# Unraveling the role of dipolar versus Dzyaloshinskii-Moriya interaction in stabilizing compact magnetic skyrmions

## TL;DR

This paper presents a micromagnetic analysis that clarifies how dipolar and Dzyaloshinskii-Moriya interactions influence the size and stability of magnetic skyrmions, emphasizing the importance of full stray field energy.

## Contribution

It introduces analytical formulas accounting for full stray field energy, distinguishing the roles of DMI and dipolar interactions in skyrmion stability and size.

## Key findings

- Dzyaloshinskii-Moriya and dipolar interactions are key to skyrmion properties.
- Analytical expressions for skyrmion radius and energy are derived.
- Full stray field energy is crucial for understanding skyrmion behavior.

## Abstract

Magnetic skyrmions have been the subject of extensive experimental studies in ferromagnetic thin films and multilayers, revealing a diversity in their size, stability and internal structure. While the orthodox skyrmion theory focuses on the Dzyaloshinskii-Moryia interaction (DMI) and neglects higher-order energy terms, it is becoming clear that the full stray field energy needs to be taken into account to understand these recent observations. Here we present a micromagnetic study based on rigorous mathematical analysis which allows to account for the full stray field energy in the thin film and low DMI regime. In this regime, the skyrmion profile is close to a Belavin-Polyakov profile, which yields analytical expressions for the equilibrium skyrmion radius and energy. The obtained formulas provide a clear identification of Dzyaloshinskii-Moryia and long-range dipolar interactions as two physical mechanisms determining skyrmion size and stability, a consideration of importance for the optimization of skyrmion characteristics for spintronic applications.