Modeling magnetization reversal in multilayers with interlayer exchange coupling

TL;DR

This paper introduces and compares three models for analyzing spin spirals in magnetic multilayers to extract exchange parameters, demonstrating their effectiveness across various structures and providing tools for broader application.

Contribution

The paper develops and evaluates three models—discrete energy, discrete torque, and continuous torque—for describing spin spiral evolution in multilayers, including asymmetric and multi-layered structures.

Findings

Discrete models outperform continuous in asymmetric and multi-layered structures.

Continuous model is better for symmetric, single-layer structures.

Open-access tool available for fitting magnetization data.

Abstract

Spin spirals form inside the magnetic layers of antiferromagnetic and noncollinearly-coupled magnetic multilayers in the presence of an external magnetic field. This spin structure can be modeled to extract the direct exchange stiffness of the magnetic layers and the strength of the interlayer exchange coupling across the spacer layer. In this article, we discuss three models to describe the evolution of the spin spiral with the strength of the external magnetic field in these coupled structures: discrete energy, discrete torque, and continuous torque. These models are expanded to accommodate multilayers with any number of ferromagnetic layers, any combination of material parameters, and asymmetry. We compare their performance when fitting to the measured magnetization data of a range of sputtered samples with one or multiple ferromagnetic layers on either side of the spacer. We find that the discrete models produce better fits than the continuous for asymmetric and multi-ferromagnetic structures and exhibit much better computational scaling with high numbers of atomic layers than the continuous model. For symmetric, single-layered structures, the continuous model produces the same fit statistics and outperforms the discrete models. Lastly, we demonstrate the methods by which one can use interfacial layers to measure the exchange stiffness of magnetic layers with low interlayer exchange coupling. An open-access website has been provided to allow the fitting of magnetization as a function of field in arbitrary coupled structures using the discrete energy model.