Modeling the shape of axisymmetric skyrmions in magnetic multilayers

TL;DR

This paper develops a detailed micromagnetic model for axisymmetric skyrmions in magnetic multilayers, accounting for dipolar fields and hybrid chiralities, and applies it to predict current-driven skyrmion dynamics.

Contribution

It introduces a comprehensive, layer-dependent model of multilayer skyrmions that includes dipolar interactions and predicts their stability and dynamics under current.

Findings

Model accurately describes multilayer skyrmion profiles.

Predicts stability criteria against elongation distortions.

Shows how to optimize skyrmion motion with current and geometry.

Abstract

We present a comprehensive micromagnetic model of isolated axisymmetric skyrmions in magnetic multilayers with perpendicular anisotropy. Most notably, the essential role of the internal dipolar field is extensively considered with a minimum amount of assumptions on the magnetization profiles. The tri-dimensional structure of the multilayered skyrmions is modeled by their radial profiles in each layer. We first compare the results of the model against a full micromagnetic description in Cartesian coordinates. Our model combines information on both layer-dependent size and chirality of the skyrmions. We also provide a convenient criterion in order to characterize the stability of skyrmions against anisotropic elongations that would break their cylindrical symmetry, which allows to confirm the stability of the determined solutions. Because this model is able to treat magnetization configurations twisted through the thickness of multilayered skyrmions, it can provide predictions on any potential hybrid chirality in skyrmions due to the interplay of Dzyaloshinskii-Moriya and dipolar interactions in multilayers. We finally apply the results of our model to the description of the current-driven dynamics of hybrid chiral skyrmions. Using the Thiele formalism, we show that we can predict the forces exerted on the multilayered skyrmions by vertical spin-polarized currents, which provides a method to conform hybrid skyrmion chiralities and spin-current injection geometries in order to optimize skyrmion motion in multilayers, to the aim of maximizing the current-induced velocity, or canceling the skyrmion Hall angle.