Enhanced Spin–Orbit Coupling in a Correlated Metal

Abstract

We investigate the correlation effects on spin-orbit coupling (SOC) in a two-orbital Hubbard model on a square lattice by applying the variational Monte Carlo method. We consider an effective SOC constant λ eff in the one-body part of the variational wave function and mainly discuss the cases of the electron number per site n = 1, that is, quarter filling. We find that λ eff is proportional to the bare value λ and depends on the electron-electron interactions through (U ′ − J ′ ) in a relatively wide parameter range in the paramagnetic (PM) phase, where U ′ is the interorbital Coulomb interaction and J ′ is the pair hopping interaction. Increasing the electron-electron interactions in the PM phase leads to a transition to an effective one-band state, in which the upper band becomes empty due to the enhanced λ eff . We also construct phase diagrams considering magnetic order. The carrier doping effect on λ eff is also investigated. We find that λ eff enhances in a strongly correlated region around the Mott transition point and it is necessary to include the correlation effects beyond the Hartree-Fock approximation to describe the enhanced SOC properly.

Correlation Renormalized and Induced Spin-Orbit Coupling

“…Note that, when finalizing this work, we became aware of another work working on correlated spin-orbit coupling with similar results. [30]…”