Principal Component Analysis of Diffuse Magnetic Scattering: a Theoretical Study

TL;DR

This study demonstrates that Principal Component Analysis can effectively analyze magnetic diffuse neutron scattering data, enabling phase diagram determination from finite-temperature measurements with minimal training data.

Contribution

It introduces a novel application of PCA to magnetic diffuse scattering data, showing high dimensionality reduction and phase boundary detection in quantum materials.

Findings

PCA achieves high dimensionality reduction of scattering data.

The algorithm can be trained with few simulated observations.

Phase boundaries are identifiable through PCA trajectories.

Abstract

We present a theoretical study of the potential of Principal Component Analysis to analyse magnetic diffuse neutron scattering data on quantum materials. To address this question, we simulate the scattering function $S\left(\mathbf{q}\right)$ for a model describing a cluster magnet with anisotropic spin-spin interactions under different conditions of applied field and temperature. We find high dimensionality reduction and that the algorithm can be trained with surprisingly small numbers of simulated observations. Subsequently, observations can be projected onto the reduced-dimensionality space defined by the learnt principal components. Constant-field temperature scans corresponds to trajectories in this space which show characteristic bifurcations at the critical fields corresponding to ground-state phase boundaries. Such plots allow the ground-state phase diagram to be accurately determined from finite-temperature measurements.