J-freezing and Hund's rules in spin-orbit-coupled multiorbital Hubbard models

TL;DR

This paper explores the phase diagram of a spin-orbit-coupled multiorbital Hubbard model using dynamical mean-field theory, revealing a generalized J-freezing crossover and its implications for magnetic order and material properties.

Contribution

It introduces the concept of J-freezing crossover in spin-orbit-coupled systems and analyzes its effects on electron behavior and magnetic ordering.

Findings

Identification of J-freezing crossover in spin-orbit-coupled models.

Distinct metallic states near fillings n=2 and n=4.

Discussion of magnetic order emergence from exciton condensation.

Abstract

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 continuous-time quantum Monte Carlo. We find that the spin-freezing crossover occurring in the metallic phase of the non-relativistic multiorbital Hubbard model can be 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 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.