# Characterizing topological properties in 2D textures with magnetic structure tensors

## TL;DR

This paper introduces a magnetic structure tensor to analyze topological properties in 2D magnetic textures, enabling the identification of defects like skyrmions.

## Contribution

A novel magnetic structure tensor and order parameter are introduced for characterizing topological defects in 2D spin textures.

## Key findings

- The order parameter identifies topological defects such as skyrmions and branching points in magnetic textures.
- The method is validated using simulations, experiments, and generalized patterns like fingerprints.
- The approach reveals insights into defect distribution and interactions in self-organized magnetic structures.

## Abstract

The spin structures, including magnetic skyrmions, have attracted great attention due to their interesting properties caused by their topology. We introduce a magnetic structure tensor as a powerful tool for characterizing topological properties in two-dimensional spin textures. We derived an order parameter from the two orthogonal components of the magnetic structure tensor. The order parameter effectively analyzes the structures of the spin patterns and identifies topological defects such as the end or branching points of linear chiral structures and magnetic skyrmions, as a pole or multipoles composed of topological quantized charges. We present several spin configurations interpreted as topological monopoles, dipoles, and quadrupoles formed by the combination of these topological poles. This approach provides valuable insights into defect distribution and interactions, validated through both simulations and experimental data. Moreover, the approach can be generally applied for effective analysis of self-organized patterns such as fingerprints.

•The magnetic structure tensor is introduced to characterize 2D chiral magnetic textures•An order parameter is defined to identify the point defects in the magnetic textures•The approach is validated through simulations, experiments, and generalized patterns

The magnetic structure tensor is introduced to characterize 2D chiral magnetic textures

An order parameter is defined to identify the point defects in the magnetic textures

The approach is validated through simulations, experiments, and generalized patterns

Engineering; Materials science; Physics