Determination of ligand field parameters of single-molecule magnets from magnetic susceptibility using deep learning based inverse models

Lanthanide-based single-molecule magnets (SMMs) have garnered extensive attention in recent decades for their potential applications in magnetic memory and quantum computing. In ligand field theory, the magnetic properties of a lanthanide ion may have to be characterized by up to 27 ligand field parameters. However, common experimental data such as temperature-dependent susceptibility curves measured on powder samples typically lack distinctive features. This leads to a massive over-parametrization, where multiple parameter sets can equally describe the data. In this work the issue is tackled by applying a deep learning architecture which combines a variational autoencoder (VAE) with an invertible neural network (INN). This VAE-INN architecture is shown to be capable of determining multiple ligand field parameter sets by extracting hidden parameters from the magnetic data and mapping them to the space of ligand field parameters. The approach is tested on simulated and experimental susceptibility data in magnetic models involving second-order ligand field parameters and is gradually extended to higher-order parameters until it is found limited by dimensionality issues. Compared with traditional least-squares fitting methods, the proposed approach exhibits enhanced generalization, robustness, and convergence. The present investigation of the VAE-INN architecture can be hoped to pave the way for further exploration of higher-order ligand field parameters.