmarking experiments, and then proposing creative and efficient designs. We utilize the superposition principle in circuit theory to separate the spin Hall magnetoresistance and spin pumping contributions in the ST-FMR experiments. We show that the proposed spin-circuit representation reproduces the standard results in literature. We further consider multilayers like a spin-valve structure with an SHE layer sandwiched by two magnetic layers and show how the corresponding spin-circuit representation can be constructed by simply writing a vector netlist and solved using circuit theory.