J Freezing and Hund's Rules in Spin-Orbit-Coupled Multiorbital Hubbard Models

We investigate the phase diagram of the spin-orbit-coupled three orbital Hubbard model at arbitrary filling by means of dynamical mean-field theory combined with the continuous-time quantum Monte Carlo method. We find that the spin-freezing crossover occurring in the metallic phase of the nonrelativistic multiorbital Hubbard model can be generalized to a J-freezing crossover, with J=L+S, in the spin-orbit-coupled case. In the J-frozen regime the correlated electrons exhibit a nontrivial flavor selectivity and energy dependence. Furthermore, in the regions near n=2 and n=4 the metallic states are qualitatively different from each other, which reflects the atomic Hund's third rule. Finally, we explore the appearance of magnetic order from exciton condensation at n=4 and discuss the relevance of our results for real materials.