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

Abstract

FIG. 2. (a) Machine-learned phase map varying Γ/|K| and J 3 /|K| through the optimal solution for α-RuCl 3 at fixed J 1 /|K| = −0.1 and J 2 /|K| = 0, with K < 0. Labeled phases include ferromagnetic [FM], zigzag [Z.Z.] and planar zigzag [Z.Z. (2D)] orders. The ellipsoidal approximation to the optimal solution is marked in panel (a) in dark-red. Due to uneven sampling of the IMA process from which the data was taken, the prediction accuracy varies in parameter space resulting in a blotchy appearance. The different colors, which represent different structure factors S (Q), are predicted by a trained neural network as explained in the main text. Panel (b) shows the surrogate predicted neutron structure factor, S Sur (Q), at numbered locations indicated in (a) and Fig. 1(c). Corresponding spin structures for the long-range ordered phases labeled 1, 3-7 are given in the SM [21]. Note that Z.Z. and Z.Z. (2D) have similar long-range order, but along different spin-orientation directions. This occurs because, as discussed in Ref. [22], when K < 0 the spin orientation in zigzag ground states depends on the sign of Γ. Due to the neutron spin polarization factor, the two S (Q) are different in the shown plane, despite yielding the same trace over spin correlations, α S αα (Q). Some of the diffuse S (Q), taken at either phase boundaries or critical points, are also shown. The S (Q) labeled 11 and 12 are for the pure AFM and FM Kitaev models.

Thermal spin dynamics of Kitaev magnets -- scattering continua and magnetic field induced phases within a stochastic semiclassical approach

“…This makes the unambiguous observation of quantum fractionalization a challenging task for scattering experiments (at least if they are not performed at temperatures several orders of magnitude below the magnetic exchange scales). On the positive side, the stochastic LLG equation employed here should be a powerful method for comparing different models to INS data at different temperatures in order to extract the microscopic Hamiltonian parameters [71].…”