# Physically-inspired computational tools for sharp detection of material inhomogeneities in magnetic imaging

## TL;DR

This paper introduces two physically-inspired data analysis tools, average latent dimension and entropy, that effectively detect subtle material inhomogeneities in magnetic imaging data, outperforming existing methods in accuracy and efficiency.

## Contribution

The work presents novel data analysis tools based on latent dimension and entropy, enabling detection of very subtle inhomogeneities in magnetic data with high robustness and computational efficiency.

## Key findings

- Able to resolve exchange differences down to 1% in Ising models
- Detects changes in easy axis anisotropy from magnetization data
- Remains robust under Gaussian noise, with less than 0.3% variation

## Abstract

Detection of material inhomogeneities is an important task in magnetic imaging and plays a significant role in understanding physical processes. For example, in spintronics, the sample heterogeneity determines the onset of current-driven magnetization motion. While often a significant effort is made in enhancing the resolution of an experimental technique to obtain a deeper insight into the physical properties, here we want to emphasize that an advantageous data analysis has the potential to provide a lot more insight into given data set, in particular when being close to the resolution limit where the noise becomes at least of the same order as the signal. In this work, we introduce two tools - the average latent dimension and average latent entropy - which allow for the detection of very subtle material inhomogeneity patterns in the data. For example, for the Ising model, we show that these tools are able to resolve exchange differences down to $1\%$. For a micromagnetic model, we demonstrate that the latent entropy can be used to detect changes in the easy axis anisotropy from magnetization data. We show that the latent entropy remains robust when imposing noise on the data, changing less than $0.3\%$ after adding Gaussian noise of the same amplitude as the signal. Furthermore, we demonstrate that these data-driven tools can be used to visualize inhomogeneities based on MOKE data of magnetic whirls and thereby can help to explicitly resolve impurities and pinning centers. To evaluate the performance of the average latent dimension and entropy, we show that they outperform common instruments ranging from standard statistics measures to state-of-the-art data analysis techniques such as Gaussian mixture models not only in recognition quality but also in the required computational cost.