The minimal spin Hamiltonian of $\alpha$-RuCl3
In plain words
Interpreting any $\alpha$-RuCl3 experiment requires its spin couplings, yet published fits disagree even on which coupling is largest. Without an agreed set, claims of spin-liquid behavior cannot be checked against theory.
Precise statement
Determine the exchange constants of alpha-RuCl3 in H = sum over nearest-neighbor bonds <ij> of type gamma of [J S_i . S_j + K S^gamma_i S^gamma_j + Gamma (S^alpha_i S^beta_j + S^beta_i S^alpha_j) + Gamma' (terms mixing gamma with alpha and beta)] + J3 sum over third neighbors of S_i . S_j, with $(\alpha, \beta, \gamma)$ a permutation of $(x, y, z)$, from a joint fit of inelastic neutron spectra, THz and ESR modes, the field-angle dependence of the critical field and the high-field magnon spectrum. An answer is one parameter set with error bars consistent with all these data, including the sign of $K$ and the ratio $K/\Gamma$.
What would settle it
A global fit of neutron, THz, ESR, magnetization and magnetostriction data using quantum many-body (beyond linear spin-wave) calculations of the spectra that yields a unique parameter set.
Status in the literature
Proposed parameter sets range from Kitaev dominated to regions with a large off-diagonal $\Gamma$ term; Maksimov and Chernyshev (Physical Review Research 2020) argued for the latter.