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$\alpha$-RuCl3 is a magnetic insulator exhibiting quantum spin liquid phasespossibly found in the Kitaev honeycomb model. Much of the effort towardsdetermining Hamiltonian parameters has focused on low magnetic field orderedphases. We study this problem in the high magnetic field limit where mean-fieldtheory is better justified. We do so by machine-learning model parameters fromover 200,000 low dimensional data points by combining available magnetization,torque, and torsion data sets. Our machine, an artificial neuralnetwork-mean-field theory (ANN-MFT) encoder, maps thermodynamic conditions(temperature and field vector) to model parameters via a fully connectedtime-reversal covariant (equivariant) neural network and then predictsobservable values using mean-field theory. To train the machine, we use PyTorchto enable backpropagation through mean-field theory with a pure PyTorchimplementation of the Newton-Raphson method. The results at $20$ K and $34.5$ Tare consistent with other parameter inference studies in the literature at lowmagnetic field but strikingly have magnitudes that scale with temperature from1.3 K up to 80 K in the $34.5-60$ T range. We conclude that the data presentsphysics beyond the scope of the mean-field theory and that strong interactionsdominate the physics of $\alpha$-RuCl$_3$ up to field strengths of at least 60Tesla.

Strong correlation effects observed by an ANN-MFT encoder trained on $\alpha$-RuCl$_3$ high magnetic field data