Quantitative and realistic description of the magnetic potential energy of spin-torque vortex oscillators

TL;DR

This paper provides a detailed, quantitative description of the magnetic potential energy and restoring forces in spin-torque vortex oscillators, highlighting how current-induced deformations affect vortex stiffness parameters.

Contribution

It introduces a method to extract stiffness expressions from micromagnetic simulations and compares them with analytical models, revealing current-dependent effects on vortex properties.

Findings

Stiffness parameters depend on vortex core position and current density.

Deformation of magnetic texture caused by Ampère-Oersted field influences vortex stiffness.

Proposed method accurately extracts exchange, magnetostatic, and Zeeman stiffness expressions.

Abstract

Understanding the dynamics of magnetic vortices has emerged as an important challenge regarding the recent development of spin-torque vortex oscillators. Either micromagnetic simulations or the analytical Thiele equation approach are typically used to study such systems theoretically. This work focuses on the precise description of the restoring forces exerted on the vortex when it is displaced from equilibrium. In particular, the stiffness parameters related to a modification of the magnetic potential energy terms are investigated. A method is proposed to extract exchange, magnetostatic and Zeeman stiffness expressions from micromagnetic simulations. These expressions are then compared to state-of-the-art analytical derivations. Furthermore, it is shown that the stiffness parameters depend not only on the vortex core position but also on the injected current density. This phenomenon is not predicted by commonly used analytical ans\"atze. We show that these findings result from a deformation of the theoretical magnetic texture caused by the current induced Amp\`ere-Oersted field.