Extraction of the interaction parameters for $\alpha-$RuCl$_3$ from neutron data using machine learning

TL;DR

This paper presents a machine learning framework to extract interaction parameters of $ ext{α-RuCl}_3$ from neutron scattering data, combining neural networks, simulations, and quantum calculations to accurately model its Hamiltonian.

Contribution

It introduces a novel machine learning-assisted approach with multiple neural network architectures for high-dimensional modeling of neutron scattering data to determine the material's Hamiltonian.

Findings

Successfully extracted the Hamiltonian parameters for $ ext{α-RuCl}_3$

Demonstrated the effectiveness of neural networks in modeling complex neutron data

Provided insights into quantum fluctuations affecting the material's properties

Abstract

Single crystal inelastic neutron scattering data contain rich information about the structure and dynamics of a material. Yet the challenge of matching sophisticated theoretical models with large data volumes is compounded by computational complexity and the ill-posed nature of the inverse scattering problem. Here we utilize a novel machine-learning-assisted framework featuring multiple neural network architectures to address this via high-dimensional modeling and numerical methods. A comprehensive data set of diffraction and inelastic neutron scattering measured on the Kitaev material $\alpha-$RuCl$_3$ is processed to extract its Hamiltonian. Semiclassical Landau-Lifshitz dynamics and Monte-Carlo simulations were employed to explore the parameter space of an extended Kitaev-Heisenberg Hamiltonian. A machine-learning-assisted iterative algorithm was developed to map the uncertainty manifold to match experimental data; a non-linear autoencoder used to undertake information compression; and Radial Basis networks utilized as fast surrogates for diffraction and dynamics simulations to predict potential spin Hamiltonians with uncertainty. Exact diagonalization calculations were employed to assess the impact of quantum fluctuations on the selected parameters around the best prediction.