First-principles approach to spin-orbital dynamics of localized electrons

Among multi-orbital systems, 5d-electron systems, which host atoms having a large atomic number, the energy scales of the Coulomb interaction and the spin-orbit coupling are comparable, leading to rich physical phenomena. When we perform material-based theoretical research, we should use the parameters obtained from first-principles calculation, and treat the Coulomb interaction and the spin-orbit coupling accurately. However, it is challenging because of the huge computational cost. However, in the strong coupling limit where electrons are localized, we can treat both at a reasonable numerical cost.

In the present study, we aim to analyze the ordered state of multi-orbital systems under the strong coupling limit by constructing an effective model combined with the band structure. We established the framework to automatically construct the localized effective model for general multi-orbital systems by applying the perturbation theory using the matrix operations. In the presentation, we will show the procedure of our analysis on 5d pyrochlore oxides as a test calculation. In addition, we show the result of the analysis using the mean-field theory as well as the classical Monte Carlo simulation for the constructed model.