Extraction of exchange parameters for K₂Ni₂(SO₄)₃ from neutron data using neural networks

K₂Ni₂(SO₄)₃ is a quantum spin liquid in which strongly frustrated magnetic interactions induce a highly entangled quantum paramagnet far below the energy scale of the magnetic interactions. Understanding complex phases in such strongly frustrated systems is challenging because traditional simulation techniques have difficulty incorporating multiple competing interactions as well as linking models and data. We performed neutron scattering measurement and used multiple neural network architectures in combination with high-dimensional modeling and numerical methods to address this. A comprehensive data set of diffraction and inelastic neutron scattering of single-crystal K₂Ni₂(SO₄)₃ was collected. Long-range magnetic order and continuous spin-wave like excitation were observed at low temperatures, which melt gradually upon heating or applying an external magnetic field. The annealing process and spin dynamics were simulated and dynamical structure factors were computed using the Sunny package in the high-dimensional space of exchange parameters. Variational autoencoders were used to compress information from simulated data. Radial basis networks were utilized as fast surrogates for diffraction and dynamics simulations to theoretically explore the phase diagrams and to predict the exchange parameters with uncertainty.