α-RuCl₃ spin Hamiltonian now fitted from magnetization curves: Bayesian optimization returns five parameters, but the Kitaev energy scale stays undetermined

The spin Hamiltonian parameters of α-RuCl₃ can be inferred from experimental magnetization curves instead of relying only on ab initio calculations based on the crystal structure. The standard approach derives model parameters from ab initio calculations based on the crystal structure, but the resulting Hamiltonian can depend sensitively on methodological details of that procedure, an issue particularly evident in α-RuCl₃, a candidate Kitaev material. The cost-minimizing parameter set is (K, Γ, Γ′, J, g_c) = (−6.0, 7.5, −0.3, −1.75, 2.3), with exchange couplings in meV, fitted jointly to experimental magnetization curves along the b and c axes.

The workflow hands the parameter search to Bayesian optimization, using the difference between solver-computed and experimental magnetization curves as the cost function that ranks candidate parameters. The method is Bayesian optimization, which builds a surrogate from already evaluated parameter points and uses it to pick the next point worth trying, cutting the number of solver calls in a five-dimensional parameter space. Five parameters are optimized: the Kitaev interaction K, the off-diagonal interactions Γ and Γ′, the Heisenberg interaction J, and the c-axis g-factor g_c; the resulting parameters are then checked against the static spin structure factor, magnetic susceptibility, and specific heat.

The structure factor, susceptibility, and specific heat separate the large-Γ scenario from the small-g_c scenario, and the cost-minimizing parameter set agrees well with the experimental structure factor and susceptibility and qualitatively with the specific heat. The cost function is insensitive to the absolute value of K and depends only weakly on Γ′ and J, so the magnetization data alone do not determine the energy scale of the Kitaev coupling, while the optimization favors a large positive Γ. The judgment rests on three computed quantities, the static spin structure factor, magnetic susceptibility, and specific heat, with good agreement for the structure factor and susceptibility and qualitative agreement for the specific heat.

The report covers a five-parameter fit to α-RuCl₃ magnetization curves along the b and c axes, together with cross-checks against the static spin structure factor, magnetic susceptibility, and specific heat. It suits researchers interested in parameter determination for quantum magnets and in data-driven modeling. The source describes the combination of Bayesian optimization and accurate low-energy solvers as an effective approach for determining parameters of spin Hamiltonians, and calls the methodology a systematic route to determining spin Hamiltonians in quantum magnets from experimental data.

The cost function is insensitive to the absolute value of the Kitaev coupling K, so magnetization data alone do not determine its energy scale; the cost function also depends only weakly on Γ′ and J, while the optimization favors a large positive Γ. Agreement with the experimental specific heat is qualitative rather than quantitative.