Influence of spin-orbit coupling on the multiorbital Hubbard model: J-freezing, Hund's rules and excitonic magnetism

We investigate the interplay between the spin-orbit coupling, Coulomb interaction and Hund’s coupling within the multiorbital Hubbard model at different fillings by means of the dynamical mean-field theory combined with continuous-time quantum Monte Carlo. We show that the spin-freezing crossover occurring in the metallic phase of the model without the spin-orbit coupling can be the generalized to a $\mathbf{J}$-freezing crossover with $\mathbf{J}=\mathbf{L}+\mathbf{S}$, in the spin-orbit-coupled case. In the $\mathbf{J}$-frozen regime the correlated electrons exhibit a non-trivial flavor dependence in the self-energy which cannot be captured by the effective crystal-field effect. Especially, in the regions near $n = 2$ and $n = 4$ the metallic phases show strong asymmetry from each other, which reflects the atomic Hund’s third rule. Finally, we explore the appearance of the excitonic magnetism near $n = 4$ and discuss the relevance of our results for real materials.\footnote{A. J. Kim {\it et al.}, arXiv:1607.05196.}