Machine learning model parameters of RuCl3 at high magnetic field

$alpha$-RuCl$_3$ is a magnetic insulator exhibiting quantum spin liquid phases possibly found in the Kitaev honeycomb model. Much of the effort towards determining Hamiltonian parameters has focused on low magnetic field ordered phases. We study this problem in the high magnetic field limit where mean-field theory becomes a good description. We do so by machine learning model parameters from 160,000 low dimensional data points that include magnetic field[1], torque[2], and torsion data[3]. Our machine, an MFT-ANN, maps thermodynamic conditions (temperature and field vector) to model parameters via a fully connected time-reversal covariant neural network and then predicts observable values using mean-field theory. To train the machine, we use PyTorch to enable backpropagation through mean-field theory with a pure PyTorch implementation of the Newton-Raphson method. The results provide a distribution of parameter values showing interaction parameters beyond the Kitaev coupling K are equally important to the physics of $\alpha$-RuCl$_3$.

[1] R. D. Johnson et. al. Phys. Rev. B ${\bf 92}, 235119 (2015).

[2] K. A. Modic et. al., Phys. Rev. B ${\bf 98}, 205110 (2018).

[3] K. A. Modic et. al., Nat. Phys. ${\bf 17}, 240 (2021).