Spin-orbit coupling and correlations in three-orbital systems

TL;DR

This paper studies how spin-orbit coupling affects electronic correlations in a three-orbital Hubbard model, revealing complex behaviors depending on electron filling and interaction strength, with implications for understanding correlated materials.

Contribution

It provides a comprehensive analysis of spin-orbit coupling effects across all fillings in a three-orbital model using dynamical mean-field theory, highlighting differences from crystal field effects.

Findings

Spin-orbit coupling modifies quasiparticle weight depending on filling and interaction strength.

At half-filling, spin-orbit coupling suppresses correlations at large U.

Different effects of spin-orbit coupling and crystal field on orbital degeneracy and correlations.

Abstract

We investigate the influence of spin-orbit coupling $\lambda$ in strongly-correlated multiorbital systems that we describe by a three-orbital Hubbard-Kanamori model on a Bethe lattice. We solve the problem at all integer fillings $N$ with the dynamical mean-field theory using the continuous-time hybridization expansion Monte Carlo solver. We investigate how the quasiparticle renormalization $Z$ varies with the strength of spin-orbit coupling. The behavior can be understood for all fillings except $N=2$ in terms of the atomic Hamiltonian (the atomic charge gap) and the polarization in the $j$-basis due to spin-orbit induced changes of orbital degeneracies and the associated kinetic energy. At $N=2$, $\lambda$ increases $Z$ at small $U$ but suppresses it at large $U$, thus eliminating the characteristic Hund's metal tail in $Z(U)$. We also compare the effects of the spin-orbit coupling to the effects of a tetragonal crystal field. Although this crystal field also lifts the orbital degeneracy, its effects are different, which can be understood in terms of the different form of the interaction Hamiltonian expressed in the respective diagonal single-particle basis.