Interplay of Coulomb interaction and spin-orbit coupling

Abstract

We employ the Gutzwiller variational approach to investigate the interplay of Coulomb interaction and spin-orbit coupling in a three-orbital Hubbard model. Already in the paramagnetic phase we find a substantial renormalization of the spin-orbit coupling that enters the effective single-particle Hamiltonian for the quasi-particles. Only close to half band-filling and for sizable Coulomb interaction we observe clear signatures of Hund's atomic rules for spin, orbital, and total angular momentum. For a finite local Hund's-rule exchange interaction we find a ferromagnetically ordered state. The spin-orbit coupling considerably reduces the size of the ordered moment, it generates a small ordered orbital moment, and it induces a magnetic anisotropy. To investigate the magnetic anisotropy energy, we use an external magnetic field that tilts the magnetic moment away from the easy axis $(1,1,1)$.

arXiv comment16 pages, 14 figures

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Cited by in corpus (9)

• J-freezing and Hund's rules in spin-orbit-coupled multiorbital Hubbard models
• Interplay between spin-orbit coupling and van Hove singularity in the Hund's metallicity of Sr${}_2$RuO${}_4$
• Spin-orbit coupling and correlations in three-orbital systems
• BaOsO${}_3$: A Hund's metal in the presence of strong spin-orbit coupling
• Exchange couplings for Mn ions in CdTe: validity of spin models for dilute magnetic II-VI semiconductors
• Enhanced Spin-Orbit Coupling in a Correlated Metal
• Gutzwiller variational approach to the two-impurity Anderson model at particle-hole symmetry
• Approximation schemes for the study of multi-band Gutzwiller wave functions
• Comparing the effective enhancement of local and non-local spin-orbit couplings on honeycomb lattices due to strong electronic correlations