Semiclassical approach to dynamics of Mott systems in the intermediate-coupling regime

Semiclassical methodologies, exemplified by Landau-Lifshitz dynamics, are indispensable tools for studying spin models, providing invaluable insights for interpreting phenomena observed in inelastic neutron scattering and resonant inelastic X-ray scattering experiments. However, the recent discovery of 4d- and 5d-electron Mott insulators in the intermediate-coupling regime demands innovative approaches that can account for the influence of charge fluctuations. The low-energy behavior of these materials is described by Hubbard-like models, featuring an intra-atomic Coulomb repulsion (U) comparable to the dominant hopping amplitude (t). Intermediate-coupling Mott insulators can exhibit non-collinear or intricate magnetic orderings, presenting promising avenues for novel transport engineering. In response, we have pioneered a semiclassical methodology facilitating large-scale computations (encompassing more than 10⁴ sites) of dynamical properties at finite temperatures across a broad spectrum of U/t values. By employing this cutting-edge approach, we successfully computed the dynamical spin structure factors of 5d-spin-orbit insulators and accounted for different experimental findings. Remarkably versatile, the method can be applied to various systems without restrictions on the type of hopping amplitudes, lattice geometries, number of relevant atomic orbitals, and electron filling fraction.